Sine wave ndi mawonekedwe osalekeza omwe amadzibwereza okha 2π radian iliyonse, kapena madigiri 360, ndipo amatha kugwiritsidwa ntchito kutengera zochitika zambiri zachilengedwe. Sine wave imadziwikanso kuti sinusoid.
Mawu akuti sine wave amachokera ku ntchito ya masamu sine, yomwe ndi maziko a mawonekedwe a waveform. Sine wave ndi imodzi mwamafunde osavuta kwambiri ndipo imagwiritsidwa ntchito kwambiri m'magawo ambiri.
M'nkhaniyi, ndifotokoza zomwe sine wave ndi chifukwa chake ndi yamphamvu kwambiri.
Kodi sine wave ndi chiyani?
A sine Wave ndi oscillation yosalala, yobwerezabwereza mwa mawonekedwe a mafunde osalekeza. Ndi masamu okhotakhota omwe amatanthauzidwa malinga ndi ntchito ya sine trigonometric, ndipo imayimiridwa mowoneka ngati mawonekedwe ozungulira. Ndi mtundu wa mafunde osalekeza omwe amadziwika ndi ntchito yosalala, nthawi ndi nthawi, ndipo amapezeka m'madera ambiri a masamu, physics, engineering, ndi processing processing.
The pafupipafupi of a sine wave ndi kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika mu nthawi yoperekedwa. Mafupipafupi a angular, otchulidwa ndi ω, ndi mlingo wa kusintha kwa mkangano wa ntchito, ndipo amayesedwa mu mayunitsi a ma radian pamphindikati. Mtengo wosakhala wa ziro wa kusintha kwa gawo, wotchulidwa ndi φ, umayimira kusintha kwa mawonekedwe a mafunde mu nthawi, ndi mtengo woipa womwe umayimira kuchedwa, ndi phindu loyimira patsogolo pamasekondi. Kuchuluka kwa ma wave wave kumayesedwa mu hertz (Hz).
Sine wave imagwiritsidwa ntchito pofotokoza phokoso la phokoso, ndipo imafotokozedwa ndi ntchito ya sine, f (t) = A tchimo (ωt + φ). Amagwiritsidwanso ntchito kufotokoza dongosolo losasunthika la kasupe pamlingo wofanana, ndipo ndi mawonekedwe ofunikira mufizikiki pomwe amasunga mawonekedwe ake afunde pamene awonjezeredwa ku sine wave ya ma frequency omwewo ndi gawo losagwirizana ndi kukula kwake. Katunduyu amadziwika kuti superposition mfundo, ndipo ndi nthawi ndi nthawi waveform katundu. Katunduyu amatsogolera kufunikira kwa kusanthula kwa Fourier, chifukwa zimapangitsa kuti zikhale zotheka kusiyanitsa momveka bwino kusintha kwa malo, x, komwe kumayimira malo mu gawo limodzi momwe mafunde akufalikira.
Chizindikiro cha mafunde chimatchedwa nambala yoweyula, k, yomwe ndi nambala ya mafunde aang'ono ndipo imayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liwiro la mzere wa kufalitsa, ν. Nambala yoweyula imakhudzana ndi ma frequency aang'ono ndi kutalika kwa mawonekedwe, λ, ndi equation λ = 2π/k. Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo (ωt + φ). Equation yowonjezereka imaperekedwa ndi y = A tchimo (kx - ωt + φ), zomwe zimapereka kusuntha kwa mafunde pa malo x pa nthawi t.
Mafunde a sine amathanso kuyimiridwa m'magawo angapo. Equation ya mafunde a ndege yoyendayenda imaperekedwa ndi y = A sin (kx - ωt + φ). Izi zitha kutanthauziridwa ngati madontho a ma vectors awiri, ndipo amagwiritsidwa ntchito pofotokoza mafunde ovuta, monga mafunde amadzi mu dziwe pomwe mwala wagwetsedwa. Ma equation ovuta kwambiri amafunikira kuti afotokoze mawu akuti sinusoid, omwe amafotokoza mawonekedwe a mafunde a sine ndi mafunde a cosine okhala ndi kusintha kwa magawo a π/2 ma radians, zomwe zimapangitsa kuti mafunde a cosine ayambe kupitilira pa sine wave. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi cosine okhala ndi gawo lochotsera.
Mafunde a sine amapezeka m'chilengedwe, kuphatikizapo mafunde a mphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine imodzi ngati kumveka bwino, ndipo mafunde a sine amagwiritsidwa ntchito kuyimira ma frequency ndi ma harmonics. Khutu la munthu limamva phokoso ngati kuphatikiza kwa mafunde a sine okhala ndi matalikidwe ndi ma frequency osiyanasiyana, ndipo kupezeka kwa ma harmonics apamwamba kuphatikiza pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake cholembera chanyimbo chokhala ndi ma frequency omwe amaseweredwa pazida zosiyanasiyana chimamveka mosiyana.
Phokoso la kuwomba m'manja limakhala ndi mafunde aperiodic, omwe samabwerezabwereza, ndipo samatsata mawonekedwe a sine wave. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula ziwerengero za nthawi. Mafunde a Sine amagwiritsidwa ntchito kufalitsa ndikusintha mawonekedwe mumayendedwe ogawidwa.
Kodi mbiri ya mafunde a sine ndi chiyani?
Sine wave ili ndi mbiri yayitali komanso yosangalatsa. Zinapezeka koyamba ndi katswiri wa masamu wa ku France Joseph Fourier mu 1822, yemwe anasonyeza kuti mafunde aliwonse a nthawi ndi nthawi akhoza kuimiridwa ngati chiŵerengero cha mafunde a sine. Kupeza kumeneku kunasintha kwambiri masamu ndi physics ndipo wakhala akugwiritsidwa ntchito kuyambira pamenepo.
• Ntchito ya Fourier inakonzedwanso ndi katswiri wa masamu wa ku Germany Carl Friedrich Gauss mu 1833, yemwe anasonyeza kuti mafunde a sine angagwiritsidwe ntchito kuimira mafunde a nthawi ndi nthawi.
• Chakumapeto kwa zaka za m'ma 19, sine wave idagwiritsidwa ntchito pofotokoza khalidwe la mabwalo amagetsi.
• Kumayambiriro kwa zaka za zana la 20, mafunde a sine ankagwiritsidwa ntchito pofotokoza khalidwe la mafunde a phokoso.
• M'zaka za m'ma 1950, mawonekedwe a sine ankagwiritsidwa ntchito pofotokoza khalidwe la mafunde a kuwala.
• M'zaka za m'ma 1960, sine wave idagwiritsidwa ntchito kufotokoza khalidwe la mafunde a wailesi.
• M'zaka za m'ma 1970, sine wave idagwiritsidwa ntchito pofotokoza khalidwe la zizindikiro za digito.
• M'zaka za m'ma 1980, sine wave idagwiritsidwa ntchito kufotokoza khalidwe la mafunde a electromagnetic.
• M'zaka za m'ma 1990, sine wave idagwiritsidwa ntchito pofotokoza khalidwe la quantum mechanical systems.
• Masiku ano, mafunde a sine amagwiritsidwa ntchito m'madera osiyanasiyana, kuphatikizapo masamu, physics, engineering, signal processing, ndi zina. Ndi chida chofunikira kwambiri chomvetsetsa momwe mafunde amagwirira ntchito ndipo chimagwiritsidwa ntchito m'njira zosiyanasiyana, kuyambira pakukonza ma audio ndi makanema mpaka kujambula kwachipatala ndi ma robotiki.
Sine Wave Masamu
Ndikulankhula za mafunde a sine, mafunde a masamu omwe amafotokoza kusinthasintha kosalala, kobwerezabwereza. Tiwona momwe mafunde a sine amatanthauziridwa, ubale pakati pa ma frequency aang'ono ndi nambala ya mafunde, ndi kusanthula kwa Fourier. Tiwonanso momwe mafunde a sine amagwiritsidwira ntchito mufizikiki, uinjiniya, ndi kukonza ma sign.
Kodi Sine Wave ndi chiyani?
Sine wave ndi kusinthasintha kosalala, kobwerezabwereza komwe kumapanga mafunde osalekeza. Ndi masamu okhotakhota, omwe amatanthauzidwa ndi trigonometric sine ntchito, ndipo nthawi zambiri amawoneka mu ma graph ndi ma waveform. Ndi mtundu wa mafunde opitilira, kutanthauza kuti ndi ntchito yosalala, yanthawi ndi nthawi yomwe imapezeka mu masamu, physics, engineering, ndi magawo opangira ma sign.
Sine wave ili ndi ma frequency wamba, omwe ndi kuchuluka kwa ma oscillation kapena ma cycle omwe amapezeka mu nthawi yoperekedwa. Izi zikuyimiridwa ndi ma frequency aang'ono, ω, omwe ndi ofanana ndi 2πf, pomwe f ndi ma frequency mu hertz (Hz). Sine wave imathanso kusinthidwa munthawi yake, ndi mtengo woyipa womwe umayimira kuchedwa ndi mtengo wabwino womwe umayimira patsogolo pamasekondi.
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a phokoso, monga momwe amafotokozera ndi ntchito ya sine. Amagwiritsidwanso ntchito kuyimira dongosolo losasunthika la masika pamlingo wofanana. Sine wave ndi lingaliro lofunikira mufizikiki, chifukwa limasunga mawonekedwe ake a mafunde akawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katunduyu, yemwe amadziwika kuti superposition principle, ndizomwe zimatsogolera ku kufunikira kwa kusanthula kwa Fourier, chifukwa zimatheketsa kusiyanitsa momveka bwino pakati pa zosintha zapamalo.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo (ωt + φ), pomwe A ndi matalikidwe, ω ndi ma frequency aang'ono, t ndi nthawi, ndipo φ ndikusintha kwa gawo. Kwa chitsanzo cha mzere umodzi, ngati mtengo wa mafundewa umatengedwa ngati waya, ndiye kuti equation ya sine wave mu miyeso iwiri ya malo amaperekedwa ndi y = A sin (kx - ωt + φ), pamene k ndi mafunde. nambala. Izi zitha kutanthauziridwa ngati zopangidwa ndi ma vector awiri, madontho.
Mafunde ovuta, monga omwe amapangidwa mwala ukagwetsedwa padziwe, amafunikira ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 ma radian, kapena poyambira mutu, akuti kumapereka mafunde a cosine, omwe amatsogolera mafunde a sine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo lochotsera.
Kuwonetsa mafunde a cosine kungathandize kuwonetsa ubale wofunikira pakati pa bwalo ndi mtundu wa 3D wovuta wa ndege, zomwe zingathandize kuwona kufunika kwa mafunde a sine pakumasulira pakati pa madambwe. Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine imodzi ngati akumveka bwino, ndipo mafunde amtundu wa sine amamvekanso.
Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira ndizomwe zimayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana.
Khutu la munthu limamva phokoso ngati la periodic komanso la aperiodic. Phokoso la nthawi ndi nthawi limapangidwa ndi mafunde a sine, pomwe phokoso la aperiodic limadziwika ngati phokoso. Phokoso limadziwika kuti ndi aperiodic, chifukwa liri ndi ndondomeko yosabwerezabwereza.
Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kuthamanga kwa kutentha ndi kuwongolera ma siginecha, komanso kusanthula kwanthawi yayitali. Mafunde a Sine amathanso kufalikira kudzera mukusintha mafomu m'machitidwe ogawidwa.
Mafunde a m'mlengalenga omwe akuyenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana. Mafundewa akamakula kwambiri, mafunde oimapo amapangidwa, monga momwe zimaonekera pamene cholemba chikukokedwa pa chingwe. Mafunde osokoneza omwe amawonekera kuchokera kumalekezero okhazikika a chingwecho amapanga mafunde oima, omwe amapezeka pamayendedwe ena otchedwa resonant frequencies. Izi zimapangidwa ndi ma frequency oyambira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi kutalika kwake, ndipo amayenderana mosiyana ndi unyinji pa utali wagawo la chingwecho.
Kodi Sine Wave Imafotokozedwa Motani?
Sine wave ndi kusinthasintha kosalala, kobwerezabwereza kwa mawonekedwe opitilira. Imatanthauzidwa masamu ngati ntchito ya trigonometric, ndipo imajambulidwa ngati sinusoid. Sine wave ndi lingaliro lofunikira mufizikiki, chifukwa limasunga mawonekedwe ake a mafunde akawonjezeredwa ku mafunde ena amtundu womwewo komanso kukula kwa gawo losagwirizana. Katunduyu amadziwika ngati mfundo yayikulu, ndipo imatsogolera kukufunika kwake pakuwunika kwa Fourier.
Mafunde a Sine amapezeka m'magawo ambiri a masamu, physics, engineering, and signal processing. Amadziwika ndi ma frequency awo, kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika munthawi yoperekedwa. Mafupipafupi a angular, ω, ndi mlingo wa kusintha kwa mkangano wa ntchito mu ma radian pamphindikati. Mtengo wosakhala wa ziro wa φ, kusintha kwa gawo, kumayimira kusintha kwa mawonekedwe onse mu nthawi, ndi mtengo woipa womwe umayimira kuchedwa, ndi phindu loyimira patsogolo pamasekondi.
Pakumveka, mafunde a sine amafotokozedwa ndi equation f = ω/2π, pomwe f ndi ma frequency a oscillations, ndipo ω ndi ma frequency aang'ono. Equation iyi imagwiranso ntchito ku dongosolo losasinthika la masika mu equilibrium. Mafunde a sine ndi ofunikiranso mu ma acoustics, chifukwa ndi mawonekedwe okhawo omwe amawonedwa ngati ma frequency amodzi ndi khutu la munthu. Sine wave imodzi imapangidwa ndi ma frequency oyambira komanso ma harmonics apamwamba, omwe onse amawoneka ngati cholemba chimodzi.
Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira ndizomwe zimayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo yomweyi yomwe imayimbidwa pazida zosiyanasiyana imamveka mosiyana. Mwachitsanzo, kuwomba m'manja kumakhala ndi mafunde aperiodic, omwe sabwerezabwereza, kuwonjezera pa mafunde a sine.
Kumayambiriro kwa zaka za m’ma 19, katswiri wa masamu wa ku France, dzina lake Joseph Fourier, anapeza kuti mafunde a sinusoidal angagwiritsidwe ntchito ngati zomangira zosavuta kufotokoza ndi kuyerekezera mafunde amtundu uliwonse, kuphatikizapo mafunde amtundu uliwonse. Kusanthula kwa Fourier ndi chida champhamvu chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde pakuyenda kwa kutentha ndi kukonza ma siginecha, komanso kusanthula kwanthawi yayitali.
