A sine wave inoenderera mberi inodzokorora yega 2π radians, kana 360 madhigirii, uye inogona kushandiswa kuenzanisira akawanda echisikigo zviitiko. Iyo sine wave inozivikanwawo se sinusoid.
Izwi rekuti sine wave rinotorwa kubva kune mathematical function sine, inova hwaro hweiyo waveform. Iyo sine wave ndeimwe yemafungu akareruka uye anoshandiswa zvakanyanya muminda yakawanda.
Muchikamu chino, ini ndichatsanangura chinonzi sine wave uye nei ine simba zvakadaro.
Chii chinonzi sine wave?
A sine Wave inotsvedzerera, inodzokorodza oscillation muchimiro cheinoenderera mberi. Iro curve yemasvomhu inotsanangurwa maererano nesine trigonometric basa, uye inomiririrwa zvine mucherechedzo senge waveform. Iyo imhando yekuenderera mberi kwemafungu inoratidzirwa nekutsetseka, nguva nenguva, uye inowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa.
The maitikiro ye sine wave inhamba yekutenderera kana kutenderera kunoitika muhuwandu hwenguva. Angular frequency, inotaridzwa ne ω, chiyero cheshanduko yenharo yebasa, uye inoyerwa muzvikamu zve radians pasekondi. Kukosha kusiri zero kwechikamu chekuchinja, kunoratidzwa ne φ, kunomiririra shanduko mune yese waveform munguva, ine kukosha kwakashata kunomiririra kunonoka, uye kukosha kwakanaka kunomiririra kumberi mumasekondi. Kuwanda kwe sine wave kunoyerwa ne hertz (Hz).
Sine wave inoshandiswa kutsanangura mafungu ezwi, uye inotsanangurwa neine basa, f (t) = Chivi (ωt + φ). Inoshandiswawo kutsanangura isina kuvharwa chitubu-misa system mukuenzanisa, uye yakakosha waveform mufizikisi sezvo ichichengetedza chimiro chayo chewave kana yawedzerwa kune imwe sine wave yenguva imwechete uye inopokana chikamu uye ukuru. Ichi chivakwa chinozivikanwa se superposition musimboti, uye inguva yenguva waveform pfuma. Ichi chivakwa chinotungamira mukukosha kweFourier ongororo, sezvo zvichiita kuti zvikwanise kusiyanisa acoustically mutsauko wenzvimbo, x, inomiririra chinzvimbo mune imwe dimment umo masaisai ari kupararira.
Hunhu hwemasaisai hunodaidzwa kuti wave nhamba, k, inova nhamba yeangular wave uye inomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber ine hukama neangular frequency uye wavelength, λ, ne equation λ = 2π/k. Equation ye sine wave mune imwe dimension inopiwa na y = A chivi (ωt + φ). Imwe equation yakawanda inopiwa ne y = Chivi (kx - ωt + φ), iyo inopa kubviswa kwemafungu panzvimbo x panguva t.
Sine masaisai anogona zvakare kumiririrwa mune akawanda spatial dimensions. Equation yemafungu endege inofamba inopiwa na y = A sin (kx – ωt + φ). Izvi zvinogona kududzirwa sechigadzirwa chedoti chemavekita maviri, uye chinoshandiswa kutsanangura masaisai akaomarara, senge mafungu emvura mudziva kana dombo radonha. Mamwe maequation akaomarara anodiwa kutsanangura izwi rekuti sinusoid, iro rinotsanangura mafungu ezvese sine uye mafungu ecosine ane chikamu chekuchinja che π/2 radians, izvo zvinopa iyo cosine wave musoro kutanga pamusoro pe sine wave. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese sine uye cosine masaisai ane phase offset.
Masaisai eSine anowanikwa mune zvakasikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine imwe seinonzwika zvakajeka, uye sine mafungu anoshandiswa kumiririra imwechete frequency uye harmonics. Nzeve yemunhu inoona ruzha semusanganiswa wemasaisai ane akasiyana amplitudes uye ma frequency, uye kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kunokonzera mutsauko mutimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chine frequency yakafanana inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana.
Ruzha rwekuombera ruoko rune mafungu eaperiodic, ayo asingadzokorore muchimiro, uye haateveri sine wave pattern. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo matombo ekuvaka ari nyore kutsanangura uye kufungidzira chero mapedhi epanguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana. Sine mafungu anoshandiswa kuparadzira uye kushandura fomu mune akagoverwa mutsara masisitimu.
Ndeipi nhoroondo yemafungu e sine?
Iyo sine wave ine nhoroondo refu uye inonakidza. Yakatanga kuwanikwa nenyanzvi yemasvomhu yekuFrance Joseph Fourier muna 1822, uyo akaratidza kuti chero nguva yenguva yaigona kumiririrwa sehuwandu hwemasaisai. Kuwanikwa uku kwakashandura ndima yemasvomhu nefizikisi uye yakashandiswa kubvira ipapo.
• Basa raFourier rakasimudzirwazve nenyanzvi yemasvomhu yekuGermany Carl Friedrich Gauss muna 1833, uyo akaratidza kuti masaisai esine aigona kushandiswa kumirira chero nguva yenguva.
• Mukupera kwezana remakore rechi19, sine wave yakashandiswa kurondedzera maitiro emagetsi emagetsi.
• Mukutanga kwezana remakore rechi20, sine wave yakashandiswa kurondedzera maitiro emafungu ekurira.
• Mumakore ekuma1950, sine wave yakashandiswa kutsanangura maitiro emafungu echiedza.
• Mumakore ekuma1960, sine wave yakashandiswa kutsanangura maitiro emafungu eredhiyo.
• Mumakore ekuma1970, iyo sine wave yakashandiswa kutsanangura maitiro ezviratidzo zvedhijitari.
• Mumakore ekuma1980, iyo sine wave yakashandiswa kutsanangura maitiro emagetsi emagetsi.
• Mumakore ekuma1990, iyo sine wave yakashandiswa kurondedzera maitiro e quantum mechanical systems.
• Nhasi, iyo sine wave inoshandiswa mumhando dzakasiyana-siyana, kusanganisira masvomhu, physics, engineering, signal processing, nezvimwe. Icho chishandiso chakakosha chekunzwisisa maitiro emasaisai uye chinoshandiswa mune dzakasiyana siyana maapplication, kubva kuodhiyo uye vhidhiyo kugadzirisa kune yekurapa imaging uye marobhoti.