Mafunde a Sine amatha kufalikira mbali iliyonse mumlengalenga, ndipo amaimiridwa ndi mafunde okhala ndi matalikidwe, ma frequency, ndikuyenda mbali zosiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Ichi ndi chodabwitsa chomwe chimachitika pamene cholemba chikukokedwa pa chingwe, ndi mafunde osokoneza akuwonekera pamapeto okhazikika a chingwe. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant, omwe amapangidwa ndi ma frequency oyambira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi kutalika kwake, ndipo amafanana ndi muzu wa sikweya wa kulemera kwake pa utali wa unit.
Mwachidule, mawu akuti sinusoid amagwiritsidwa ntchito pofotokoza mawonekedwe a mafunde a sine ndi mafunde a cosine, ndikusintha kwagawo kwa π/2 ma radians, kutanthauza kuti mafunde a cosine amakhala ndi mutu ndipo sine wave imatsalira kumbuyo. Mawu akuti sinusoidal amagwiritsidwa ntchito palimodzi kutanthauza mafunde onse a sine ndi cosine okhala ndi gawo lochotsera. Izi zikuwonetsedwa ndi mafunde a cosine pachithunzi pamwambapa. Ubale wofunikira umenewu pakati pa sine ndi cosine ukhoza kuwonedwa pogwiritsa ntchito chitsanzo cha ndege cha 3D, chomwe chikuwonetseranso ubwino wa kumasulira kwa mfundozi m'madera osiyanasiyana. Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikizapo mphepo, phokoso, ndi mafunde.
Kodi Ubale Pakati pa Angular Frequency ndi Wave Number ndi Chiyani?
Sine wave ndi njira ya masamu yomwe imalongosola kusinthasintha kosalala, kobwerezabwereza. Ndi mafunde osalekeza, omwe amadziwikanso kuti sinusoidal wave kapena sinusoid, ndipo amatanthauzidwa malinga ndi ntchito ya trigonometric sine. Grafu ya sine wave ikuwonetsa mawonekedwe a mafunde omwe amazungulira pakati pa mtengo wapamwamba ndi wocheperako.
Mafupipafupi a angular, ω, ndi mlingo wa kusintha kwa mtsutso wa ntchito, woyesedwa mu ma radian pamphindikati. Mtengo wosakhala wa ziro wa φ, kusintha kwa gawo, kumayimira kusintha kwa mawonekedwe onse oyenda kutsogolo kapena kumbuyo kwa nthawi. Mtengo wolakwika umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola mumasekondi. Frequency, f, ndi kuchuluka kwa ma oscillation kapena mikombero yomwe imachitika mu sekondi imodzi, kuyezedwa mu hertz (Hz).
Sine wave ndi yofunika mu fizikisi chifukwa imasunga mawonekedwe ake a mafunde ikawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katundu wa nthawi ndi nthawi ma waveforms amadziwika kuti superposition mfundo ndipo ndizomwe zimatsogolera ku kufunika kwa kusanthula kwa Fourier. Izi zimapangitsa kuti ikhale yapadera kwambiri ndipo ndichifukwa chake imagwiritsidwa ntchito muzosintha zapamalo x, zomwe zimayimira malo mugawo limodzi. Mafundewa amafalikira ndi chizindikiro chodziwika, k, chotchedwa nambala yoweyula kapena nambala ya mafunde aang'ono, yomwe imayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liwiro la mzere wa kufalitsa, ν. Nambala ya mafunde, k, imagwirizana ndi mafupipafupi a angular, ω, ndi kutalika kwa mawonekedwe, λ, ndi equation λ = 2π/k.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo (ωt + φ). Equation iyi imapereka kusuntha kwa mafunde pamalo aliwonse x nthawi iliyonse t. Chitsanzo cha mzere umodzi chikuganiziridwa, pamene mtengo wa mafundewa umaperekedwa ndi y = A tchimo (ωt + φ).
M'magawo awiri kapena kupitilira apo, equation imafotokoza mafunde oyenda ndege. Malo x amaperekedwa ndi x = A tchimo (kx – ωt + φ). Equation iyi imatha kutanthauziridwa ngati ma vector awiri, omwe amapangidwa ndi madontho.
Mafunde ovuta, monga omwe amapangidwa mwala ukagwetsedwa m'dziwe lamadzi, amafunikira ma equation ovuta kuwafotokozera. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 radians (kapena 90 °) kumapangitsa kuti cosine wave kuyamba mutu, motero akuti amatsogolera sine wave. Izi zimatsogolera ku ubale wofunikira pakati pa ntchito za sine ndi cosine, zomwe zitha kuwonedwa ngati bwalo mumtundu wa 3D wovuta wa ndege.
Kufunika kwa kumasulira kwa lingaliroli kumadera ena kukuwonetsedwa ndi mfundo yakuti mawonekedwe a mafunde omwewo amapezeka m'chilengedwe, kuphatikizapo mafunde a mphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde amtundu umodzi kuti amamveka bwino. Mafunde a Sine ndi oyimira ma frequency amodzi ndi ma harmonics, ndipo khutu la munthu limatha kutulutsa mafunde a sine ndi ma harmonics omveka. Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana.
Kuwomba m'manja kumakhala ndi mafunde aperiodic, omwe sachitika nthawi, kapena osabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde a square. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula ziwerengero za nthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina ogawa. Izi ndizofunikira kuti mufufuze kufalikira kwa mafunde mumiyeso iwiri kapena kupitilira apo. Mafunde a m'mlengalenga omwe akuyenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Zimenezi n’zofanana ndi zimene zimachitika munthu akakoleza cholemba pa chingwe; mafunde osokoneza akuwonekera kuchokera kumapeto okhazikika a chingwe, ndipo mafunde oyimirira amapezeka pazifukwa zina, zomwe zimatchedwa kuti resonant frequencies. Ma frequency awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafuridwe amtundu wa chingwe amafanana ndi kutalika kwake komanso mosiyana ndi muzu wa sikweya wa kulemera kwake pautali wa unit.
Kodi Fourier Analysis ndi chiyani?
Sine wave ndi kusinthasintha kosalala, kobwerezabwereza komwe kumafotokozedwa masamu ngati mafunde osalekeza. Imadziwikanso kuti sinusoidal wave, ndipo imatanthauzidwa ndi ntchito ya trigonometric sine. Grafu ya sine wave ndi yosalala, yokhotakhota nthawi ndi nthawi yomwe imagwiritsidwa ntchito m'masamu, physics, engineering, ndi magawo opangira ma sign.
Ma frequency wamba, kapena kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika mu kuchuluka kwa nthawi, kumaimiridwa ndi chilembo chachi Greek ω (omega). Izi zimadziwika kuti ma frequency aang'ono, ndipo ndi mlingo womwe mkangano wantchito umasinthira mayunitsi a ma radian.
Sine wave imatha kusinthidwa munthawi ndi kusintha kwa gawo, komwe kumaimiridwa ndi chilembo chachi Greek φ (phi). Mtengo wolakwika umayimira kuchedwa, ndipo mtengo wabwino umayimira patsogolo pamasekondi. Kuchuluka kwa ma wave wave kumayesedwa mu hertz (Hz).
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a mawu, ndipo imafotokozedwa ndi sine ntchito f (t) = A tchimo (ωt + φ). Oscillations amtundu uwu amawonedwa mu undamped kasupe-mass dongosolo pa equilibrium.
Sine wave ndi yofunika mu fizikisi chifukwa imasunga mawonekedwe ake a mafunde ikawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katunduyu, wotchedwa superposition principle, ndi omwe amatsogolera ku kufunika kwake pakuwunika kwa Fourier. Izi zimapangitsa kuti ikhale yapadera kwambiri ndipo ndichifukwa chake imagwiritsidwa ntchito pofotokoza zamitundu yosiyanasiyana.
Mwachitsanzo, ngati x akuyimira gawo la mafunde omwe akufalikira, ndiye kuti chizindikiro cha k (nambala yoweyula) chimayimira kufanana pakati pa mafunde aang'ono ω ndi liwiro la mzere wa kufalikira ν. Nambala ya mafunde k imagwirizana ndi ma frequency aang'ono ω ndi kutalika kwa mawonekedwe λ (lambda) ndi equation k = 2π/λ. Frequency f ndi liniya liwiro v amagwirizana ndi equation v = fλ.
Equation ya sine wave mu gawo limodzi ndi y = A tchimo (ωt + φ). Equation iyi ikhoza kukhala yowonjezereka kwa miyeso yambiri, ndi chitsanzo cha mzere umodzi, mtengo wa mafunde pa nthawi iliyonse x nthawi iliyonse t imaperekedwa ndi y = A tchimo (kx - ωt + φ).
Mafunde ovuta, monga omwe amawonedwa mwala ukagwetsedwa m'dziwe, amafunikira ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe awa, ndipo amaphatikiza mafunde a sine ndi mafunde a cosine okhala ndi gawo.
Kuwonetsa mafunde a cosine, ubale wofunikira pakati pa ma wave a sine ndi cosine wave ndi wofanana ndi ubale wapakati pa bwalo ndi mtundu wa 3D wovuta wa ndege. Izi ndizothandiza powonera phindu la kumasulira kwa mafunde a sine pakati pa madera osiyanasiyana.
Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito kuyimira ma frequency ndi ma harmonics.
Khutu la munthu limamva phokoso lophatikizana ndi mafunde a sine ndi phokoso lanthawi ndi nthawi, ndipo kupezeka kwa ma harmonics apamwamba kuphatikiza pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana.
Kuwomba m'manja, komabe, kumakhala ndi mafunde aperiodic, omwe sabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde a square.
Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kuthamanga kwa kutentha ndi kuwongolera ma siginecha, komanso kusanthula kwanthawi yayitali. Mafunde a Sine amatha kufalikira popanda kusintha mawonekedwe awo pamakina ogawa, chifukwa chake amafunikira kusanthula kufalikira kwa mafunde.
Mafunde a m'mlengalenga omwe akuyenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Izi zimawonekera pamene cholemba chikudulidwa pa chingwe, ndipo mafunde osokoneza amawonekera pamapeto okhazikika a chingwecho. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant. Ma frequency awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi kutalika kwake, ndipo amayenderana mosiyana ndi unyinji pa utali wagawo la chingwecho.
Mafunde a Sine ndi Cosine
Mu gawoli, ndikambirana za kusiyana pakati pa mafunde a sine ndi cosine, kusintha kwa gawo ndi chiyani, komanso momwe mafunde a sine amasiyanirana ndi mafunde a cosine. Ndikhala ndikuwunikanso kufunikira kwa mafunde a sine mu masamu, physics, engineering, and sign processing.
Kodi Kusiyana Pakati pa Sine ndi Cosine Waves ndi Chiyani?
Mafunde a Sine ndi cosine amagwira ntchito nthawi ndi nthawi, yosalala, komanso yosalekeza yomwe imagwiritsidwa ntchito kufotokoza zochitika zambiri zachilengedwe, monga mafunde a phokoso ndi kuwala. Amagwiritsidwanso ntchito mu engineering, ma sign processing, ndi masamu.
Kusiyana kwakukulu pakati pa mafunde a sine ndi cosine ndikuti mafunde a sine amayambira pa ziro, pomwe mafunde a cosine amayambira pakusintha kwa π/2 radians. Izi zikutanthauza kuti mafunde a cosine ali ndi mutu woyambira poyerekeza ndi mawonekedwe a sine.
Mafunde a sine ndi ofunikira mufizikiki chifukwa amasunga mawonekedwe awo akaphatikizidwa pamodzi. Katunduyu, yemwe amadziwika kuti superposition principle, ndizomwe zimapangitsa kusanthula kwa Fourier kukhala kothandiza kwambiri. Zimapangitsanso mafunde a sine kukhala apadera, chifukwa amatha kugwiritsidwa ntchito kuyimira ma frequency amodzi.
Mafunde a cosine nawonso ndi ofunikira mufizikiki, chifukwa amagwiritsidwa ntchito pofotokoza kusuntha kwa misa pa kasupe molingana. Equation ya sine wave ndi f = oscillations/nthawi, pomwe f ndi ma frequency a wave ndipo ω ndi ma frequency aang'ono. Equation iyi imapereka kusuntha kwa mafunde pamalo aliwonse x ndi nthawi t.
Mu miyeso iwiri kapena kupitilira apo, sinus wave imatha kufotokozedwa ndi mafunde a ndege oyenda. Nambala ya mafunde k ndi chizindikiro cha mawonekedwe a mafunde, ndipo imagwirizana ndi mafupipafupi a angular ω ndi kutalika kwa mawonekedwe λ. Equation ya sine wave mu miyeso iwiri kapena kupitilira apo imapereka kusuntha kwa mafunde pamalo aliwonse x ndi nthawi t.
Mafunde ovuta, monga omwe amapangidwa ndi mwala wogwetsedwa padziwe, amafunikira ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito pofotokoza mafunde okhala ndi mawonekedwe ofanana ndi mafunde a sine kapena cosine wave, monga kusintha kwa gawo. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde a sine ndi mafunde a cosine okhala ndi gawo lochotsera.
Mafunde a sine amapezeka m'chilengedwe, kuphatikizapo mafunde a mphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka bwino, komanso limatha kuzindikira kukhalapo kwa ma harmonics apamwamba kuphatikiza pa ma frequency ofunikira. Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso.
Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde aliwonse a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida champhamvu chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha ndi kukonza ma siginecha. Amagwiritsidwanso ntchito posanthula ziwerengero ndi mndandanda wa nthawi.
Mafunde a Sine amatha kufalikira mbali iliyonse mumlengalenga, ndipo amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency omwe akuyenda mbali zosiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Izi zimachitika pamene cholemba chikokedwa pa chingwe, pamene mafunde amawonekera pamapeto okhazikika a chingwe. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant. Mafuridwe omveka a chingwe amafanana ndi kutalika kwake, ndipo amafanana ndi kulemera kwake pautali wa unit.
Kodi Phase Shift ndi chiyani?
Sine wave ndi kusinthasintha kosalala, kobwerezabwereza komwe kumapitilira nthawi ndi malo. Ndi masamu opindika omwe amafotokozedwa ndi trigonometric sine ntchito ndipo nthawi zambiri amagwiritsidwa ntchito kuyimira mafunde amphamvu, mafunde opepuka, ndi mafunde ena mu masamu, physics, engineering, and sign processing fields. Ma frequency wamba (f) a sine wave ndi kuchuluka kwa kuzungulira kapena kuzungulira komwe kumachitika mu sekondi imodzi, ndipo kumayesedwa mu hertz (Hz).