Sine Wave Mathematics
Ini ndichave ndichitaura nezve sine mafungu, masvomhu curve inotsanangura yakatsetseka, inodzokorodza oscillation. Tichatarisa kuti sine mafungu anotsanangurwa sei, hukama pakati peangular frequency uye wave nhamba, uye chii chinonzi Fourier ongororo. Isu tichaongorora zvakare kuti sine mafungu anoshandiswa sei mufizikisi, engineering, uye chiratidzo chekugadzirisa.
Chii chinonzi Sine Wave?
A sine wave iderere, inodzokorodza oscillation inoumba mafungu anoenderera. Iro curve yemasvomhu, inotsanangurwa netrigonometric sine basa, uye inowanzoonekwa mumagirafu nemasaisai. Iyo imhando yeinoenderera mberi wave, zvichireva kuti yakatsetseka, periodic basa rinoitika mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda.
Sine wave ine yakajairika frequency, inova nhamba yekutenderera kana kutenderera kunoitika mune yakapihwa huwandu hwenguva. Izvi zvinomiririrwa neangular frequency, ω, iyo yakaenzana ne 2πf, apo f iri frequency mu hertz (Hz). A sine wave inogonawo kuchinjwa nekufamba kwenguva, ine kukosha kwakashata kunomiririra kunonoka uye kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine wave inowanzo shandiswa kutsanangura mawiji eruzha, sekutsanangurwa kwaanoitwa nebasa resine. Inoshandiswawo kumiririra isina undamped spring-mass system pakuenzanisa. Iyo sine wave ipfungwa yakakosha mufizikisi, sezvo ichichengeta wave wave chimiro kana yawedzerwa kune imwe sine wave yeiyo frequency yakafanana uye inopokana chikamu uye ukuru. Ichi chivakwa, chinozivikanwa semusimboti wepamusoro, ndicho chinotungamira mukukosha kwekuongorora kweFourier, sezvo zvichiita kuti zvikwanise kusiyanisa zvine mutsindo pakati pezvakasiyana-siyana.
Equation ye sine wave mune imwe dimension inopiwa ne y = A chivi (ωt + φ), apo A ndiyo amplitude, ω ndiyo inotenderera, t inguva, uye φ ndiyo chikamu chekuchinja. Kune muenzaniso wemutsara mumwechete, kana kukosha kwesaisai kuchionekwa sewaya, ipapo equation ye sine wave mune maviri spatial dimensions inopiwa ne y = A sin (kx - ωt + φ), apo k is wave. nhamba. Izvi zvinogona kududzirwa sechigadzirwa chemavekita maviri, doti chigadzirwa.
Masaisai akaomarara, seaya akagadzirwa kana dombo radonhedzwa mudziva, anoda mamwe maequation akaomarara. Izwi rokuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwezvose sine wave uye cosine wave. A phase shift of π/2 radians, kana kutanga musoro, inonzi inopa cosine wave, inotungamira sine wave. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa.
Kuenzanisira cosine wave kunogona kubatsira kuratidza hukama hwakakosha pakati pedenderedzwa uye 3D yakaoma ndege modhi, iyo inogona kubatsira kuona kukosha kwemasaisai esine mukududzira pakati pemadomasi. Iyi wave wave inoitika mumasikirwo, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona imwe sine mafungu seanonzwika zvakajeka, uye sine wave inomiririra yeimwe frequency harmonics inonzwisisika zvakare.
Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency ndiko kunokonzera kusiyanisa kwetimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana.
Nzeve yemunhu inonzwa senge nguva nenguva uye aperiodic. Ruzha rweperiodic runoumbwa neine mafungu, nepo aperiodic ruzha runoonekwa seruzha. Noise inoratidzwa seaperiodic, sezvo iine maitiro asina kudzokorora.
Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo matombo ekuvaka ari nyore kutsanangura uye kufungidzira chero mapedhi epanguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa uye kugadzirisa zviratidzo, uye kuongorora kwenhamba yenguva dzakatevedzana. Sine mafungu anogona zvakare kupararira kuburikidza nekuchinja mafomu mune akagoverwa mutsara masisitimu.
Masaisai eSine anofamba akapesana muchadenga anomiririrwa nemasaisai ane maamplitude uye frequency yakafanana. Kana masaisai aya akakwidibira, patani yemasaisai inogadzirwa inogadzirwa, sezvinoonekwa kana noti yadhonzwa patambo. Masaisai anopindira anoratidzwa kubva kumagumo etambo anogadzira masaisai akamira, anoitika pane mamwe ma frequency anozivikanwa se resonant frequencies. Izvi zvinoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo maresonant frequencies etambo anoenzana nehurefu hwayo, uye akapesana akaenzana nehuremu pahurefu hweyuniti yetambo.
Sine Wave Inotsanangurwa Sei?
A sine wave inotsvedzerera, inodzokorodza oscillation yeinoenderera mberi waveform. Inotsanangurwa masvomhu sechinhu chetrigonometric, uye ine graphed se sinusoid. Iyo sine wave ipfungwa yakakosha mufizikisi, sezvo ichichengeta wave wave chimiro kana ichiwedzerwa kune mamwe sine mafungu eiyo yakafanana frequency uye yekupokana chikamu ukuru. Iyi pfuma inozivikanwa semusimboti wepamusoro, uye inotungamira mukukosha kwayo mukuongorora kweFourier.
Sine masaisai anowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, mainjiniya, uye masaini kugadzirisa. Ivo vanozivikanwa nekuwanda kwavo, nhamba ye oscillations kana ma cycle anoitika mune imwe nguva. Angular frequency, ω, chiyero cheshanduko yenharo yebasa mumaradians pasekondi. A non-zero value ye φ, the phase shift, inomiririra kushanduka kwese waveform munguva, ine kukosha kwakashata kunomiririra kunonoka, uye kukosha kwakanaka kunomiririra mberi mumasekondi.
Muruzha, sine wave inotsanangurwa neiyo equation f = ω/2π, apo f ndiyo frequency yeascillations, uye ω ndiyo inotenderera frequency. Iyi equation inoshandawo kune isina kuvharwa chitubu-mass system muequilibrium. Sine mafungu akakosha zvakare mune acoustics, sezvo ari iwo ega waveform anonzwisiswa seamwe frequency nenzeve yemunhu. Imwe sine wave inoumbwa neiyo yakakosha frequency uye yakakwirira harmonics, ayo ese anonzwisiswa seamwechete noti.
Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency ndiko kunokonzera kusiyanisa kwetimbre. Ichi ndicho chikonzero nei rwiyo rumwe chete rwemimhanzi runoridzwa pazviridzwa zvakasiyana kurira zvakasiyana. Kuombera neruoko, semuenzaniso, kune masaisai eaperiodic, ayo asingadzokorore, kuwedzera kune sine masaisai.
Mukutanga kwezana ramakore rechi 19, nyanzvi yemasvomhu yokuFrance Joseph Fourier akawana kuti masaisai e<em>sinusoidal anogona kushandiswa sezvivharo zvokuvakisa zviri nyore kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekuongorora chinoshandiswa kudzidza masaisai mukuyerera kwekushisa uye kugadzirisa zviratidzo, pamwe nekuongorora kwenhamba yenguva dzakatevedzana.
Sine masaisai anogona kupararira chero divi muchadenga, uye anomiririrwa nemasaisai ane amplitude, frequency, uye achifamba akapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Ichi ndicho chiitiko chimwechete chinoitika kana chinyorwa chikabvutwa patambo, masaisai ari kupindira achiratidzwa pamagumo etambo. Mafungu akamira anoitika pane mamwe mafrequency, anonzi resonant frequencies, ayo anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Mafambiro anoita tambo anoenzana nehurefu hwayo, uye akaenzana neskweya mudzi wehuremu hwayo pahurefu hwayo.
Muchidimbu, izwi rekuti sinusoid rinoshandiswa kutsanangura mafungu maitiro eese uye mafungu ecosine, aine chikamu chekuchinja che π/2 radians, zvichireva kuti cosine wave ine musoro wekutanga uye sine wave inosarira kumashure. Izwi rokuti sinusoidal rinoshandiswa pamwechete kureva zvose sine uye cosine masaisai ane phase offset. Izvi zvinoratidzwa necosine wave mumufananidzo uri pamusoro. Hukama hwakakosha uhu pakati pe sine uye cosine hunogona kuoneswa pachishandiswa 3D yakaoma plane modhi, iyo inotaridzazve kubatsira kwekuturikira pfungwa idzi munzvimbo dzakasiyana siyana. The wave pattern inoitika muzvisikwa, kusanganisira mumhepo, ruzha, uye masaisai akareruka.
Chii chiri Hukama pakati peAngular Frequency uye Wave Number?
Sine wave igoko remasvomhu rinotsanangura kutsetseka, kudzokororwa kutenderera. Iyo inoenderera mberi wave, inozivikanwawo se sinusoidal wave kana sinusoid, uye inotsanangurwa maererano neiyo trigonometric sine basa. Girafu resine wave rinoratidza waveform inotenderera pakati pehukuru uye hushoma kukosha.
Angular frequency, ω, chiyero cheshanduko yenharo yebasa, inoyerwa mumaradians pasekondi. A non-zero value ye φ, the phase shift, inomiririra kuchinja mune yose waveform kana mberi kana kumashure munguva. A negative value inomiririra kunonoka, ukuwo value yakanaka inomiririra kumberi mumasekonzi. Iyo frequency, f, inhamba yekutenderera kana kutenderera kunoitika musekondi imwe, kuyerwa mu hertz (Hz).
Sine wave yakakosha mufizikisi nekuti inochengeta wave wave kana yawedzerwa kune imwe sine wave yenguva imwecheteyo uye inopokana chikamu uye ukuru. Iyi pfuma yeperiodic waveforms inozivikanwa semusimboti wepamusoro uye ndiyo inotungamira mukukosha kwekuongorora kweFourier. Izvi zvinoita kuti ive acoustically yakasarudzika uye ndosaka ichishandiswa mune spatial variable x, inomiririra chinzvimbo mune imwe dimension. Masaisai anopararira aine hunhu parameter, k, inodaidzwa kuti wave nhamba kana angular wave nhamba, inomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber, k, ine hukama neangular frequency, ω, uye wavelength, λ, ne equation λ = 2π/k.
Equation ye sine wave mune imwe dimension inopiwa na y = A chivi (ωt + φ). Equation iyi inopa kusimuka kwe wave pane chero chinzvimbo x chero nguva t. Muenzaniso wemutsara mumwechete unofungidzirwa, uko kukosha kwefungu kunopiwa ne y = A chivi (ωt + φ).
Mumativi maviri kana anopfuura enzvimbo, equation inotsanangura masaisai endege inofamba. Nzvimbo x inopiwa ne x = A chivi (kx - ωt + φ). Iyi equation inogona kududzirwa semavheji maviri, chigadzirwa chacho chiri chigadzirwa chedoti.
Masaisai akaomarara, seaya anogadzirwa kana dombo radonhedzwa mudziva remvura, anoda mamwe maequation akaoma kunzwisisa kuti aatsanangure. Izwi rokuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwezvose sine wave uye cosine wave. A phase shift of π/2 radians (kana 90°) inopa cosine wave kutanga musoro, saka inonzi inotungamira sine wave. Izvi zvinotungamira kuhukama hwakakosha pakati pe sine uye cosine mabasa, ayo anogona kuoneswa sedenderedzwa mune 3D yakaoma ndege modhi.
Kubatsira kweshanduro yeiyi pfungwa kune mamwe matunhu kunoratidzwa nenyaya yekuti masaisai akafanana anoitika mumasikirwo, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona masaisai eine imwe seinonzwika zvakajeka. Sine mafungu anomiririra imwe chete frequency uye harmonics, uye nzeve yemunhu inokwanisa kuburitsa sine mafungu ane inonzwisisika harmonics. Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kunokonzera mutsauko wetimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana.
Ruzha rwekuombera ruoko rune masaisai eaperiodic, asiri enguva nenguva, kana ane maitiro asingadzokorore. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero nguva yemasaisai, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana.
Sine masaisai anogona kupararira mukuchinja fomu kuburikidza neakagoverwa mutsara masisitimu. Izvi zvinodiwa kuti uongorore kupararira kwemafungu muzvikamu zviviri kana kupfuura. Masaisai eSine anofamba akapesana muchadenga anomiririrwa nemasaisai ane maamplitude uye frequency yakafanana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Izvi zvakafanana nezvinoitika kana katsamba kakadonhedzwa patambo; masaisai anopindira anoratidzwa kubva kumagumo etambo, uye masaisai akamira anoitika pane mamwe mafrequency, anonzi maresonant frequencies. Aya ma frequency anoumbwa neakakosha frequency uye yakakwirira harmonics. Mafambiro anoita tambo anoenzana nehurefu hwayo uye anoenzana neskweya mudzi wehuremu hwayo pahurefu hwayo.
Chii chinonzi Fourier Analysis?
A sine wave iderere, inodzokorodza oscillation iyo inotsanangurwa masvomhu semafungu anoramba achienderera. Iyo inozivikanwawo se sinusoidal wave, uye inotsanangurwa neiyo trigonometric sine basa. Girafu ye sine wave yakatsetseka, periodic curve iyo inoshandiswa mumasvomhu, fizikisi, mainjiniya, uye masignal processing fields.