Mafupipafupi a angular (ω) ndi mlingo wa kusintha kwa mkangano wa ntchito mu ma radian pamphindikati, ndipo umagwirizana ndi ma frequency wamba ndi equation ω = 2πf. Mtengo wolakwika wa φ umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola m'masekondi.
Mafunde a sine nthawi zambiri amagwiritsidwa ntchito pofotokoza mafunde a phokoso, chifukwa amatha kusunga mawonekedwe awo akaphatikizidwa pamodzi. Katunduyu amabweretsa kufunikira kwa kusanthula kwa Fourier, komwe kumapangitsa kuti athe kusiyanitsa momveka bwino mitundu yosiyanasiyana ya malo. Mwachitsanzo, kusintha kwa x kumayimira malo mu gawo limodzi, ndipo fundelo limafalikira molunjika pa chizindikiro cha k, chomwe chimatchedwa nambala yoweyula. Nambala ya mafunde aang'ono imayimira kufanana pakati pa ma frequency aang'ono (ω) ndi liniya liwiro la kufalitsa (ν). Nambala yoweyula imakhudzana ndi mafunde apakati komanso kutalika kwa mafunde (λ) ndi equation λ = 2π/k.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo (ωt + φ), pamene A ndi matalikidwe, ω ndi mafupipafupi aang'ono, t ndi nthawi, ndipo φ ndi kusintha kwa gawo. Equation iyi ikhoza kusinthidwa kuti ipereke kusuntha kwa mafunde pamalo aliwonse x nthawi iliyonse t pamzere umodzi, mwachitsanzo, y = A tchimo (kx - ωt + φ). Poganizira mafunde mu magawo awiri kapena kupitilira apo, ma equation ovuta kwambiri amafunikira.
Mawu akuti sinusoid nthawi zambiri amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe ofanana ndi mafunde a sine. Izi zikuphatikiza mafunde a cosine, omwe amakhala ndi gawo la ma radian π/2, kutanthauza kuti ali ndi poyambira mutu poyerekeza ndi mafunde a sine. Mawu akuti sinusoidal nthawi zambiri amagwiritsidwa ntchito pamodzi kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo.
Kuwonetsa mafunde a cosine, ubale wofunikira pakati pa mafunde a sine ndi mafunde a cosine ukhoza kuwonedwa ndi bwalo mumtundu wa 3D wovuta wa ndege. Izi ndizothandiza pakumasulira pakati pa madera, chifukwa mafunde omwewo amachitikira m'chilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka. Khutu la munthu limatha kuzindikira mafunde amtundu umodzi ngati mafunde omveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito ngati ma toni amtundu umodzi.
Ma Harmonics ndi ofunikiranso pamawu, monga momwe khutu la munthu limamva phokoso ngati kusakanikirana kwa mafunde a sine ndi ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira. Kukhalapo kwa ma harmonics apamwamba kuphatikiza pazifukwa zoyambira kusiyanasiyana kwa mawu. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana. Komabe, phokoso lopangidwa ndi kuwomba pamanja limakhala ndi mafunde aperiodic, kutanthauza kuti silinapangidwe ndi mafunde a sine.
Mafunde a nthawi ndi nthawi atha kuyerekezedwa pogwiritsa ntchito zida zosavuta zomangira mafunde a sinusoidal, monga momwe adatulukira katswiri wa masamu wa ku France Joseph Fourier. Izi zikuphatikizapo mafunde a square, omwe amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kuthamanga kwa kutentha ndi kuwongolera ma siginecha, komanso kusanthula kwanthawi yayitali.
Mafunde a Sine amatha kufalikira popanda kusintha mawonekedwe mumayendedwe ogawidwa, ndipo nthawi zambiri amafunikira kusanthula kufalikira kwa mafunde. Mafunde a sine amatha kuyenda mbali ziwiri mumlengalenga, ndipo amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency. Pamene mafunde awiri akulowera mbali zosiyana akulirakulira, mafunde oima amapangidwa. Zimenezi n’zofanana ndi pamene cholemba chikukokedwa pa chingwe, monga momwe mafunde osokoneza amawonekera kumapeto kwa chingwecho. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant. Ma frequency awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafupipafupi omveka a chingwe amafanana ndi kutalika kwa chingwe, ndipo amasiyana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Sine Wave Imasiyana Bwanji ndi Cosine Wave?
Sine wave ndi mawonekedwe osalekeza omwe amazungulira mosalala, mobwerezabwereza. Ndi ntchito ya trigonometric yojambulidwa pa ndege yokhala ndi mbali ziwiri, ndipo ndiye mawonekedwe ofunikira mu masamu, physics, engineering, and sign processing. Zimadziwika ndi mafupipafupi ake, kapena chiwerengero cha oscillations chomwe chimachitika mu nthawi yoperekedwa, ndi maulendo ake aang'ono, omwe ndi chiwerengero cha kusintha kwa mkangano wa ntchitoyo mu radians pamphindi. Sine wave imatha kusinthidwa munthawi yake, ndi mtengo woyipa womwe umayimira kuchedwa ndi mtengo wabwino womwe umayimira patsogolo pamasekondi.
Mafunde a Sine amagwiritsidwa ntchito kufotokoza mafunde a phokoso, ndipo nthawi zambiri amatchedwa sinusoids. Ndiwofunika mu sayansi ya zamoyo chifukwa amasunga mawonekedwe awo a mafunde akaphatikizidwa pamodzi, ndipo ndi maziko a kusanthula kwa Fourier, komwe kumawapangitsa kukhala apadera kwambiri. Amagwiritsidwanso ntchito pofotokoza zosintha zapamalo, ndi nambala yoweyula yomwe imayimira kufanana pakati pa ma frequency aang'ono ndi liwiro la mzere wofalitsa.
Sine wave imagwiritsidwanso ntchito pofotokoza mawonekedwe amtundu umodzi, monga waya. Mukapangidwa kukhala miyeso iwiri, equation imafotokoza mafunde oyenda ndege. Nambala ya mafundeyi imatanthauzidwa ngati vector, ndipo madontho a mafunde awiri ndi mafunde ovuta.
Sine mafunde amagwiritsidwanso ntchito pofotokoza kutalika kwa mafunde amadzi mu dziwe pamene mwala wagwetsedwa. Ma equation ovuta kwambiri amafunikira kuti afotokoze mawu akuti sinusoid, omwe amafotokoza mawonekedwe a mafunde, kuphatikiza mafunde a sine ndi cosine okhala ndi kusintha kwa gawo. Sine wave imapangitsa kuti cosine wave ndi ma radian π/2, kapena chiyambi cha mutu, motero ntchito ya cosine imatsogolera ntchito ya sine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde a sine ndi cosine okhala ndi gawo lochotsera.
Kuwonetsa mafunde a cosine ndi ubale wofunikira ku bwalo mumtundu wa 3D complex plane, womwe umathandizira kuwona kufunika kwake m'magawo omasulira. Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde amtundu umodzi ngati akumveka bwino, komanso mafunde a sine ma frequency amtundu umodzi ndi ma harmonics awo. Khutu la munthu limamva ngati mafunde a sine okhala ndi phokoso lanthawi ndi nthawi, komanso kukhalapo kwa ma harmonics apamwamba kuphatikiza pazifukwa zazikulu zosinthira ma timbre.
Ichi ndichifukwa chake nyimbo zapafupipafupi zomwe zimaseweredwa pazida zosiyanasiyana zimamveka mosiyana. Phokoso la kuwomba m'manja, mwachitsanzo, lili ndi mafunde aperiodic, omwe sabwerezabwereza, osati mafunde a periodic sine. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida champhamvu chophunzirira mafunde, monga kuyenda kwa kutentha ndi kukonza ma siginecha, komanso kusanthula kwanthawi yayitali. Mafunde a Sine amathanso kufalikira posintha mawonekedwe kudzera pamakina ogawidwa, omwe amafunikira kusanthula kufalikira kwa mafunde. Mafunde a sine omwe amayenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency omwewo, ndipo akasunthidwa, mawonekedwe oyimirira amapangidwa. Izi zimawonedwa pamene cholemba chikudulidwa pa chingwe, monga mafunde osokoneza akuwonekera ndi mapeto okhazikika a chingwe. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant, ndipo amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Sine Wave Imamveka Motani?
Ndikukhulupirira kuti mudamvapo za mafunde a sine, koma mukudziwa momwe amamvekera? M'chigawo chino, tiwona momwe mafunde a sine amakhudzira phokoso la nyimbo, ndi momwe amachitira ndi ma harmonics kuti apange timbres zapadera. Tikambirananso momwe mafunde a sine amagwiritsidwira ntchito pokonza ma siginecha ndi kufalitsa mafunde. Pakutha kwa gawoli, mumvetsetsa bwino za mafunde a sine komanso momwe amakhudzira mawu.
Kodi Sine Wave Imamveka Bwanji?
Sine wave ndi kusuntha kosalekeza, kosalala, kobwerezabwereza komwe kumapezeka muzochitika zambiri zachilengedwe, kuphatikiza mafunde amphamvu, mafunde opepuka, komanso kuyenda kwa misa pa kasupe. Ndi masamu opindika omwe amafotokozedwa ndi trigonometric sine ntchito, ndipo nthawi zambiri amajambula ngati mawonekedwe a waveform.
Kodi sine wave imveka bwanji? Sine wave ndi mafunde opitilira, kutanthauza kuti alibe zopumira mu mawonekedwe a waveform. Ndi ntchito yosalala, nthawi ndi nthawi yokhala ndi ma frequency, kapena kuchuluka kwa ma oscillation omwe amapezeka munthawi yoperekedwa. Mafupipafupi ake aang'ono, kapena mlingo wa kusintha kwa mkangano wa ntchito mu ma radian pamphindikati, umayimiridwa ndi chizindikiro ω. Mtengo wolakwika umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola mumasekondi.
Kuchuluka kwa mafunde a sine kumayesedwa mu hertz (Hz), ndipo ndi chiwerengero cha oscillation pa sekondi iliyonse. Sine wave ndi phokoso lomveka lomwe limafotokozedwa ndi ntchito ya sine, f (t) = A tchimo (ωt + φ), pamene A ndi matalikidwe, ω ndi mafupipafupi a angular, ndipo φ ndi kusintha kwa gawo. Kusintha kwagawo kwa π/2 ma radian kumapangitsa kuti mafundewo ayambe mutu, motero nthawi zambiri amatchedwa ntchito ya cosine.
Mawu oti "sinusoid" amagwiritsidwa ntchito pofotokoza mawonekedwe a mafunde a sine wave, komanso mafunde a cosine okhala ndi gawo. Izi zikuwonetseredwa ndi mafunde a cosine, omwe amatsalira kumbuyo kwa sine wave ndikusintha kwagawo kwa π/2 ma radian. Ubale wofunikira uwu pakati pa mafunde a sine ndi cosine umaimiridwa ndi bwalo mumtundu wa 3D wovuta wa ndege, womwe umathandizira kuwona phindu la kumasulira pakati pa madera.
Mafunde amtundu wa sine wave amapezeka mwachilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka momveka bwino, ndipo zoyimira za ma frequency a single frequency zimagwiritsidwa ntchito popanga zolemba zanyimbo. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusinthasintha kwa mawu. Ichi ndichifukwa chake nyimbo yofanana yoyimba pazida zosiyanasiyana imamveka mosiyana.
Komabe, phokoso lopangidwa ndi dzanja la munthu silimangopangidwa ndi mafunde a sine, chifukwa limakhalanso ndi mafunde a aperiodic. Mafunde aaperiodic sabwerezabwereza ndipo alibe chitsanzo, pomwe mafunde a sine amakhala nthawi ndi nthawi. Katswiri wa masamu wa ku France, Joseph Fourier, anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida champhamvu chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito kaŵirikaŵiri pokonza zizindikiro ndi kusanthula mawerengero a nthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina ogawa, ndipo amafunikira kusanthula kufalikira kwa mafunde. Mafunde amphamvu akuyenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency omwewo, ndipo mafundewa akamapitilira, mawonekedwe oyimirira amapangidwa. Zimenezi n’zofanana ndi zimene zimachitika munthu akakoleza cholemba pa chingwe; mafunde osokoneza amapangidwa, ndipo pamene mafundewa akuwonetsedwa ndi mapeto okhazikika a chingwe, mafunde oyimirira amapezeka pazifukwa zina, zomwe zimatchedwa resonant frequencies. Ma frequency omveka awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi kutalika kwake, ndipo amafanana ndi muzu wa sikweya wa kulemera kwake pa utali wa unit.
Kodi Udindo wa Harmonics mu Sound ndi chiyani?
Sine wave ndi kusinthasintha kosalekeza, kosalala, kobwerezabwereza komwe kumapezeka m'magawo ambiri a masamu, physics, engineering, and sign processing. Ndi mtundu wa mafunde opitirira omwe amafotokozedwa ndi ntchito ya trigonometric, kawirikawiri sine kapena cosine, ndipo imayimiridwa ndi graph. Zimachitika m'masamu, fiziki, uinjiniya, ndi magawo opangira ma sign.
Mafupipafupi wamba wa sine wave, kapena kuchuluka kwa ma oscillation omwe amapezeka mu nthawi yoperekedwa, imayimiridwa ndi ma frequency aang'ono ω, omwe ndi ofanana ndi 2πf, pomwe f ndi ma frequency mu hertz. Mtengo wolakwika wa φ umayimira kuchedwa kwa masekondi, pomwe mtengo wabwino umayimira kutsogola mumasekondi.
Mafunde a sine nthawi zambiri amagwiritsidwa ntchito pofotokoza mafunde a mawu, chifukwa ndiwo mawonekedwe ofunikira kwambiri a mafunde. Amafotokozedwa ndi ntchito ya sine, f = A tchimo (ωt + φ), pamene A ndi matalikidwe, ω ndi mafupipafupi a angular, t ndi nthawi, ndipo φ ndi kusintha kwa gawo. Kusintha kwa gawo la π/2 ma radian kumapangitsa kuti mafundewo ayambe mutu, motero amanenedwa kuti ndi ntchito ya cosine, yomwe imatsogolera ntchito ya sine. Mawu akuti "sinusoidal" amagwiritsidwa ntchito kutanthauza mafunde a sine ndi mafunde a cosine okhala ndi gawo lochotsera.