Iyo yakajairika frequency, kana huwandu hwekutenderera kana kutenderera kunoitika mune yakapihwa huwandu hwenguva, inomiririrwa nerechigiriki vara ω (omega). Izvi zvinozivikanwa seangular frequency, uye ndiwo mwero wekuchinja kwegakava rebasa mumayuniti emaradians.
Sine wave inogona kuchinjwa munguva nechikamu chekuchinja, icho chinomiririrwa netsamba yechiGiriki φ (phi). Kosi isina kunaka inomiririra kunonoka, uye kukosha kwakanaka kunomiririra kumberi mumasekonzi. Kuwanda kwe sine wave kunoyerwa ne hertz (Hz).
Sine wave inowanzoshandiswa kurondedzera masaisai eruzha, uye inotsanangurwa nesine basa f(t) = Chivi (ωt + φ). Oscillations yemhando iyi inoonekwa mune isina kuvharwa spring-mass system pakuenzanisa.
Iyo sine wave yakakosha mufizikisi nekuti inochengeta chimiro chayo chewave kana yawedzerwa kune imwe sine wave yenguva imwechete uye inopokana chikamu uye ukuru. Iyi pfuma, inodaidzwa kuti superposition musimboti, ndiyo inotungamira mukukosha kwayo mukuongorora kweFourier. Izvi zvinoita kuti ive acoustically yakasarudzika uye ndosaka ichishandiswa kutsanangura nzvimbo dzakasiyana.
Semuyenzaniso, kana x achimiririra nzvimbo yesaisai iri kupararira, zvino chimiro chechimiro k (nhamba yemasaisai) inomiririra kuenzanisa pakati peangular frequency ω uye kumhanya kwemutsara wekuparadzira ν. Wavenumber k ine hukama neangular frequency ω uye wavelength λ (lambda) neiyo equation k = 2π/λ. Iyo frequency f uye mutsara kumhanya v zvine hukama neiyo equation v = fλ.
Equation ye sine wave mune imwe dimension ndeye y = A chivi (ωt + φ). Iyi equation inogona kuve yakajairwa kune akawanda dimensions, uye kune imwechete mutsara muenzaniso, kukosha kwemafungu pane chero nguva x chero nguva t inopiwa ne y = A chivi (kx - ωt + φ).
Masaisai akaoma kunzwisisa, seaya anoonekwa kana dombo radonhedzwa mudziva, anoda mamwe maequation akaoma kunzwisisa. Izwi rekuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu uhu, uye rinosanganisira sine mafungu uye cosine mafungu ane phase offset.
Kuenzanisira cosine wave, hukama hwakakosha pakati pe sine wave uye cosine wave hwakafanana nehukama huri pakati pedenderedzwa uye 3D yakaoma plane modhi. Izvi zvinobatsira pakuona kubatsira kweshanduro ye sine mafungu pakati penzvimbo dzakasiyana.
The wave pattern inoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inogona kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anowanzo shandiswa kumiririra imwechete frequency uye harmonics.
Nzeve yemunhu inoona ruzha nemusanganiswa wemasaisai esine uye periodic ruzha, uye kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency kunokonzera mutsauko mumutimu. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana.
Kuombera neruoko, zvisinei, kune masaisai eaperiodic, ayo asingadzokorore. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero nguva yemasaisai, kusanganisira masikweya masaisai.
Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa uye kugadzirisa zviratidzo, uye kuongorora kwenhamba yenguva dzakatevedzana. Sine mafungu anogona kupararira pasina kushandura chimiro chavo mune akagoverwa mutsara masisitimu, ndosaka ivo vachidikanwa kuongorora wave kupararira.
Masaisai eSine anofamba akapesana muchadenga anomiririrwa nemasaisai ane maamplitude uye frequency yakafanana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Izvi zvinoonekwa kana chinyorwa chinodonhedzwa patambo, uye masaisai anopindira anoratidzwa pamagumo akagadziriswa etambo. Masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Aya ma frequency anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo maresonant frequencies etambo anoenzana nehurefu hwayo, uye akapesana akaenzana nehuremu pahurefu hweyuniti yetambo.
Sine uye Cosine Mafungu
Muchikamu chino, ndichave ndichikurukura mutsauko uripo pakati pe sine uye cosine waves, chii chinonzi phase shift, uye kuti sine wave inosiyana sei kubva kune cosine wave. Ini ndichave ndichiongororawo kukosha kwe sine mafungu mumasvomhu, fizikisi, mainjiniya, uye masaini kugadzirisa.
Ndeupi Musiyano Pakati peSine neCosine Waves?
Sine uye cosine masaisai anoita nguva nenguva, akatsetseka, uye anoenderera mberi anoshandiswa kutsanangura zvakawanda zvinoitika zvakasikwa, zvakaita seruzha uye chiedza. Iwo anoshandiswawo muinjiniya, chiratidzo chekugadzirisa, uye masvomhu.
Musiyano mukuru uripo pakati pe sine ne cosine waves ndewekuti sine wave inotangira pa zero, ukuwo cosine wave ichitangira pachikamu chekuchinja che π/2 radians. Izvi zvinoreva kuti cosine wave ine musoro wekutanga kana ichienzaniswa neine wave.
Sine masaisai akakosha mufizikisi nekuti anochengeta masaisai awo kana awedzerwa pamwechete. Ichi chivakwa, chinozivikanwa se superposition musimboti, ndicho chinoita kuti ongororo yeFourier ibatsire. Iyo zvakare inoita sine mafungu acoustically akasiyana, sezvo anogona kushandiswa kumiririra imwe frequency.
Mafungu eCosine akakoshawo mufizikisi, sezvo achishandiswa kutsanangura mafambiro ehuwandu pachirimo mukuenzana. Equation ye sine wave is f = oscillations/nguva, apo f iri frequency yemasaisai uye ω ndiyo mafungu eangular. Iyi equation inopa kutamiswa kwesaisai pane chero chinzvimbo x uye nguva t.
Mune mativi maviri kana anopfuura, sine wave inogona kutsanangurwa nekufamba kwendege wave. Iyo wave nhamba k chimiro cheiyo wave, uye ine hukama neangular frequency ω uye wavelength λ. Equation ye sine wave muzvikamu zviviri kana kudarika inopa kutamiswa kwesaisai pane chero chinzvimbo x uye nguva t.
Masaisai akaomarara, seaya akagadzirwa nedombo rakadonhedzwa mudziva, anoda mamwe maequation akaomarara. Izwi rokuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwakafanana nehwe sine wave kana cosine wave, senge phase shift. Izwi rokuti sinusoidal rinoshandiswa kureva pamwechete kureva sine mafungu uye cosine masaisai ane phase offset.
Masaisai eSine anowanikwa mune zvakasikwa, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye inogona zvakare kuziva kuvepo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency. Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira.
Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chinoshandiswa kudzidza masaisai, akadai sekuyerera kwekushisa uye kugadzirisa masaini. Inoshandiswawo mukuongorora kwenhamba uye nguva dzakatevedzana.
Sine masaisai anogona kupararira chero divi muchadenga, uye anomiririrwa nemasaisai ane amplitude uye frequency ari kufamba akapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Izvi zvinoitika kana chinyorwa chikabvutwa patambo, sezvo masaisai anoratidzwa pamagumo etambo. Mafungu akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Iwo maresonant frequencies etambo anoenzana nehurefu hwayo, uye zvakapesana nehupamhi hwayo pahurefu hwayo.
Chii chinonzi Phase Shift?
A sine wave inotsvedzerera, inodzokorodza oscillation inoenderera mune zvese nguva nenzvimbo. Imasvomhu curve inotsanangurwa ne trigonometric sine basa uye inowanzoshandiswa kumiririra masaisai eruzha, masaisai emwenje, uye mamwe masaisai mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda. Iyo yakajairwa frequency (f) ye sine wave inhamba yekutenderera kana kutenderera kunoitika musekondi imwe, uye inoyerwa mu hertz (Hz).
Angular frequency (ω) chiyero cheshanduko yenharo yebasa mumaradians pasekondi, uye inoenderana neyakajairwa frequency neiyo equation ω = 2πf. Kukosha kwakashata kwe φ kunomiririra kunonoka, nepo kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine masaisai anowanzo shandiswa kurondedzera masaisai eruzha, sezvo achikwanisa kuchengetedza chimiro chavo chesaisai kana awedzerwa pamwechete. Ichi chivakwa chinotungamira mukukosha kweFourier ongororo, izvo zvinoita kuti zvikwanise kusiyanisa acoustically akasiyana siyana enzvimbo. Semuenzaniso, shanduko x inomiririra chinzvimbo mune imwe dimension, uye wave inopararira munzira yehunhu parameter k, inonzi nhamba yemafungu. Angular wave nhamba inomiririra kuenzana pakati peangular frequency (ω) uye mutsara wekumhanya kwekuparadzira (ν). Wavenumber ine hukama neangular frequency uye wavelength (λ) ne equation λ = 2π/k.
Equation ye sine wave mune imwe dimension inopiwa ne y = A chivi (ωt + φ), apo A ndiyo amplitude, ω ndiyo inotenderera, t inguva, uye φ ndiyo chikamu chekuchinja. Iyi equation inogona kuve yakajairwa kuti ipe kutamiswa kwemafungu pane chero chinzvimbo x chero nguva t mumutsetse mumwe, semuenzaniso, y = Chivi (kx - ωt + φ). Paunenge uchifunga nezve wave mune maviri kana anopfuura mativi enzvimbo, yakaoma equations inodiwa.
Izwi rokuti sinusoid rinowanzo shandiswa kutsanangura masaisai ane hunhu hwakafanana nehwe sine wave. Izvi zvinosanganisira masaisai ecosine, ane chikamu chekuchinja che π/2 radians, zvichireva kuti vane musoro wekutangisa zvichienzaniswa nemasaisai esine. Izwi rekuti sinusoidal rinowanzo shandiswa pamwechete kureva ese mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa.
Kuenzanisira cosine wave, hukama hwakakosha pakati pe sine wave uye cosine wave hunogona kuoneswa nedenderedzwa mune ye3D yakaoma plane modhi. Izvi zvinobatsira pakuturikira pakati pemadomasi, semasaisai akafanana anoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu e sine imwe seanonzwika akajeka, uye sine mafungu anowanzo shandiswa seanomiririra imwe frequency toni.
Harmonics yakakoshawo mukunzwika, sezvo nzeve yemunhu inoona ruzha senge musanganiswa wemasaisai e sine uye yakakwirira ma harmonics mukuwedzera kune yakakosha frequency. Kuvapo kwepamusoro harmonics mukuwedzera kune zvakakosha zvinokonzeresa mutsauko wetimbre yekurira. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana. Zvakadaro, ruzha rwunobudiswa nekurova kweruoko rwune masaisai eaperiodic, zvichireva kuti haruna kuumbwa nemasaisai eine.
Mafungu eruzha enguva nenguva anogona kuenzaniswa pachishandiswa zvivharo zviri nyore zvemasaisai e sinusoidal, sezvakawanikwa nenyanzvi yemasvomhu yekuFrance Joseph Fourier. Izvi zvinosanganisira masikweya mafungu, ayo anoumbwa neakakosha frequency uye yakakwirira harmonics. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa uye kugadzirisa zviratidzo, uye kuongorora kwenhamba yenguva dzakatevedzana.
Mafungu eSine anokwanisa kuparadzira pasina kushandura fomu mune akagoverwa mutsara masisitimu, uye anowanzo kudiwa kuongorora wave kuparadzira. Sine masaisai anogona kufamba nemativi maviri muchadenga, uye anomiririrwa nemasaisai ane amplitude uye frequency. Kana masaisai maviri achifamba akapesana akadarika, patani yemasaisai inogadzirwa. Izvi zvakafanana nepanodonhedzwa katsamba patambo, sezvo masaisai ari kupindira anoratidzwa panoperera tambo. Masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Aya ma frequency anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo ma frequency eresonant etambo anoenzana nehurefu hwetambo, uye anopesana nehupamhi pahurefu hwechikamu chetambo.
Iyo Sine Wave Inosiyana Sei neCosine Wave?
A sine wave chimiro chinoenderera chinotenderera mune yakatsetseka, inodzokorodza pateni. Iro trigonometric basa rakadhirowewa pane maviri-dimensional ndege, uye ndiyo yakakosha waveform mumasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Iyo inoratidzirwa nehuwandu hwayo, kana nhamba ye oscillations inoitika munguva yakatarwa, uye ayo angular frequency, iyo chiyero chekuchinja kwegakava rebasa mu radians pasekondi. Sine wave inogona kuchinjwa nekufamba kwenguva, ine kukosha kwakashata kunomiririra kunonoka uye kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine mafungu anowanzoshandiswa kurondedzera masaisai enzwi, uye anowanzo kunzi sinusoids. Iwo akakosha mufizikisi nekuti anochengeta wave wave chimiro kana awedzerwa pamwechete, uye ndiwo hwaro hwekuongorora kweFourier, izvo zvinoita kuti dzisave dzakasiyana. Iwo anoshandiswawo kurondedzera spatial variables, nenhamba yemafungu inomiririra kuenzana pakati peangular frequency uye mutsara wekumhanya kwekuparadzira.