Kuwonetsa izi, mafunde a cosine ndi ubale wofunikira pakati pa bwalo ndi mtundu wa ndege wa 3D wovuta, womwe umathandizira kuwona kufunika kwake pakumasulira kumadera ena. Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala.
Khutu la munthu limatha kuzindikira mafunde amtundu umodzi kuti amamveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito ngati chiwonetsero cha ma frequency amtundu umodzi. Khutu la munthu limamva phokoso ngati kuphatikiza kwa mafunde a sine ndi ma harmonics, ndi kuwonjezera kwa mafunde osiyanasiyana omwe amachititsa kuti mafunde asinthe komanso kusintha kwa timbre. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake cholembera chanyimbo chokhala ndi ma frequency omwe amaseweredwa pazida zosiyanasiyana chimamveka mosiyana.
Komabe, phokoso silimangopangidwa ndi mafunde a sine ndi ma harmonics, monga mawu opangidwa ndi manja ali ndi mafunde aperiodic. Mafunde aaperiodic sakhala nthawi ndi nthawi ndipo amakhala ndi mawonekedwe osabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi zomangira zosavuta zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mawonekedwe aliwonse a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito kaŵirikaŵiri pokonza zizindikiro ndi kusanthula mawerengero a nthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina ogawidwa, ndipo amafunikira kusanthula kufalikira kwa mafunde. Mafunde amphamvu akuyenda mosiyanasiyana mumlengalenga amatha kuyimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency omwewo, ndipo akamadutsa, mawonekedwe oyimirira amapangidwa. Izi ndi zomwe zimachitika pamene cholemba chikudulidwa pa chingwe: mafunde osokoneza amawonekera pamapeto okhazikika a chingwe, ndipo mafunde oyimirira amachitika pamayendedwe ena, omwe amatchedwa ma frequency a resonant. Ma frequency omveka awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi utali wake, ndipo amafanana ndi muzu wa sikweya wa unyinji pa utali wa unit wa chingwecho.
Kodi Sine Wave Imakhudza Bwanji Kumveka kwa Phokoso?
Sine wave ndi kusinthasintha kosalekeza, kosalala, kobwerezabwereza komwe ndi gawo lofunikira pa masamu, physics, engineering, and signal processing. Ndi mtundu wa mafunde osalekeza omwe amagwira ntchito mosalala, nthawi ndi nthawi ndipo amapezeka mu masamu, physics, engineering, and signal processing fields. Ma frequency wamba a sine wave ndi kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika mu unit of time. Izi zimasonyezedwa ndi ω = 2πf, pomwe ω ndi ma frequency aang'ono ndipo f ndi ma frequency wamba. Mafupipafupi a angular ndi kuchuluka kwa kusintha kwa mkangano wa ntchito ndipo amayezedwa mu ma radian pa sekondi iliyonse. Mtengo wosakhala wa ziro wa ω umayimira kusintha kwa mawonekedwe onse a mafunde mu nthawi, osonyezedwa ndi φ. Mtengo wolakwika wa φ umayimira kuchedwa ndipo mtengo wabwino umayimira kutsogola m'masekondi.
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a mawu, ndipo imafotokozedwa ndi sine function f = sin(ωt). Oscillations amawonekeranso mu dongosolo losasunthika la masika pamlingo wofanana, ndipo mafunde a sine ndi ofunikira mufizikiki chifukwa amasunga mawonekedwe awo a mafunde akaphatikizidwa pamodzi. Katunduyu wa mafunde a sine amabweretsa kufunikira kwake pakuwunika kwa Fourier, zomwe zimapangitsa kuti ikhale yapadera kwambiri.
Pamene funde la sine likuyimiridwa mu gawo limodzi la malo, equation imapereka kusamuka kwa mafunde pa malo x pa nthawi t. Chitsanzo cha mzere umodzi chimaganiziridwa, pomwe mtengo wa mafunde pa mfundo x umaperekedwa ndi equation. Mu miyeso yambiri ya malo, equation imalongosola mafunde a ndege oyendayenda, pomwe malo x amaimiridwa ndi vector ndipo wavenumber k ndi vector. Izi zitha kutanthauziridwa ngati madontho a ma vector awiriwa.
Mafunde ovuta, monga mafunde amadzi m'dziwe pamene mwala wagwetsedwa, amafuna ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 ma radian akuti kumapangitsa kuti mafunde a cosine ayambe mutu, pomwe amatsogolera mafunde a sine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo lochotsera, monga momwe zikuwonetsedwera ndi mafunde a cosine.
Ubale wofunikira uwu pakati pa mafunde a sine ndi cosine ukhoza kuwonedwa ndi bwalo mumtundu wa 3D wovuta wa ndege. Mtunduwu ndiwothandiza pakumasulira pakati pa madera osiyanasiyana, monga momwe mafunde amachitikira m'chilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka. Khutu la munthu limatha kuzindikira mafunde amtundu umodzi, kumveka bwino komanso koyera. Mafunde a Sine amayimiranso ma single frequency harmonics, omwe khutu la munthu limatha kuzindikira.
Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo zapafupipafupi zomwe zimaseweredwa pazida zosiyanasiyana zimamveka mosiyana. Kuwomba m'manja kumakhala ndi mafunde aperiodic, osati mafunde a sine, chifukwa ndi phokoso la nthawi ndi nthawi. Phokoso limawonedwa ngati laphokoso, lomwe limadziwika kuti ndi la aperiodic, lokhala ndi mawonekedwe osabwerezabwereza.
Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kuthamanga kwa kutentha ndi kuwongolera ma siginecha ndi kusanthula kwanthawi yayitali. Mafunde a Sine amathanso kufalikira kudzera mukusintha mafomu mumayendedwe ogawidwa, omwe amafunikira kusanthula kufalikira kwa mafunde. Mafunde a m'mlengalenga omwe akuyenda mosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana. Mafundewa akamakulirakulira, mafunde oyimirira amapangidwa, monga momwe timawonera pamene cholemba chikukokedwa pa chingwe. Mafunde osokoneza omwe amawonekera kuchokera kumalekezero okhazikika a chingwecho amapanga mafunde oima omwe amapezeka pamayendedwe ena, omwe amatchedwa ma frequency a resonant. Ma frequency omveka awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Sine Waves ngati Zida Zowunikira
Ndilankhula za mafunde a sine ndi momwe amagwiritsidwira ntchito ngati zida zowunikira pakuwongolera ma siginecha, kusanthula kwanthawi ndi kufalitsa mafunde. Tiwona momwe mafunde a sine amagwiritsidwira ntchito kufotokoza kusinthasintha kosalala, kobwerezabwereza komanso momwe amagwiritsidwira ntchito mu masamu, physics, engineering ndi zina. Tiwonanso momwe mafunde a sine angagwiritsire ntchito kusanthula kufalikira kwa mafunde ndi momwe amagwiritsidwira ntchito pakuwunika kwa Fourier. Pomaliza, tikambirana momwe ma sine mafunde amagwiritsidwira ntchito kupanga mawu komanso momwe amagwiritsidwira ntchito mu nyimbo.
Kodi Signal Processing ndi chiyani?
Sine wave ndi chida chofunikira kwambiri chomwe chimagwiritsidwa ntchito pokonza ma siginecha ndi kusanthula nthawi. Ndiwo mtundu wa mawonekedwe osalekeza, omwe amadziwika ndi oscillation yosalala, yobwerezabwereza ndi maulendo amodzi. Mafunde a sine amagwiritsidwa ntchito pofotokoza zochitika zosiyanasiyana zakuthupi, kuphatikizapo mafunde a phokoso, mafunde a kuwala, ndi kuyenda kwa misa pa kasupe.
Kukonza ma sign ndi njira yosanthula ndikusintha ma signature. Amagwiritsidwa ntchito m'magawo osiyanasiyana, kuphatikiza masamu, physics, engineering, komanso kupanga ma audio ndi makanema. Njira zopangira ma siginecha zimagwiritsidwa ntchito kusanthula ma siginecha, kuzindikira mawonekedwe, ndi kuchotsa zidziwitso kuchokera kwa iwo.
Kusanthula kwa nthawi ndi njira yowunikira mfundo zomwe zasonkhanitsidwa pakapita nthawi. Amagwiritsidwa ntchito kuzindikiritsa zochitika ndi machitidwe mu data, komanso kulosera zamtsogolo. Kusanthula kwa nthawi kumagwiritsidwa ntchito m'magawo osiyanasiyana, kuphatikiza zachuma, zachuma, ndi uinjiniya.
Kufalikira kwa mafunde ndi njira yomwe mafunde amayenda modutsa pakati. Imawunikidwa pogwiritsa ntchito masamu osiyanasiyana, kuphatikiza ma wave equation ndi sine wave equation. Kufalikira kwa mafunde kumagwiritsidwa ntchito kuwunika momwe mafunde amamvekedwe, mafunde opepuka, ndi mitundu ina ya mafunde.
Kodi Time Series Analysis ndi chiyani?
Mafunde a Sine ndi chida chofunikira chowunikira zochitika zosiyanasiyana zakuthupi, kuyambira mafunde amawu mpaka mafunde owala. Kusanthula kwa nthawi ndi njira yowunikira mfundo zomwe zasonkhanitsidwa pakapita nthawi, kuti muzindikire mawonekedwe ndi machitidwe. Amagwiritsidwa ntchito pophunzira machitidwe a dongosolo pakapita nthawi, komanso kulosera za machitidwe amtsogolo.
Kusanthula kwanthawi kumatha kugwiritsidwa ntchito kusanthula mafunde a sine. Itha kugwiritsidwa ntchito kuzindikira ma frequency, matalikidwe, ndi gawo la sine wave, komanso kuzindikira kusintha kulikonse mu mawonekedwe a mafunde pakapita nthawi. Itha kugwiritsidwanso ntchito kuzindikira mawonekedwe aliwonse omwe ali mu mawonekedwe a mafunde, monga periodicities kapena mayendedwe.
Kusanthula kwa nthawi kungagwiritsidwenso ntchito kuzindikira kusintha kulikonse kwa matalikidwe kapena gawo la sine wave pakapita nthawi. Izi zitha kugwiritsidwa ntchito kuzindikira kusintha kulikonse mudongosolo komwe kungayambitse kusintha kwa mawonekedwe, monga kusintha kwa chilengedwe kapena dongosolo lokha.
Kusanthula kwa nthawi kutha kugwiritsidwanso ntchito kuzindikira njira zilizonse zomwe zili mumayendedwe, monga ma periodicities kapena mayendedwe. Izi zitha kugwiritsidwa ntchito kuzindikira njira zilizonse zomwe zili m'dongosololi zomwe zingayambitse kusintha kwa mawonekedwe, monga kusintha kwa chilengedwe kapena dongosolo lomwe.
Kusanthula kwa mndandanda wa nthawi kungagwiritsidwenso ntchito kuzindikira kusintha kulikonse kwa ma frequency a sine wave pakapita nthawi. Izi zitha kugwiritsidwa ntchito kuzindikira kusintha kulikonse mudongosolo komwe kungayambitse kusintha kwa mawonekedwe, monga kusintha kwa chilengedwe kapena dongosolo lokha.
Kusanthula kwa nthawi kutha kugwiritsidwanso ntchito kuzindikira njira zilizonse zomwe zili mumayendedwe, monga ma periodicities kapena mayendedwe. Izi zitha kugwiritsidwa ntchito kuzindikira njira zilizonse zomwe zili m'dongosololi zomwe zingayambitse kusintha kwa mawonekedwe, monga kusintha kwa chilengedwe kapena dongosolo lomwe.
Kusanthula kwanthawi ndi chida champhamvu chowunikira mafunde a sine ndipo chitha kugwiritsidwa ntchito kuzindikira mawonekedwe ndi momwe mafunde amayendera pakapita nthawi. Itha kugwiritsidwanso ntchito kuzindikira njira zilizonse zomwe zingayambitse mafundewa kuti asinthe, monga kusintha kwa chilengedwe kapena dongosolo lomwe.
Kodi Kufalitsa kwa Wave Kumawunikiridwa bwanji?
Mafunde a Sine ndi mtundu wa mawonekedwe osalekeza omwe angagwiritsidwe ntchito kusanthula kufalikira kwa mafunde. Ndi zosalala, zobwerezabwereza zomwe zimapezeka mu masamu, fizikiki, uinjiniya, ndi kukonza ma sign. Mafunde a Sine amadziwika ndi ma frequency awo (f), kuchuluka kwa ma oscillation omwe amapezeka munthawi yoperekedwa, komanso ma frequency awo aang'ono (ω), womwe ndi mlingo womwe mkangano wantchito umasinthira mayunitsi a ma radian.
Mafunde a Sine amagwiritsidwa ntchito pofotokoza zochitika zosiyanasiyana, kuphatikizapo mafunde a phokoso, mafunde a kuwala, ndi kuyenda kwa misa pa kasupe. Ndiwofunikanso pakuwunika kwa Fourier, zomwe zimawapangitsa kukhala apadera kwambiri. Sine wave ikhoza kuyimiridwa mumzere umodzi ndi mzere umodzi, ndi mtengo wa mafunde pa malo operekedwa mu nthawi ndi malo. M'miyeso ingapo, equation ya sine wave imalongosola mafunde a ndege oyenda, okhala ndi malo (x), nambala ya mafunde (k), ndi ma frequency aang'ono (ω).
Sinusoids ndi mtundu wa ma waveform omwe amaphatikizapo mafunde a sine ndi cosine, komanso mawonekedwe aliwonse okhala ndi gawo la π/2 radians (chiyambi chamutu). Izi zimatsogolera ku ubale wofunikira pakati pa mafunde a sine ndi cosine, omwe amatha kuwonedwa mumtundu wa 3D wovuta wa ndege. Mtunduwu ndiwothandiza pakumasulira ma waveform pakati pa madambwe osiyanasiyana.
Mafunde a sinusoidal amapezeka m'chilengedwe, kuphatikiza mafunde amphepo ndi mafunde amadzi. Khutu la munthu limatha kuzindikira mafunde a sine imodzi kuti amamveka bwino, koma mawu nthawi zambiri amakhala ndi mafunde angapo, omwe amatchedwa ma harmonics. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusinthasintha kwa mawu. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana.
Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde aliwonse a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida champhamvu chophunzirira mafunde, ndipo chimagwiritsidwa ntchito poyendetsa kutentha komanso kukonza ma sign. Amagwiritsidwanso ntchito pofufuza zowerengera za nthawi.