Iyo sine wave inoshandiswawo kutsanangura imwe-dimension wave, senge waya. Kana yakajairwa kuita mativi maviri, equation inotsanangura mafungu endege inofamba. The wave number inodudzirwa sevector, uye dot product yemasaisai maviri iwaisai yakaoma.
Sine waves anoshandiswawo kutsanangura kureba kwemafungu emvura mudziva kana dombo radonha. Mamwe maequation akaomarara anodiwa kutsanangura izwi rekuti sinusoid, iro rinotsanangura maitiro emafungu, kusanganisira sine uye cosine mafungu ane phase shift. Sine wave inokandira cosine wave ne π/2 radians, kana kutanga musoro, saka basa recosine rinotungamira basa resine. Izwi rekuti sinusoidal rinoshandiswa kutaura pamwechete kureva sine uye cosine masaisai ane phase offset.
Kuenzanisira cosine wave hukama hwakakosha kune denderedzwa mu 3D yakaoma plane modhi, iyo inobatsira kuona kukosha kwayo munzvimbo dzeshanduro. Iyi wave wave inoitika mumasikirwo, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inogona kuona mafungu ane sine seanonzwika akajeka, uye sine wave inomiririra yeimwe frequencies uye harmonics yavo. Nzeve yemunhu inoona ruzha senge sine wave ine periodic ruzha, uye kuvapo kwepamusoro maharmonics mukuwedzera kune zvakakosha zvinokonzeresa kusiana kwetimbre.
Ichi ndicho chikonzero nei rwiyo rwemhanzi rweimwe frequency inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana. Ruzha rwekuombera ruoko, semuenzaniso, rine masaisai eaperiodic, asingadzokorore, pane kuti periodic sine waves. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvaka ari nyore kutsanangura uye kuita fungidziro ye periodic waveform, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekudzidza masaisai, sekuyerera kwekushisa uye kugadzirisa masaini, pamwe nekuongorora kwenhamba yenguva dzakatevedzana. Sine mafungu anogona zvakare kupararira mukuchinja mafomu kuburikidza neakagoverwa mutsara masisitimu, ayo anodiwa kuongorora wave kupararira. Sine masaisai anofamba akapesana muchadenga anomiririrwa nemasaisai ane amplitude yakafanana uye frequency, uye kana akaiswa pamusoro, patani yemasaisai inogadzirwa. Izvi zvinocherechedzwa kana chinyorwa chinodonhedzwa patambo, sezvo masaisai anopindira anoratidzwa neakagadziriswa magumo etambo. Mafungu akamira anoitika pane mamwe mafrequency, anonzi resonant frequencies, uye anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo mazariro etambo anoenzana nehurefu hwetambo uye zvakapesana nehupamhi pahurefu hwechikamu chetambo.
Ko Sine Wave Inonzwika Sei?
Ndine chokwadi chekuti wakambonzwa nezve mafungu e sine, asi unoziva kuti anonzwika sei? Muchikamu chino, tichaongorora kuti sine mafungu anokanganisa sei ruzha rwemimhanzi, uye kuti anodyidzana sei neharmonics kugadzira akasiyana matimbu. Isu tichazokurukurawo mashandisirwo e sine mafungu mukugadzirisa masaini uye kuparadzira wave. Pakupera kwechikamu chino, iwe unenge wave nekunzwisisa kuri nani kwemasaisai e sine uye maitiro aanoita ruzha.
Ko Sine Wave Inonzwika Sei?
A sine wave inoenderera, yakatsetseka, inodzokorodza oscillation inowanikwa mune zvakawanda zvechisikigo zviitiko, kusanganisira masaisai eruzha, masaisai emwenje, uye kunyangwe kufamba kwehuwandu pachitubu. Iyo masvomhu curve inotsanangurwa neiyo trigonometric sine basa, uye inowanzoitwa graphed senge waveform.
Ko sine wave inonzwika sei? A sine wave is a continuous wave, zvichireva kuti haina mabreak mu waveform. Iyo inotsvedzerera, periodic basa ine frequency, kana nhamba yeoscillations inoitika munguva yakatarwa. Yayo angular frequency, kana chiyero cheshanduko yenharo yebasa mumaradians pasekondi, inomiririrwa nechiratidzo ω. A negative value inomiririra kunonoka, ukuwo value yakanaka inomiririra kumberi mumasekonzi.
Kuwanda kwe sinus wave kunoyerwa mu hertz (Hz), uye ndiyo nhamba yekutenderera pasekondi. A sine wave iwizha rinonzwika rinotsanangurwa nesine function, f(t) = Chivi (ωt + φ), apo A ndiyo amplitude, ω ndiyo mafungu eangular, uye φ ndiyo chikamu chekuchinja. Kuchinja kwechikamu che π/2 radians kunopa wave kutanga musoro, saka inowanzonzi basa recosine.
Izwi rekuti "sinusoid" rinoshandiswa kurondedzera mafungu maitiro e sine wave, pamwe neiyo cosine wave ine phase offset. Izvi zvinoratidzwa necosine wave, iyo inosara kuseri kwe sine wave nechikamu chekuchinja che π/2 radians. Hukama hwakakosha uhu pakati pemasaisai e sine uye cosine hunomiririrwa nedenderedzwa mumhando ye 3D yakaoma ndege, iyo inobatsira kuona kukosha kweshanduro pakati pemadomasi.
Iyo wave pateni ye sine wave inoitika mumasikirwo, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine wave inomiririra yeimwe frequency harmonics inoshandiswa kugadzira zvinyorwa zvemimhanzi. Kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency kunokonzera mutsauko wetimbre yekurira. Ichi ndicho chikonzero nei rwiyo rumwe chete rwemimhanzi runoridzwa pazviridzwa zvakasiyana ruchanzwika zvakasiyana.
Nekudaro, ruzha rwunogadzirwa neruoko rwemunhu haruna kuumbwa nemasaisai ane sine chete, sezvo painewo mafungu aperiodic. Mafungu eAperiodic haadzokorore uye haana pateni, nepo sine mafungu ari periodic. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvaka ari nyore kutsanangura uye kufungidzira chero ipi zvayo yenguva yemasaisai, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana.