Mafunde a Sine amatha kufalikira mbali iliyonse mumlengalenga, ndipo amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency omwe amayenda mosiyanasiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Ichi ndi chitsanzo chomwecho chomwe chimapangidwa pamene cholemba chikudulidwa pa chingwe, chifukwa cha mafunde omwe amawonekera pamapeto okhazikika a chingwe. Mafunde oyimirira amapezeka pama frequency ena, omwe amadziwika kuti ma frequency a resonant, omwe amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwake, ndipo amafanana ndi kulemera kwake pautali wa unit.
Sine Wave Spectrum
Ndikambilana za sine wave sipekitiramu, kuphatikiza ma frequency ake, kutalika kwa mafunde, ndi momwe angagwiritsire ntchito kupanga mamvekedwe osiyanasiyana. Tiwunika masamu opindika omwe amafotokoza kusinthasintha kosalala, kobwerezabwereza, ndi momwe amagwiritsidwira ntchito m'masamu, fizikisi, uinjiniya, ndi magawo opangira ma sign. Tiwonanso momwe ma sine wave ndi ofunikira mufizikiki komanso chifukwa chake amagwiritsidwa ntchito pakuwunika kwa Fourier. Pomaliza, tikambirana momwe ma wave wave amagwiritsidwira ntchito pomveka komanso momwe khutu la munthu limazindikirira.
Kodi Frequency ya Sine Wave ndi chiyani?
Sine wave ndi mawonekedwe osalekeza omwe amayenda mosalala, mobwerezabwereza. Ndi gawo lofunikira pazochitika zambiri zakuthupi ndi masamu, monga mawu, kuwala, ndi ma siginecha amagetsi. Mafupipafupi a sine wave ndi kuchuluka kwa ma oscillation omwe amapezeka mu nthawi yoperekedwa. Amayezedwa mu Hertz (Hz) ndipo nthawi zambiri amawonetsedwa mozungulira sekondi iliyonse. Ubale pakati pa ma frequency ndi wavelength ndikuti kumtunda kwa ma frequency, kufupikitsa kwa kutalika kwa mafunde.
Mafunde a Sine amagwiritsidwa ntchito kupanga zomveka zosiyanasiyana, kuphatikiza vibrato, tremolo, ndi chorus. Pophatikiza mafunde angapo a sine ama frequency osiyanasiyana, ma waveform ovuta amatha kupangidwa. Izi zimadziwika kuti zowonjezera kaphatikizidwe, ndipo zimagwiritsidwa ntchito mumitundu yambiri yamawu. Kuonjezera apo, mafunde a sine angagwiritsidwe ntchito kupanga zotsatira zosiyanasiyana, monga kusintha kwa gawo, flanging, ndi phasing.
Mafunde a sine amagwiritsidwanso ntchito pokonza ma siginecha, monga kusanthula kwa Fourier, komwe kumagwiritsidwa ntchito pophunzira kachulukidwe ka mafunde ndi kayendedwe ka kutentha. Amagwiritsidwanso ntchito posanthula ziwerengero ndi kusanthula nthawi.
Mwachidule, mafunde a sine ndi mawonekedwe osalekeza omwe amayenda mosalala, mobwerezabwereza. Amagwiritsidwa ntchito popanga zomveka zosiyanasiyana, ndipo amagwiritsidwanso ntchito pokonza zizindikiro ndi kusanthula ziwerengero. Kuchuluka kwa mafunde a sine ndi chiwerengero cha ma oscillation omwe amapezeka mu nthawi yoperekedwa, ndipo mgwirizano pakati pa mafupipafupi ndi kutalika kwa mafunde ndi kuti kumtunda kwafupipafupi, kufupikitsa kwa kutalika kwake.
Kodi Ubale Pakati pa Frequency ndi Wavelength ndi Chiyani?
Sine wave ndi kusinthasintha kosalekeza, kosalala, kobwerezabwereza komwe kumapezeka m'magawo ambiri a masamu, physics, engineering, and sign processing. Imatanthauzidwa ndi ntchito ya trigonometric sine, ndipo imayimiridwa mowoneka ngati mawonekedwe ozungulira. Sine wave ili ndi ma frequency, omwe ndi kuchuluka kwa ma oscillation kapena ma cycle omwe amapezeka mu nthawi yoperekedwa. Mafupipafupi a angular, otchulidwa ndi ω, ndi mlingo wa kusintha kwa mkangano wa ntchito, woyezedwa mu ma radian pamphindikati. Mawonekedwe onsewa samawonekera nthawi imodzi, koma amasinthidwa nthawi ndi kusintha kwa gawo, komwe kumatanthauzidwa ndi φ, komwe kumayesedwa mumasekondi. Mtengo wolakwika umayimira kuchedwa, ndipo mtengo wabwino umayimira patsogolo pamasekondi. Kuchuluka kwa mafunde a sine kumayesedwa mu hertz (Hz), ndipo ndi chiwerengero cha ma oscillation omwe amapezeka mu sekondi imodzi.
Sine wave ndi mawonekedwe ofunikira mufizikiki, chifukwa imasunga mawonekedwe ake ikawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katundu wa mawonekedwe a nthawi ndi nthawi amadziwika kuti superposition mfundo, ndipo ndi katundu amene amatsogolera ku kufunika kwa kusanthula kwa Fourier. Izi zimapangitsa kuti ikhale yapadera kwambiri, chifukwa ndi mawonekedwe okhawo omwe angagwiritsidwe ntchito kupanga kusintha kwa malo. Mwachitsanzo, ngati x ikuyimira malo omwe ali pawaya, ndiye kuti funde la sine la ma frequency opatsidwa ndi kutalika kwa mafunde lidzafalikira pa waya. Mawonekedwe a mafundewa amadziwika kuti nambala yoweyula, k, yomwe ndi nambala ya mafunde aang'ono ndipo imayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liwiro la mzere wa kufalitsa, ν. Nambala yoweyula imakhudzana ndi ma frequency aang'ono ndi kutalika kwa mawonekedwe, λ, ndi equation λ = 2π/k.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A sin(ωt + φ), pomwe A ndiye matalikidwe, ω ndi ma frequency aang'ono, t ndi nthawi, ndipo φ ndikusintha kwagawo. Equation iyi ikhoza kusinthidwa kuti ipereke kusuntha kwa mafunde pamalo opatsidwa, x, panthawi yoperekedwa, t. Kwa chitsanzo cha mzere umodzi, mtengo wa mafunde pa malo operekedwa umaperekedwa ndi y = A sin(kx - ωt + φ), pamene k ndi nambala yoweyula. Pamene miyeso yambiri ya malo ikuganiziridwa, equation yovuta kwambiri imafunika kufotokoza mafunde.
Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mawonekedwe a waveform omwe ali ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 ma radian akuti kumapangitsa kuti mafunde a sine ayambe mutu, popeza mafunde a sine amatsitsa mafunde a cosine ndi kuchuluka kwake. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo lochotsera. Izi zikuwonetsedwa mu graph yomwe ili pansipa, yomwe ikuwonetsa mafunde a cosine okhala ndi kusintha kwagawo kwa ma radian π/2.
Ubale wofunikira pakati pa sine wave ndi bwalo zitha kuwonedwa pogwiritsa ntchito mtundu wa 3D wovuta wa ndege. Izi ndizothandiza kumasulira mawonekedwe a mafunde m'magawo osiyanasiyana, monga momwe mafundewa amachitikira m'chilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka. Khutu la munthu limatha kuzindikira mafunde amtundu umodzi kuti amamveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito ngati ma toni amtundu umodzi. Ma Harmonics amapezekanso m'mawu, monga khutu la munthu limatha kuzindikira ma harmonics kuwonjezera pa ma frequency ofunikira. Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira ndizomwe zimayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake cholembera chanyimbo chafupipafupi chomwe chimaseweredwa pazida zosiyanasiyana chidzamveka mosiyana.
Phokoso la kuwomba pamanja limakhalanso ndi mafunde aperiodic, omwe ndi mafunde omwe sakhala nthawi ndi nthawi. Mafunde a sine amakhala nthawi ndi nthawi, ndipo phokoso lomwe limamveka ngati phokoso limadziwika ndi mafunde aperiodic, okhala ndi mawonekedwe osabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde aliwonse a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida champhamvu chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kuyenda kwa kutentha ndi kukonza ma siginecha, komanso kusanthula kwanthawi yayitali. Mafunde a Sine angagwiritsidwenso ntchito kufalitsa kudzera mukusintha mafomu m'magawo ogawa. Izi zimafunika kuti tiwunikenso kufalikira kwa mafunde mbali ziwiri mumlengalenga, chifukwa mafunde okhala ndi matalikidwe ofanana ndi mafupipafupi omwe amayenda mbali zosiyanasiyana amapitilira kupanga mawonekedwe oyimirira. Izi ndi zomwe zimamveka pamene cholemba chikudulidwa pa chingwe, monga momwe mafunde amawonekera kumapeto kwa chingwecho. Mafunde oyimirira amapezeka pamayendedwe ena, omwe amatchedwa ma frequency a resonant a chingwe. Ma frequency awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Sine Wave Ingagwiritsidwe Ntchito Motani Kupanga Zojambula Zosiyanasiyana?
Sine wave ndi mawonekedwe osalekeza omwe amayenda mosalala, mobwerezabwereza. Ndi imodzi mwamafunde ofunikira kwambiri ndipo imagwiritsidwa ntchito m'magawo ambiri a masamu, physics, engineering, and sign processing. Mafunde a Sine amadziwika ndi ma frequency awo, omwe ndi kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika mu nthawi yoperekedwa. Mafupipafupi a angular, omwe ndi mlingo wa kusintha kwa mkangano wa ntchito mu ma radian pamphindikati, umagwirizana ndi ma frequency wamba ndi equation ω = 2πf.
Mafunde a Sine amagwiritsidwa ntchito kwambiri popanga mawu ndipo atha kugwiritsidwa ntchito popanga mawu osiyanasiyana. Mwa kuphatikiza mafunde osiyanasiyana a sine ndi ma frequency osiyanasiyana, matalikidwe, ndi magawo, phokoso lambiri lingapangidwe. Sine wave yokhala ndi ma frequency amodzi amadziwika kuti "maziko" ndipo ndiye maziko a zolemba zonse zanyimbo. Pamene mafunde ambiri a sine okhala ndi ma frequency osiyanasiyana aphatikizidwa, amapanga "harmonics" omwe ndi ma frequency apamwamba omwe amawonjezera kumveka kwa mawu. Powonjezera ma harmonics, phokoso likhoza kumveka kuti likhale lovuta komanso losangalatsa. Kuphatikiza apo, posintha gawo la sine wave, phokosolo limatha kumveka ngati likuchokera mbali zosiyanasiyana.
Sine mafunde amagwiritsidwanso ntchito mu acoustics kuyeza kukula kwa mafunde a phokoso. Poyesa kukula kwa mafunde a sine, mphamvu ya phokoso imatha kudziŵika. Izi ndizothandiza poyeza kukweza kwa mawu kapena kudziwa kuchuluka kwa mawu.
Pomaliza, mafunde a sine ndi mawonekedwe ofunikira m'malo ambiri asayansi ndi uinjiniya. Amagwiritsidwa ntchito popanga zomveka zosiyanasiyana ndipo amagwiritsidwanso ntchito poyeza mphamvu ya mafunde a phokoso. Mwa kuphatikiza mafunde osiyanasiyana a sine ndi ma frequency osiyanasiyana, matalikidwe, ndi magawo, phokoso lambiri lingapangidwe.
Kodi Sine Curve Ingafotokoze Bwanji Mafunde?
M'chigawo chino, ndikambirana za momwe ma curve a sine angagwiritsire ntchito kufotokozera mafunde, mgwirizano pakati pa piritsi la sine ndi mafunde a ndege, ndi momwe curve ya sine ingagwiritsire ntchito kuwona mawonekedwe a mafunde. Tiwona kufunikira kwa mafunde a sine mu masamu, fizikisi, uinjiniya, ndi kukonza ma siginecha, ndi momwe amagwiritsidwira ntchito kuyimira mafunde amawu ndi mafunde ena.
Kodi Sine Curve Imayimira Bwanji Mafunde?
Sine wave ndi njira yosalala, yobwerezabwereza yomwe imakhala yosalekeza ndipo imakhala ndi mawonekedwe ozungulira omwe amafotokozedwa ndi sine trigonometric function. Ndi mtundu wa mafunde osalekeza omwe ndi osalala komanso osasintha, ndipo amapezeka mu masamu, physics, engineering, ndi magawo opangira ma sign. Amadziwika ndi ma frequency, omwe ndi kuchuluka kwa ma oscillation kapena ma cycle omwe amapezeka mu nthawi yoperekedwa. Mafupipafupi a angular, ω, ndi mlingo umene mtsutso wa ntchito umasintha mu mayunitsi a ma radian pamphindikati. Mawonekedwe osakhala amtundu wonse amawoneka atasinthidwa nthawi ndi kusintha kwa gawo, φ, komwe kumayesedwa mumasekondi. Mtengo wolakwika umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola mumasekondi.
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a phokoso, ndipo imafotokozedwa ndi ntchito ya sine, f = A tchimo (ωt + φ). Oscillations amapezekanso mu dongosolo losasunthika la masika panthawi yofanana, ndipo sine wave ndi yofunika kwambiri mufizikiki chifukwa imakhalabe ndi mawonekedwe ake pamene ikuwonjezeredwa ku sine wave ya ma frequency omwewo ndi gawo losagwirizana ndi kukula kwake. Katundu wa ma waveform awa ndi omwe amatsogolera kufunikira kwake pakuwunika kwa Fourier, zomwe zimapangitsa kuti zikhale zapadera kwambiri.
Pamene mafunde akufalikira mu gawo limodzi, kusintha kwa malo, x, kumayimira malo omwe mafundewa akufalikira, ndipo chizindikiro cha khalidwe, k, chimatchedwa nambala yoweyula. Nambala ya mafunde aang'ono imayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liwiro la mzere wa kufalikira, ν. Nambala yamafunde imagwirizana ndi ma frequency aang'ono, λ (lambda) ndiye kutalika kwa mafunde, ndipo f ndi ma frequency. The equation v = λf amapereka sine wave mu gawo limodzi. Equation yokhazikika imaperekedwa kuti ipereke kusuntha kwa mafunde pamalo, x, panthawi, t.
Pamene chitsanzo cha mzere umodzi chikuganiziridwa, mtengo wa mafunde pa malo aliwonse a danga umaperekedwa ndi equation x = A tchimo (kx - ωt + φ). Kwa miyeso iwiri ya malo, equation imalongosola mafunde oyendayenda a ndege. Akatanthauziridwa ngati ma vector, chopangidwa ndi ma vector awiriwa ndi madontho.
Kwa mafunde ovuta, monga mafunde amadzi mu dziwe pamene mwala wagwetsedwa, ma equation ovuta amafunikira. Mawu akuti sinusoid amagwiritsidwa ntchito pofotokoza mawonekedwe a mafunde a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 ma radian akuti kumapangitsa kuti mafunde a cosine ayambe mutu, pomwe amatsogolera mafunde a sine. Sine wave imachepetsa mafunde a cosine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde a sine ndi mafunde a cosine okhala ndi gawo, kuwonetsa ubale wofunikira pakati pa ziwirizi. Bwalo lachitsanzo cha ndege cha 3D chovuta chitha kugwiritsidwa ntchito kuti muwone phindu la kumasulira pakati pa madera awiriwa.
Mafunde omwewo amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka momveka bwino, ndipo mafunde a sine amaimira ma frequency ndi ma harmonics amodzi. Khutu la munthu limamva phokoso ngati mafunde a sine okhala ndi ma harmonics omveka kuwonjezera pa ma frequency ofunikira. Kuphatikizidwa kwa mafunde osiyanasiyana a sine kumabweretsa mawonekedwe osiyana, omwe amasintha timbre ya phokoso. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo zapafupipafupi zomwe zimaseweredwa pazida zosiyanasiyana zimamveka mosiyana.
Phokoso la kuwomba m'manja lili ndi mafunde aperiodic, omwe sachitika nthawi ndi nthawi, ndipo mafunde a sine amakhala nthawi ndi nthawi. Phokoso lomwe limawoneka ngati laphokoso limadziwika kuti ndi la aperiodic, lokhala ndi mawonekedwe osabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde apakati. Kusanthula kwa Fourier ndi chida chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula mawerengero a nthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina amzere ogawidwa, ndipo pamafunika kusanthula kufalikira kwa mafunde. Mafunde a m'mlengalenga omwe akuyenda mosiyanasiyana mumlengalenga amatha kuyimiridwa ngati mafunde okhala ndi matalikidwe ofanana komanso mafunde omwe amayenda mosiyanasiyana. Mafunde awiriwa akamakula, mafunde oyimirira amapangidwa. Zimenezi n’zofanana ndi pamene cholemba chikukokedwa pa chingwe, pamene mafunde oloŵerera amawonekera kumapeto kwa chingwecho. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant. Phokoso lopangidwa lachidziwitso chovulidwa pa chingwe limapangidwa ndi ma frequency ndi ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Ubale Pakati pa Sine Curve ndi Plane Wave ndi Chiyani?
Sine wave ndi kusinthasintha kosalala, kobwerezabwereza kwa mawonekedwe opitilira. Ndi masamu okhotakhota omwe amatanthauzidwa malinga ndi ntchito ya sine trigonometric, ndipo nthawi zambiri amajambula ngati curve yosalala, sinusoidal. Sine mafunde amapezeka m'madera ambiri a masamu, physics, engineering, ndi ma signal processing fields.
Sine wave imadziwika ndi ma frequency ake wamba, kuchuluka kwa ma oscillation kapena kuzungulira komwe kumachitika munthawi yoperekedwa. mpata. Mafupipafupi a angular, ω, ndi mlingo wa kusintha kwa mtsutso wa ntchito, ndipo amayezedwa mu mayunitsi a ma radian pa sekondi iliyonse. Mawonekedwe osakhala amtundu wonse amawoneka atasinthidwa nthawi, ndikusintha kwa gawo, φ, ωt masekondi. Mtengo wolakwika umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola mumasekondi.
Sine wave imagwiritsidwanso ntchito pofotokoza mafunde a mawu. Zimafotokozedwa ndi ntchito ya sine, f (t) = A tchimo (ωt + φ), pamene A ndi matalikidwe, ω ndi mafupipafupi a angular, ndipo φ ndi kusintha kwa gawo. Oscillations amawonekeranso mu dongosolo losasunthika la masika pamlingo wofanana.
Mafunde a sine ndi ofunikira mufizikiki chifukwa amasunga mawonekedwe awo akaphatikizidwa pamodzi. Katunduyu, yemwe amadziwika kuti superposition principle, amatsogolera ku kufunikira kwa kusanthula kwa Fourier, komwe kumapangitsa kuti athe kusiyanitsa momveka bwino pakati pa zosintha zapamalo. Mwachitsanzo, ngati x akuyimira malo mu gawo limodzi, ndiye kuti funde limafalikira ndi chizindikiro, k, chotchedwa nambala yoweyula. Nambala ya mafunde aang'ono, k, imayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liwiro la mzere wa kufalikira, ν. Nambala ya mafunde, k, imagwirizana ndi mafupipafupi a angular, ω, ndi kutalika kwa mawonekedwe, λ, ndi equation λ = 2π/k.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo(ωt + φ). Equation iyi imapereka kusuntha kwa mafunde pamalo opatsidwa, x, panthawi yoperekedwa, t. Kwa chitsanzo cha mzere umodzi, ngati mtengo wa mafundewa umatengedwa kuti ndi waya, ndiye mu miyeso iwiri ya malo, equation imalongosola mafunde oyenda ndege. Maonekedwe, x, ndi ma wavenumber, k, amatha kutanthauziridwa ngati ma vectors, ndipo chopangidwa ndi awiriwa ndi madontho.
Mafunde ovuta, monga omwe amawonekera m'dziwe pamene mwala wagwetsedwa, amafuna ma equation ovuta kuwafotokozera. Mawu akuti sinusoid amagwiritsidwa ntchito pofotokoza mawonekedwe a mafunde omwe amafanana ndi mafunde a sine. Mafunde a cosine ndi ofanana ndi mafunde a sine, koma ndi kusintha kwa gawo la π/2 ma radian, kapena poyambira mutu. Izi zimatsogolera ku sine wave kutsetsereka kwa cosine wave. Mawu akuti sinusoidal amagwiritsidwa ntchito palimodzi kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo lochotsera.
Kuwonetsa mafunde a cosine ndi ubale wofunikira ku bwalo mumtundu wa 3D wovuta wa ndege, womwe ungagwiritsidwe ntchito kuwonetsa phindu la mafunde a sine pakumasulira pakati pa madambwe. Mafunde amtunduwu amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka momveka bwino, ndipo mafunde a sine amaimira ma frequency ndi ma harmonics amodzi. Khutu la munthu limamva phokoso ngati mafunde a sine okhala ndi ma harmonics kuwonjezera pa ma frequency ofunikira. Izi zimabweretsa kusintha kwa timbre. Chifukwa chomwe nyimbo zoimbira zimaseweredwa pazida zosiyanasiyana zimamveka mosiyana ndi chifukwa phokosoli lili ndi mafunde aperiodic kuphatikiza mafunde a sine. Phokoso la Aperiodic limadziwika ngati phokoso, ndipo phokoso limadziwika ndi kukhala ndi mawonekedwe osabwerezabwereza.
Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira yosavuta yofotokozera komanso kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde a square. Kusanthula kwa Fourier ndi chida champhamvu chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula ziwerengero za nthawi. Mafunde a Sine amathanso kufalikira popanda kusintha mawonekedwe mumachitidwe ogawidwa. Izi ndizofunikira kuti mufufuze kufalikira kwa mafunde mbali ziwiri mumlengalenga, ndipo imayimiridwa ndi mafunde okhala ndi matalikidwe ofanana ndi ma frequency, koma akuyenda mosiyanasiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Izi zimawonekera pamene cholemba chikokedwa pa chingwe, ndipo mafunde osokoneza amawonekera pamapeto okhazikika a chingwecho. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant, ndipo amapangidwa ndi ma frequency oyambira komanso ma harmonics apamwamba. Mafuridwe omveka a chingwe amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Sine Curve Ingagwiritsidwe Ntchito Motani Kuti Muwone Mafunde a Mafunde?
Sine wave ndi kusinthasintha kosalekeza, kosalala, kobwerezabwereza komwe kumafotokozedwa ndi masamu opindika. Ndi mtundu wa mafunde opitirira omwe amatanthauzidwa ndi trigonometric sine ntchito, yomwe imajambulidwa ngati mawonekedwe a waveform. Zimachitika m'masamu, fiziki, uinjiniya, ndi magawo opangira ma sign.
Sine wave ili ndi ma frequency wamba, omwe ndi kuchuluka kwa ma oscillation kapena ma cycle omwe amapezeka mu nthawi yoperekedwa. Izi zikuyimiridwa ndi ma frequency aang'ono, ω, omwe ndi ofanana ndi 2πf, pomwe f ndi ma frequency mu hertz (Hz). Sine wave imatha kusinthidwa munthawi yake, ndi mtengo woyipa womwe umayimira kuchedwa ndi mtengo wabwino womwe umayimira patsogolo pamasekondi.
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a phokoso, monga momwe amafotokozera ndi ntchito ya sine. Mafupipafupi a sine wave, f, ndi kuchuluka kwa ma oscillation pamphindikati. Izi ndizofanana ndi kugwedezeka kwa dongosolo losasunthika la masika pamlingo wofanana.
Sine wave ndi yofunika mu fizikisi chifukwa imasunga mawonekedwe ake a mafunde ikawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katunduyu wa sine wave amadziwika kuti superposition principle ndipo ndi nthawi yanthawi yama waveform. Katunduyu amabweretsa kufunikira kwa kusanthula kwa Fourier, komwe kumapangitsa kuti athe kusiyanitsa momveka bwino pakati pamitundu yosiyanasiyana yamalo.
Mwachitsanzo, ngati x akuyimira gawo lomwe mafunde akufalikira, ndiye chizindikiro cha k, chotchedwa nambala yoweyula, chimayimira kufanana pakati pa ma frequency aang'ono, ω, ndi liniya liwiro la kufalitsa, ν. Nambala yoweyula imakhudzana ndi ma frequency aang'ono ndi kutalika kwa mawonekedwe, λ, ndi equation λ = 2π/k.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A tchimo (ωt + φ), pamene A ndi matalikidwe, ω ndi mafupipafupi a angular, t ndi nthawi, ndipo φ ndi kusintha kwa gawo. Ngati chitsanzo cha mzere umodzi chikuganiziridwa, ndiye kuti mtengo wa mafunde pa nthawi iliyonse x nthawi iliyonse t imaperekedwa ndi y = A tchimo (kx - ωt + φ).
Mu miyeso yambiri ya malo, equation ya sine wave imaperekedwa ndi y = A tchimo (kx - ωt + φ), pamene A ndi matalikidwe, k ndi nambala ya mafunde, x ndi malo, ω ndi mafupipafupi aang'ono, t ndi nthawi, ndipo φ ndiye kusintha kwa gawo. Equation iyi ikufotokoza mafunde a ndege oyenda.
Kuthandiza kwa sine wave sikumangotanthauza kumasulira m'magawo akuthupi. Mafunde omwewo amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala. Khutu la munthu limatha kuzindikira mafunde a sine ngati akumveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito kuyimira ma frequency amtundu umodzi.
Khutu la munthu limathanso kuzindikira phokoso lomwe limapangidwa ndi ma frequency ndi ma harmonics apamwamba. Mafupipafupi a chingwechi amafanana ndi kutalika kwa chingwe ndipo amafanana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Mwachidule, mawu akuti sinusoid amagwiritsidwa ntchito pofotokoza mafunde omwe ali ndi mawonekedwe a sine wave ndi cosine wave. Sine wave akuti ili ndi gawo la π/2 radians, lomwe ndi lofanana ndi chiyambi cha mutu, pomwe mafunde a cosine akuti amatsogolera mafunde a sine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine, okhala ndi gawo lochotsera. Izi zikuwonetseredwa ndi mafunde a cosine, omwe ndi ubale wofunikira mu bwalo mumtundu wa 3D wovuta wa ndege womwe umagwiritsidwa ntchito kuwonetsa phindu la sine wave pomasulira m'magawo akuthupi.
Sine Waves ndi Phase
Mu gawo ili, ndikuwona mgwirizano pakati pa mafunde a sine ndi gawo. Ndikambirana momwe gawo limakhudzira mafunde a sine ndi momwe angagwiritsire ntchito kupanga ma waveform osiyanasiyana. Ndiperekanso zitsanzo zowonetsera momwe gawo lingagwiritsire ntchito pazinthu zosiyanasiyana.
Kodi Ubale Pakati pa Sine Wave ndi Phase ndi Chiyani?
Sine wave ndi oscillation yosalala, yobwerezabwereza yomwe imakhala yosalekeza komanso imakhala ndi ma frequency amodzi. Ndi masamu opindika omwe amatanthauzidwa ndi trigonometric sine ntchito, ndipo nthawi zambiri amaimiridwa ndi graph. Mafunde a Sine amapezeka m'magawo ambiri a masamu, physics, engineering, and signal processing.
Kuchuluka kwa mafunde a sine ndi kuchuluka kwa ma oscillation kapena mikombero yomwe imachitika munthawi yoperekedwa, ndipo imatanthauzidwa ndi chilembo chachi Greek ω (omega). Mafupipafupi a angular ndi kuchuluka kwa kusintha kwa mkangano wa ntchito, ndipo amayesedwa mu mayunitsi a ma radian pa sekondi iliyonse. Mawonekedwe osagwirizana ndi mafunde amatha kuwoneka atasinthidwa nthawi, ndikusintha kwa φ (phi) mumasekondi. Mtengo wolakwika umayimira kuchedwa, pomwe mtengo wabwino umayimira kutsogola mumasekondi. Kuchuluka kwa ma wave wave kumayesedwa mu hertz (Hz).
Sine wave nthawi zambiri imagwiritsidwa ntchito pofotokoza mafunde a phokoso, monga momwe amafotokozera ndi ntchito ya sine. Mwachitsanzo, f = 1/T, pamene T ndi nthawi ya oscillation, ndi f ndi pafupipafupi oscillation. Izi ndizofanana ndi dongosolo losasunthika la masika mu mgwirizano.
Sine wave ndi yofunika mu fizikisi chifukwa imasunga mawonekedwe ake a mafunde ikawonjezeredwa ku sine wave ya ma frequency omwewo komanso gawo losagwirizana ndi kukula kwake. Katunduyu wokhala ndi nthawi ndi chinthu chomwe chimatsogolera kukufunika kwake pakuwunika kwa Fourier, zomwe zimapangitsa kuti zikhale zapadera.
Pamene mafunde akufalikira mumlengalenga, kusintha kwa malo x kumayimira malo mu gawo limodzi. Mafundewa ali ndi chizindikiro k, chotchedwa nambala yoweyula, yomwe imayimira kufanana pakati pa ma frequency aang'ono ω ndi liwiro la mzere wa kufalitsa ν. Nambala ya mafunde k imagwirizana ndi ma frequency aang'ono ω ndi kutalika kwa mawonekedwe λ (lambda) ndi equation λ = 2π/k. Kuthamanga kwa f ndi liwiro la mzere v kumalumikizidwa ndi equation v = λf.
Equation ya sine wave mu gawo limodzi imaperekedwa ndi y = A sin(ωt + φ), pomwe A ndi matalikidwe, ω ndi ma frequency aang'ono, t ndi nthawi, ndipo φ ndiye kusintha kwa gawo. Equation iyi imapereka kusuntha kwa mafunde pamalo opatsidwa x ndi nthawi t. Chitsanzo cha mzere umodzi chimaganiziridwa, chokhala ndi mtengo wa y = A tchimo(ωt + φ) pa onse x.
M'malo osiyanasiyana, equation ya mafunde a ndege yoyenda imaperekedwa ndi y = A sin(kx - ωt + φ). Equation iyi imatha kutanthauziridwa ngati ma vector awiri mundege yovuta, ndipo chotuluka cha ma vekta awiriwo ndichopanga madontho.
Mafunde ovuta, monga mafunde amadzi m'dziwe pamene mwala wagwetsedwa, amafuna ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mafunde okhala ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la π/2 ma radian kumapatsa cosine wave kuyambika, ndipo akuti amatsogolera mafunde a sine. Izi zikutanthawuza kuti mafunde a sine amachotsa cosine wave. Mawu akuti sinusoidal nthawi zambiri amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine, okhala ndi kapena opanda gawo.
Kuwonetsa mafunde a cosine, ubale wofunikira pakati pa mafunde a sine ndi mafunde a cosine ukhoza kuwonedwa ndi mtundu wa 3D wovuta wa ndege. Chitsanzochi ndi chothandiza pomasulira mafunde omwe amapezeka m'chilengedwe, kuphatikizapo mafunde amphepo, mafunde a phokoso, ndi mafunde a kuwala.
Khutu la munthu limatha kuzindikira mafunde amtundu umodzi, kumveka bwino komanso koyera. Mafunde a Sine nthawi zambiri amagwiritsidwa ntchito ngati ma toni amtundu umodzi, komanso ma harmonics. Khutu la munthu limamva phokoso ngati kuphatikiza kwa mafunde a sine, ndi kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira omwe amachititsa kusintha kwa timbre. Ichi ndichifukwa chake cholembera chanyimbo chokhala ndi ma frequency omwewo chimaseweredwa pazida zosiyanasiyana chimamveka mosiyana.
Kuwomba m'manja, komabe, kumakhala ndi mafunde aperiodic, omwe sachitika nthawi ndi nthawi komanso osabwerezabwereza. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde a square. Kusanthula kwa Fourier ndi chida champhamvu chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula ziwerengero za mndandanda wanthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina ogawidwa, ndipo amafunikira kusanthula kufalikira kwa mafunde. Mafunde amtundu wina amatha kuyenda mbali ziwiri mumlengalenga, ndipo amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana koma akuyenda mosiyanasiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Zimenezi n’zofanana ndi kapepala kamene kamakokedwa pa chingwe, pamene mafunde amaonekera kumapeto kwa chingwecho. Mafunde oyimirira amapezeka pama frequency ena, omwe amatchedwa ma frequency a resonant. Ma frequency awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Mafupipafupi omveka a chingwe amafanana ndi kutalika kwa chingwe, ndipo amasiyana mosiyana ndi kulemera kwa unit kutalika kwa chingwe.
Kodi Phase Imakhudza Bwanji Sine Wave?
Sine wave ndi mtundu wa mawonekedwe osalekeza omwe amadziwika ndi kusinthasintha kosalala, kobwerezabwereza. Ndi njira ya masamu yomwe imatanthauzidwa ndi ntchito ya trigonometric ndipo imagwiritsidwa ntchito mu masamu, physics, engineering, ndi minda yopangira zizindikiro. Ma frequency wamba a sine wave ndi kuchuluka kwa ma oscillation kapena ma cycle omwe amapezeka mu nthawi yoperekedwa, nthawi zambiri amayezedwa masekondi. Mafupipafupi a angular, otchulidwa ndi ω, ndi mlingo wa kusintha kwa mtsutso wa ntchito, nthawi zambiri umayesedwa mu ma radian. Mawonekedwe osakhala amtundu wonse amawoneka atasinthidwa nthawi ndi kuchuluka kwa φ, kuyeza mumasekondi. Chigawo cha ma frequency ndi hertz (Hz), womwe ndi wofanana ndi kutsika kumodzi pamphindikati.
Sine wave imagwiritsidwa ntchito pofotokoza mafunde a phokoso, ndipo imafotokozedwa ndi ntchito ya sine, f (t) = A tchimo (ωt + φ). Mtundu uwu wa mawonekedwe amawonekeranso mu dongosolo losasunthika la masika pamlingo wofanana. Mafunde a Sine ndi ofunikira mufizikiki chifukwa amasunga mawonekedwe awo akaphatikizidwa pamodzi, yomwe ndi chinthu chodziwika kuti superposition principle. Katunduyu amatsogolera kufunikira kwa kusanthula kwa Fourier, komwe kumapangitsa kuti athe kusiyanitsa momveka bwino mawu amodzi ndi ena.
Mu gawo limodzi, funde la sine likhoza kuimiridwa ndi mzere umodzi. Mwachitsanzo, mtengo wa mafunde pa waya ukhoza kuimiridwa ndi mzere umodzi. Kwa miyeso yambiri ya malo, equation yowonjezereka imafunika. Equation iyi imalongosola kusuntha kwa mafunde pamalo enaake, x, panthawi inayake, t.
Mafunde ovuta, monga mafunde amadzi mu dziwe pambuyo pogwetsa mwala, amafuna ma equation ovuta kwambiri. Mawu akuti sinusoid amagwiritsidwa ntchito kutanthauza mawonekedwe a waveform okhala ndi mawonekedwe a sine wave ndi cosine wave. Kusintha kwa gawo la ma radian π/2 ndikofanana ndi chiyambi cha mutu, ndipo ndi chimodzimodzi kunena kuti ntchito ya cosine imatsogolera ntchito ya sine, kapena kuti sine imalepheretsa cosine. Mawu akuti sinusoidal amagwiritsidwa ntchito kutanthauza mafunde onse a sine ndi mafunde a cosine okhala ndi gawo lochotsera.
Kuwonetsa mafunde a cosine, ubale wofunikira pakati pa mafunde a sine ndi mafunde a cosine ukhoza kuwonedwa pogwiritsa ntchito bwalo mumtundu wa 3D wovuta wa ndege. Izi ndizothandiza pakumasulira pakati pa madera osiyanasiyana, monga momwe mafunde amachitikira m'chilengedwe, kuphatikiza mafunde amphepo, mafunde amawu, ndi mafunde opepuka.
Khutu la munthu limatha kuzindikira mafunde amtundu umodzi kuti amamveka bwino, ndipo mafunde a sine nthawi zambiri amagwiritsidwa ntchito kuyimira ma frequency ndi ma harmonics amodzi. Mafunde osiyanasiyana akaphatikizidwa palimodzi, mawonekedwe ake amasintha, omwe amasintha kamvekedwe ka mawu. Kukhalapo kwa ma harmonics apamwamba kuwonjezera pa ma frequency ofunikira kumayambitsa kusiyanasiyana kwa timbre. Ichi ndichifukwa chake nyimbo yoyimba pazida zosiyanasiyana imamveka mosiyana.
Phokoso la kuwomba m'manja lili ndi mafunde aperiodic, omwe sachitika nthawi ndi nthawi, mosiyana ndi mafunde a sine, omwe amakhala nthawi ndi nthawi. Katswiri wa masamu wa ku France Joseph Fourier anapeza kuti mafunde a sinusoidal ndi njira zosavuta zomangira zomwe zingagwiritsidwe ntchito kufotokoza ndi kuyerekezera mafunde a nthawi ndi nthawi, kuphatikizapo mafunde a square. Kusanthula kwa Fourier ndi chida champhamvu chowunikira chomwe chimagwiritsidwa ntchito pofufuza mafunde, monga kutentha kwa kutentha, ndipo chimagwiritsidwa ntchito mobwerezabwereza pokonza ma siginecha ndi kusanthula ziwerengero za nthawi.
Mafunde a Sine amatha kufalikira posintha mawonekedwe kudzera pamakina ogawa. Kusanthula kufalikira kwa mafunde, mafunde a sine omwe amayenda mbali zosiyanasiyana mumlengalenga amaimiridwa ndi mafunde okhala ndi matalikidwe ndi ma frequency ofanana, koma akuyenda mbali zosiyana. Mafundewa akamakula, mafunde oyimirira amapangidwa. Ichi ndi chitsanzo chomwe chimapangidwa pamene cholemba chikokedwa pa chingwe. Mafunde osokoneza omwe amawonekera kuchokera kumalekezero okhazikika a chingwecho amapanga mafunde oima omwe amapezeka pamayendedwe ena, omwe amatchedwa ma frequency a resonant. Ma frequency omveka awa amapangidwa ndi ma frequency ofunikira komanso ma harmonics apamwamba. Maulendo omveka a chingwe amafanana ndi utali wa chingwecho ndipo amafanana mosiyana ndi muzu wa sikweya wa unyinji pa utali wagawo la chingwecho.
Kodi Gawo Lingagwiritsidwe Ntchito Motani Kupanga Ma Waveform Osiyanasiyana?
Mafunde a Sine ndi mtundu wa mawonekedwe osalekeza omwe ndi osalala komanso obwerezabwereza, ndipo angagwiritsidwe ntchito kufotokoza zochitika zosiyanasiyana mu masamu, physics, engineering, ndi processing signal. Amatanthauzidwa ndi ntchito ya trigonometric, ndipo amatha kujambulidwa ngati njira yosalala, yopindika. Kuchuluka kwa mafunde a sine ndi kuchuluka kwa ma oscillation kapena mikombero yomwe imachitika munthawi yoperekedwa, yomwe nthawi zambiri imayesedwa mu Hertz (Hz). Mafupipafupi a angular, ω, ndi mlingo umene mtsutso wa ntchito umasintha, kuyeza mu ma radian pamphindikati. Sine wave imatha kuwoneka ngati ikusuntha nthawi, ndikusuntha kwa gawo, φ, kuyeza mumasekondi. Nambala yolakwika imayimira kuchedwa, pomwe mtengo wabwino umayimira patsogolo.
Gawo ndi gawo lofunikira la sine wave, ndipo lingagwiritsidwe ntchito kupanga ma waveform osiyanasiyana. Pamene mafunde awiri a sine okhala ndi ma frequency omwewo ndi gawo losagwirizana ndi kukula kwake akuphatikizidwa, mawonekedwe ake obwera ndi mawonekedwe a nthawi ndi nthawi okhala ndi katundu yemweyo. Katunduyu amatsogolera kufunikira kwa kusanthula kwa Fourier, komwe kumapangitsa kuti zitheke kuzindikira ndi kusanthula ma siginecha apadera.
Gawo lingagwiritsidwe ntchito kupanga ma waveform osiyanasiyana m'njira zotsatirazi:
• Mwa kusintha gawo la sine wave, likhoza kupangidwa kuti liyambe pa nthawi yosiyana. Izi zimadziwika ngati kusintha kwa gawo, ndipo zitha kugwiritsidwa ntchito kupanga ma waveform osiyanasiyana.
• Powonjezera mafunde a sine ndi mafupipafupi osiyanasiyana ndi gawo la sine wave yofunikira, mawonekedwe ovuta angapangidwe. Izi zimadziwika kuti harmonic, ndipo zitha kugwiritsidwa ntchito popanga mawu osiyanasiyana.
• Mwa kuphatikiza mafunde a sine ndi ma frequency ndi magawo osiyanasiyana, mawonekedwe oyimirira amatha kupangidwa. Izi zimadziwika ngati ma frequency a resonant, ndipo zitha kugwiritsidwa ntchito popanga mawu osiyanasiyana.
• Mwa kuphatikiza mafunde a sine ndi ma frequency ndi magawo osiyanasiyana, mawonekedwe ovuta angapangidwe. Izi zimadziwika kuti kusanthula kwa Fourier, ndipo zitha kugwiritsidwa ntchito kusanthula kufalikira kwa mafunde.
Pogwiritsa ntchito gawo kuti mupange ma waveform osiyanasiyana, ndizotheka kupanga zomveka zosiyanasiyana ndikusanthula kufalikira kwa mafunde. Ichi ndi chinthu chofunikira kwambiri cha mafunde a sine, ndipo chimagwiritsidwa ntchito m'magawo osiyanasiyana, kuphatikiza ma acoustics, ma sign processing, ndi physics.
Ndani Amagwiritsa Ntchito Sine Waves M'misika?
Monga Investor, ndikutsimikiza kuti mudamvapo za sine mafunde ndi udindo wawo m'misika yazachuma. Munkhaniyi, ndikuwona kuti ma sine mafunde ndi chiyani, momwe angagwiritsire ntchito kulosera, komanso ubale pakati pa mafunde a sine ndi kusanthula kwaukadaulo. Pakutha kwa nkhaniyi, mumvetsetsa bwino momwe mafunde a sine angagwiritsire ntchito phindu lanu m'misika.
Kodi Udindo wa Sine Waves M'misika Yazachuma ndi Chiyani?
Sine mafunde ndi mtundu wa masamu okhotakhota omwe amafotokoza mosalala, mobwerezabwereza oscillation mu mafunde mosalekeza. Amadziwikanso kuti mafunde a sinusoidal ndipo amagwiritsidwa ntchito mu masamu, physics, engineering, ndi magawo opangira ma sign. Mafunde a Sine ndi ofunikira m'misika yazachuma, chifukwa angagwiritsidwe ntchito kulosera ndikusanthula zomwe zikuchitika.
M'misika yazachuma, mafunde a sine amagwiritsidwa ntchito kuzindikira ndi kusanthula zomwe zikuchitika. Zitha kugwiritsidwa ntchito kuzindikira milingo yothandizira ndi kukana, komanso kuzindikira zomwe zingatheke kulowa ndi kutuluka. Mafunde a Sine angagwiritsidwenso ntchito kuzindikira ndi kusanthula machitidwe, monga mutu ndi mapewa, nsonga ziwiri ndi zapansi, ndi ma chart ena.
Mafunde a Sine amagwiritsidwanso ntchito pakuwunika kwaukadaulo. Kusanthula kwaukadaulo ndikusanthula kwamayendedwe amitengo ndi machitidwe m'misika yazachuma. Akatswiri aukadaulo amagwiritsa ntchito mafunde a sine kuti azindikire zomwe zikuchitika, kuthandizira ndi kukana, komanso malo olowera ndi kutuluka. Amagwiritsanso ntchito mafunde a sine kuti azindikire mawonekedwe, monga mutu ndi mapewa, nsonga ziwiri ndi zapansi, ndi ma chart ena.
Sine mafunde angagwiritsidwenso ntchito kulosera. Pofufuza zochitika zam'mbuyo ndi zamakono, akatswiri aukadaulo amatha kuneneratu za mayendedwe amitengo yamtsogolo. Pofufuza mafunde a sine, amatha kuzindikira malo omwe angathe kulowa ndi kutuluka, komanso kuthandizira ndi kukana.
Sine mafunde ndi chida chofunikira kwa akatswiri akatswiri pa misika zachuma. Zitha kugwiritsidwa ntchito kuzindikira ndi kusanthula zomwe zikuchitika, milingo yothandizira ndi kukana, komanso malo olowera ndi kutuluka. Angagwiritsidwenso ntchito kulosera za kayendetsedwe ka mitengo yamtsogolo. Mwa kusanthula mafunde a sine, akatswiri aukadaulo amatha kumvetsetsa bwino misika ndikupanga zisankho zodziwika bwino.
Kodi Mafunde a Sine Angagwiritsidwe Ntchito Motani Kuneneratu?
Mafunde a Sine amagwiritsidwa ntchito m'misika yazachuma kusanthula zomwe zikuchitika ndikulosera. Ndi mtundu wa mawonekedwe ozungulira omwe amazungulira pakati pa mfundo ziwiri, ndipo angagwiritsidwe ntchito kuzindikira machitidwe ndi zomwe zikuchitika m'misika. Mafunde a Sine amagwiritsidwa ntchito pakuwunika kwaukadaulo ndipo angagwiritsidwe ntchito kulosera zamtsogolo zamitengo yamtsogolo.
Nazi njira zina zomwe mafunde a sine angagwiritsire ntchito m'misika:
• Kuzindikiritsa milingo yothandizira ndi kukana: Mafunde a Sine angagwiritsidwe ntchito pozindikira kuchuluka kwa chithandizo ndi kukana m'misika. Poyang'ana nsonga ndi nsonga za sine wave, amalonda amatha kuzindikira malo omwe mtengo ungapeze chithandizo kapena kukana.
• Kuzindikiritsa kusintha kwazomwe zikuchitika: Poyang'ana pa sine wave, amalonda amatha kuzindikira zomwe zingasinthidwe. Ngati sine wave ikuwonetsa kutsika, amalonda amatha kuyang'ana madera omwe angathandizidwe komwe kungasinthe.
• Kuzindikiritsa mitengo yamitengo: Mafunde a Sine angagwiritsidwe ntchito kuzindikira mitengo yamitengo m'misika. Poyang'ana pa sine wave, amalonda amatha kuzindikira madera omwe angathe kuthandizidwa ndi kukana, komanso zomwe zingatheke kusintha.
• Kuneneratu: Poyang'ana pa sine wave, amalonda akhoza kulosera za kayendetsedwe ka mitengo yamtsogolo. Poyang'ana nsonga ndi nsonga za sine wave, amalonda amatha kuzindikira madera omwe angathe kuthandizidwa ndi kukana, komanso zomwe zingatheke kusintha.
Mafunde a Sine angakhale chida chothandiza kwa amalonda omwe akuyang'ana kuti azilosera m'misika. Poyang'ana pa sine wave, amalonda amatha kuzindikira madera omwe angathe kuthandizidwa ndi kukana, komanso zomwe zingatheke kusintha. Pogwiritsa ntchito mafunde a sine, amalonda amatha kupanga zisankho zodziwika bwino pazamalonda awo ndikuwonjezera mwayi wawo wopambana.
Kodi Ubale Pakati pa Sine Waves ndi Technical Analysis ndi Chiyani?
Mafunde a Sine amagwiritsidwa ntchito m'misika yazachuma kuwunika momwe mitengo imayendera komanso kulosera zakuyenda kwamitengo yamtsogolo. Amagwiritsidwa ntchito ndi akatswiri ofufuza zaumisiri kuti azindikire zomwe zikuchitika, kuthandizira ndi kukana, komanso kuzindikira zomwe zingatheke kulowa ndi kutuluka.
Mafunde a Sine ndi mtundu wa mawonekedwe a nthawi ndi nthawi, kutanthauza kuti amabwereza pakapita nthawi. Amadziwika ndi kugwedezeka kwawo kosalala, kobwerezabwereza ndipo amagwiritsidwa ntchito kufotokoza zochitika zosiyanasiyana mu masamu, physics, engineering, ndi processing processing. M'misika yazachuma, mafunde a sine amagwiritsidwa ntchito kuzindikira machitidwe obwereza mayendedwe amitengo.
Ubale pakati pa mafunde a sine ndi kusanthula kwaukadaulo ndikuti mafunde a sine atha kugwiritsidwa ntchito kuzindikira machitidwe obwereza mayendedwe amitengo. Akatswiri aukadaulo amagwiritsa ntchito mafunde a sine kuti azindikire zomwe zikuchitika, kuthandizira ndi kukana, ndikuzindikira malo omwe angathe kulowa ndi kutuluka.
Sine mafunde angagwiritsidwenso ntchito kulosera za kayendedwe ka mitengo yamtsogolo. Powunika machitidwe am'mbuyomu amitengo, akatswiri aukadaulo amatha kuzindikira machitidwe obwerezabwereza ndikugwiritsa ntchito machitidwewa kuti adzineneratu zakuyenda kwamitengo yamtsogolo.
Sine mafunde amagwiritsidwanso ntchito kuzindikira kuzungulira m'misika. Powunika momwe mitengo imayendera pakapita nthawi, akatswiri aukadaulo amatha kuzindikira maulendo obwerezabwereza ndikugwiritsa ntchito mizunguliroyi kuti azilosera za mayendedwe amtsogolo amitengo.
Mwachidule, mafunde a sine amagwiritsidwa ntchito m'misika yazachuma kuwunika momwe mitengo ikuyendera komanso kulosera zakuyenda kwamitengo yamtsogolo. Amagwiritsidwa ntchito ndi akatswiri ofufuza zaumisiri kuti azindikire zomwe zikuchitika, kuthandizira ndi kukana, komanso kuzindikira zomwe zingatheke kulowa ndi kutuluka. Sine mafunde atha kugwiritsidwanso ntchito kulosera za mayendedwe amitengo m'tsogolo posanthula machitidwe am'mbuyomu amitengo ndikuzindikira momwe mitengo imabwerezedwa.
kusiyana
Sine wave vs simulated sine wave
Sine Wave vs Simulated Sine Wave:
• Sine wave ndi mawonekedwe osalekeza omwe amatsatira njira ya sinusoidal ndipo amagwiritsidwa ntchito mu masamu, physics, engineering, ndi processing processing.
• Simulated sine wave ndi mawonekedwe opangira mafunde opangidwa ndi makina osinthira mphamvu kuti ayesere mawonekedwe a sine wave.
• Sine mafunde amakhala ndi ma frequency ndi gawo limodzi, pomwe mafunde a sine opangidwa amakhala ndi ma frequency angapo ndi magawo.
• Mafunde a sine amagwiritsidwa ntchito kuimira mafunde a phokoso ndi mitundu ina ya mphamvu, pamene mafunde amtundu wa sine amagwiritsidwa ntchito popanga zipangizo zamagetsi.
• Mafunde a sine amapangidwa ndi magwero achilengedwe, pamene mafunde a sine opangidwa ndi magetsi amapangidwa ndi magetsi.
• Sine mafunde amagwiritsidwa ntchito pounika Fourier pophunzira kachulukidwe ka mafunde, pomwe mafunde oyeserera amagwiritsidwa ntchito kupatsa mphamvu zamagetsi.
• Mafunde a sine amagwiritsidwa ntchito kuimira mafunde a phokoso, pamene mafunde amtundu wa sine amagwiritsidwa ntchito popangira magetsi.
FAQ za sine wave
Kodi thambo ndi mafunde amphamvu?
Ayi, thambo si mafunde amphamvu. Sine wave ndi masamu opindika omwe amafotokoza kusinthasintha kosalala, kobwerezabwereza, ndipo ndi mawonekedwe osalekeza okhala ndi ma frequency amodzi. Chilengedwe, komabe, ndi dongosolo lovuta komanso lamphamvu lomwe limasintha nthawi zonse ndikusintha.
Chilengedwe chili ndi zigawo zosiyanasiyana, kuphatikizapo zinthu, mphamvu, ndi nthawi ya mlengalenga. Zigawozi zimagwirizana wina ndi mzake m'njira zosiyanasiyana, zomwe zimapangitsa kuti pakhale zochitika zosiyanasiyana, kuyambira kupangidwa kwa milalang'amba mpaka kusinthika kwa moyo. Chilengedwe chimayang'aniridwanso ndi malamulo a physics, ozikidwa pa masamu a masamu.
Chilengedwe si mafunde a sine, koma chili ndi mafunde ambiri. Mwachitsanzo, mafunde a mawu ndi mafunde a sine, ndipo amapezeka m’chilengedwe chonse. Mafunde a kuwala nawonso ndi mafunde a sine, ndipo amapezeka m’chilengedwe chonse. Kuphatikiza apo, chilengedwe chili ndi mafunde amitundu yambiri, monga mafunde a electromagnetic, mafunde amphamvu yokoka, ndi mafunde a quantum.
Chilengedwecho chimapangidwanso ndi tinthu tambirimbiri tosiyanasiyana, monga mapulotoni, manyutroni, ndi ma electron. Tinthu tating'onoting'ono timeneti timalumikizana m'njira zosiyanasiyana, zomwe zimapangitsa kuti pakhale zochitika zosiyanasiyana, kuyambira kupangidwa kwa maatomu mpaka kusinthika kwa nyenyezi.
Pomaliza, thambo si mafunde a sine, koma lili ndi mafunde ambiri. Mafunde a sinewa amapezeka ngati mafunde a phokoso, mafunde a kuwala, ndi mitundu ina ya mafunde. Chilengedwecho chimapangidwanso ndi tinthu tambirimbiri tosiyanasiyana tomwe timalumikizana m’njira zosiyanasiyana, zomwe zimapangitsa kuti pakhale zochitika zosiyanasiyana.
Ubale wofunikira
Matalikidwe:
• Matalikidwe ndi kusuntha kwakukulu kwa mafunde a sine kuchoka pamalo ake ofanana.
• Imayesedwa ndi mayunitsi a mtunda, monga mamita kapena mapazi.
• Zimagwirizananso ndi mphamvu ya mafunde, ndi ma amplitudes apamwamba omwe ali ndi mphamvu zambiri.
• Kukula kwa sine wave ndi kolingana ndi muzu wa sikweya wa ma frequency ake.
• Kukula kwa mafunde a sine kumagwirizananso ndi gawo lake, ndi ma amplitudes apamwamba omwe ali ndi kusintha kwakukulu kwa gawo.
Kawirikawiri Yankho:
• Kuyankha pafupipafupi ndi muyeso wa momwe makina amayankhira ku ma frequency osiyanasiyana olowetsa.
• Nthawi zambiri amayezedwa mu ma decibel (dB) ndipo ndi muyeso wa kupindula kapena kuchepetsedwa kwa dongosolo pa ma frequency osiyanasiyana.
• Kuyankha pafupipafupi kwa sine wave kumatsimikiziridwa ndi matalikidwe ake ndi gawo.
• Sine wave yokhala ndi matalikidwe apamwamba adzakhala ndi mayankho pafupipafupi kuposa omwe ali ndi matalikidwe otsika.
• Kuyankha kwafupipafupi kwa mafunde a sine kumakhudzidwanso ndi gawo lake, ndi magawo apamwamba omwe amachititsa kuyankha kwafupipafupi.
Sawtooth:
• Mawonekedwe a sawtooth ndi mtundu wa mawonekedwe a nthawi ndi nthawi omwe amakwera kwambiri komanso kugwa pang'onopang'ono.
• Nthawi zambiri amagwiritsidwa ntchito mu kaphatikizidwe zomvetsera ndipo amagwiritsidwanso ntchito mu mitundu ina ya digito chizindikiro processing.
• Chiwombankhanga cha sawtooth chimafanana ndi chiwombankhanga cha sine chifukwa ndi mawonekedwe a nthawi, koma ali ndi mawonekedwe osiyana.
• Mphuno ya sawtooth imakhala ndi kukwera kwakukulu ndi kugwa pang'onopang'ono, pamene mafunde a sine akukwera pang'onopang'ono ndi kugwa pang'onopang'ono.
• Mawonekedwe a sawtooth amakhala ndi ma frequency apamwamba kuposa ma sine wave, ndipo nthawi zambiri amagwiritsidwa ntchito popanga ma audio kuti apange phokoso laukali.
• Kuthamanga kwa ma sawtooth kumagwiritsidwanso ntchito mu mitundu ina ya makina a digito, monga kusinthasintha kwafupipafupi ndi kusintha kwa gawo.
Kutsiliza
Mafunde a Sine ndi gawo lofunikira pazasayansi, masamu, uinjiniya, kukonza ma sign, ndi zina zambiri. Ndiwo mtundu wa mafunde osalekeza omwe ali ndi phokoso losalala, lobwerezabwereza, ndipo nthawi zambiri amagwiritsidwa ntchito pofotokoza mafunde a phokoso, mafunde a kuwala, ndi zina. Mafunde a Sine ndi ofunikiranso pakuwunika kwa Fourier, zomwe zimawapangitsa kukhala apadera kwambiri komanso kuwalola kuti agwiritsidwe ntchito pazosintha zapamalo. Kumvetsetsa mafunde a sine kungatithandize kumvetsetsa bwino kufalikira kwa mafunde, kukonza ma siginecha, ndi kusanthula kwanthawi.
Ndine Joost Nusselder, woyambitsa Neaera komanso wotsatsa malonda, abambo, ndipo ndimakonda kuyesa zida zatsopano ndi gitala pamtima pa zomwe ndimakonda, ndipo pamodzi ndi gulu langa, ndakhala ndikupanga zolemba zakuya zamabulogu kuyambira 2020. kuthandiza owerenga okhulupirika ndi maupangiri ojambulira ndi gitala.