Mafungu eSine anogona kupararira mukuchinja mafomu kuburikidza neakagoverwa mutsara masisitimu, uye anodiwa kuti uongorore wave kupararira. Masaisai eSine anofamba akapesana muchadenga anomiririrwa nemasaisai ane hukuru hwakafanana uye frequency, uye kana masaisai aya akadarika, patani yemasaisai inogadzirwa. Izvi zvakafanana nezvinoitika kana katsamba kakadonhedzwa patambo; masaisai anopindira anosikwa, uye kana masaisai aya achiratidzwa nemagumo akagadziriswa etambo, masaisai akamira anoitika pane mamwe mafrequency, anonzi maresonant frequencies. Aya ma frequency resonant anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Mafambiro anoita tambo anoenzana nehurefu hwayo, uye akaenzana neskweya mudzi wehuremu hwayo pahurefu hwayo.
Ndeipi Basa reHarmonics muInzwi?
A sine wave inoenderera, yakatsetseka, inodzokorodza oscillation inowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Irwo rudzi rwekuenderera mberi kwemafungu anotsanangurwa ne trigonometric function, kazhinji sine kana cosine, uye inomiririrwa negirafu. Izvo zvinoitika mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda.
Iyo yakajairwa frequency ye sine wave, kana huwandu hwekutenderera hunoitika muhuwandu hwenguva, hunomiririrwa neangular frequency ω, iyo yakaenzana ne 2πf, apo f iri frequency mu hertz. Kukosha kwakashata kwe φ kunomiririra kunonoka mumasekonzi, nepo kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine masaisai anowanzo shandiswa kutsanangura masaisai eruzha, sezvo ari iwo anonyanya kukosha eizwi masaisai. Izvo zvinotsanangurwa ne sine basa, f = A chivi (ωt + φ), apo A ndiyo amplitude, ω inguva yeangular, t inguva, uye φ ndiyo chikamu chekuchinja. A phase shift of π/2 radians inopa wave kutanga musoro, saka inonzi ibasa re cosine, rinotungamira basa re sine. Izwi rekuti "sinusoidal" rinoshandiswa kureva pamwe chete kune sine mafungu uye cosine mafungu ane chikamu chinobvisa.
Kuenzanisira izvi, cosine wave hukama hwakakosha pakati pedenderedzwa uye 3D yakaoma ndege modhi, iyo inobatsira kuona kukosha kwayo mukuturikira kune mamwe madomasi. Iyi wave wave inoitika mumasikirwo, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza.
Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anowanzo shandiswa seanomiririra imwechete frequency harmonics. Nzeve yemunhu inoona ruzha semusanganiswa wemasaisai e sine uye maharmonics, pamwe nekuwedzera kwemasaisai akasiyana-siyana achikonzera imwe waveform uye shanduko yetimbre. Kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kukonzeresa mutsauko wetimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chine frequency yakafanana inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana.
Nekudaro, ruzha haruna kungoumbwa neine mafungu uye harmonics, sezvo ruzha rwakagadzirwa nemaoko rune aperiodic mafungu zvakare. Mafungu eAperiodic haasi-periodic uye ane maitiro asina kudzokorora. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal zvivharo zviri nyore zvekuvakisa zvinogona kushandiswa kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana.
Mafungu eSine anogona kupararira mukuchinja fomu kuburikidza neakagoverwa mutsara masisitimu, uye anodiwa kuti uongorore wave wave kuparadzira. Sine masaisai anofamba akapesana muchadenga anogona kumiririrwa nemasaisai ane amplitude yakafanana uye frequency, uye kana achinge akwidibira, patani yemasaisai inogadzirwa. Izvi ndizvo zvinoitika kana chinyorwa chikabvutwa patambo: masaisai anopindira anoratidzwa pamagumo etambo, uye masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Aya ma frequency resonant anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Mafambiro anorira etambo anoenzana nehurefu hwayo, uye akapesana akaenzana neskweya mudzi wehuremu pahurefu hweyuniti yetambo.
Sei Sine Wave Inobata Sei Ruzha rweInzwi?
A sine wave inoenderera, yakatsetseka, inodzokorodza oscillation icho chikamu chakakosha chemasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Iyo imhando yekuenderera mberi wave ine yakatsetseka, periodic basa uye inoitika mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda. Iyo yakajairwa frequency ye sine wave inhamba yekutenderera kana kutenderera kunoitika muchikamu chenguva. Izvi zvinomiririrwa ne ω = 2πf, uko ω ndiyo mafungu eakona uye f ndiyo yakajairika frequency. Angular frequency ndiyo mwero wekushanduka kwenharo yebasa uye inoyerwa nemaradians pasekondi. Iyo isiri-zero kukosha kwe ω inomiririra shanduko mune yese waveform munguva, inoratidzwa ne φ. Kukosha kwakashata kwe φ kunomiririra kunonoka uye kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine wave inowanzoshandiswa kurondedzera masaisai eruzha, uye inotsanangurwa nesine basa f = chivi(ωt). Oscillations inoonekwawo mune isina kuvharwa chitubu-mass system pakuenzana, uye sine mafungu akakosha mufizikisi nekuti anochengeta chimiro chawo chewave kana awedzerwa pamwechete. Ichi chivakwa chesine mafungu chinotungamira mukukosha kwacho muFourier ongororo, izvo zvinoita kuti ive yakasarudzika.
Kana sine wave inomiririrwa mune imwe nzvimbo, equation inopa kutamiswa kwesaisai panzvimbo x panguva t. Muenzaniso mutsetse mumwechete unotariswa, uko kukosha kwesaisai pane imwe nzvimbo x kunopihwa neiyo equation. Munzvimbo dzakawanda dzenzvimbo, equation inotsanangura mafungu endege inofamba, apo nzvimbo x inomiririrwa nevector uye wavenumber k ivector. Izvi zvinogona kududzirwa sedoti chigadzirwa chemavekita maviri.
Masaisai akaomarara, semasaisai emvura mudziva kana dombo radonhedzwa, anoda mamwe maequation akaoma kunzwisisa. Izwi rokuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwezvose sine wave uye cosine wave. A phase shift of π/2 radians inonzi inopa cosine wave kutanga, sezvo ichitungamira sine wave. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa, sezvinoratidzwa necosine wave.
Uhu hukama hwakakosha pakati pe sine uye cosine mafungu hunogona kuoneswa nedenderedzwa mune 3D yakaoma ndege modhi. Uyu modhi unobatsira pakuturikira pakati penzvimbo dzakasiyana, semasaisai anoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai emwenje. Nzeve yemunhu inogona kuziva masaisai eine imwe chete, inonzwika zvakajeka uye yakachena. Sine mafungu zvakare anomiririra imwe chete frequency harmonics, iyo nzeve yemunhu inogona kuona.
Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kukonzeresa mutsauko wetimbre. Ichi ndicho chikonzero nei rwiyo rwemhanzi rweimwe frequency inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana. Ruzha rwekuombera ruoko rune masaisai aperiodic, kwete sine mafungu, sezvo iri ruzha rweperiodic. Inoonekwa seruzha, ruzha runoratidzwa seaperiodic, ine chimiro chisina kudzokorora.
Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo matombo ekuvaka ari nyore kutsanangura uye kufungidzira chero mapedhi epanguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, akadai sekuyerera kwekushisa uye kugadzirisa masaini uye kuongororwa kwenhamba yenguva dzakatevedzana. Sine mafungu anogona zvakare kupararira kuburikidza nekuchinja mafomu mune akagoverwa mutsara masisitimu, ayo anodiwa kuongorora wave kupararira. Masaisai eSine anofamba akapesana muchadenga anomiririrwa nemasaisai ane maamplitude uye frequency yakafanana. Kana masaisai aya akakwidibira, patani yemasaisai inogadzirwa inogadzirwa, sezvinoonekwa kana noti yadhonzwa patambo. Kupindira masaisai anotaridzwa kubva kumagumo etambo anogadzira masaisai akamira anoitika pane mamwe mafrequency, anonzi maresonant frequencies. Aya ma frequency resonant anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo mazariro etambo anoenzana nehurefu hwetambo uye zvakapesana nehupamhi pahurefu hwechikamu chetambo.
Sine Waves seAnalytical Tools
Ini ndichataura nezve sine mafungu uye mashandisirwo aanoitwa sematurusi ekuongorora mukugadzirisa chiratidzo, nguva yekuongorora uye kuparadzira wave. Isu tichaongorora kuti sine mafungu anoshandiswa sei kutsanangura akatsetseka, anodzokororwa oscillations uye mashandisirwo aanoitwa mumasvomhu, fizikisi, engineering uye mamwe minda. Isu tichatarisa zvakare kuti sine mafungu anogona kushandiswa sei kuongorora wave kuparadzira uye mashandisirwo aanoitwa muFourier ongororo. Chekupedzisira, tichakurukura kuti sine mafungu anoshandiswa sei kugadzira ruzha uye kuti anoshandiswa sei mumhanzi.
Chii chinonzi Signal Processing?
Sine mafungu chinhu chakakosha chinoshandiswa mukugadzirisa zviratidzo uye nguva yekuongorora. Iwo imhando yekuenderera mberi waveform, inoratidzirwa neyakatsetseka, inodzokorodza oscillation ine imwechete frequency. Sine mafungu anoshandiswa kutsanangura zvakasiyana-siyana zvemuviri, kusanganisira masaisai eruzha, masaisai akareruka, uye kufamba kwehuwandu pachitubu.
Signal processing ndiyo nzira yekuongorora nekugadzirisa zviratidzo. Inoshandiswa munzvimbo dzakasiyana siyana, kusanganisira masvomhu, fizikisi, engineering, uye odhiyo nemavhidhiyo kugadzirwa. Maitiro ekugadzirisa masaini anoshandiswa kuongorora masaini, kuona mapatani, uye kubvisa ruzivo kubva kwavari.
Time series analysis ndiyo nzira yekuongorora mapoinzi edata akaunganidzwa nekufamba kwenguva. Inoshandiswa kuona mafambiro uye mapatani mune data, uye kufanotaura nezvezviitiko zvenguva yemberi. Nguva yekuongorora yakatevedzana inoshandiswa muzvikamu zvakasiyana, kusanganisira zvehupfumi, mari, uye engineering.
Wave propagation inzira iyo masaisai anofamba nepakati. Inoongororwa pachishandiswa zvakasiyana-siyana zvemasvomhu equation, kusanganisira wave equation uye sine wave equation. Wave propagation inoshandiswa kuongorora maitiro emasaisai anonzwika, masaisai emwenje, uye mamwe marudzi emasaisai.
Chii chinonzi Time Series Analysis?
Sine waves chinhu chakakosha chekuongorora zvakasiyana-siyana zvemuviri, kubva kumafungu eruzha kusvika kune chiedza masaisai. Nguva yakatevedzana yekuongorora inzira yekuongorora mapoinzi edata akaunganidzwa kwenguva yakati rebei, kuitira kuona mapatani uye mafambiro. Inoshandiswa kudzidza maitiro ehurongwa nekufamba kwenguva, uye kufanotaura nezve maitiro emangwana.
Nguva yakatevedzana yekuongorora inogona kushandiswa kuongorora sine mafungu. Inogona kushandiswa kuona frequency, amplitude, uye chikamu che sine wave, pamwe nekuona chero shanduko mune waveform nekufamba kwenguva. Inogona zvakare kushandiswa kuona chero yakadzika mapatani mune waveform, senge periodicities kana maitiro.
Nguva yakatevedzana yekuongorora inogona zvakare kushandiswa kuona chero shanduko muamplitude kana chikamu che sine wave nekufamba kwenguva. Izvi zvinogona kushandiswa kuona chero shanduko muhurongwa dzingave dziri kukonzera kuti waveform ichinje, sekuchinja kwezvakatipoteredza kana system yacho pachayo.
Nguva yekutevedzana yekuongorora inogona zvakare kushandiswa kuona chero ari pasi pemaitiro mune waveform, senge periodicities kana maitiro. Izvi zvinogona kushandiswa kuona chero ari pasi pemaitiro ari muhurongwa angave ari kukonzera kuti waveform ichinje, sekuchinja kwezvakatipoteredza kana system yacho pachayo.
Nguva yakatevedzana yekuongorora inogona zvakare kushandiswa kuona chero shanduko muhuwandu hweiyo sine wave nekufamba kwenguva. Izvi zvinogona kushandiswa kuona chero shanduko muhurongwa dzingave dziri kukonzera kuti waveform ichinje, sekuchinja kwezvakatipoteredza kana system yacho pachayo.
Nguva yekutevedzana yekuongorora inogona zvakare kushandiswa kuona chero ari pasi pemaitiro mune waveform, senge periodicities kana maitiro. Izvi zvinogona kushandiswa kuona chero ari pasi pemaitiro ari muhurongwa angave ari kukonzera kuti waveform ichinje, sekuchinja kwezvakatipoteredza kana system yacho pachayo.
Nguva yakatevedzana ongororo chishandiso chine simba chekuongorora sine mafungu uye chinogona kushandiswa kuona mapatani uye maitiro mune waveform nekufamba kwenguva. Inogona zvakare kushandiswa kuona chero ari pasi pemaitiro muhurongwa angave ari kuita kuti waveform ichinje, sekuchinja kwezvakatipoteredza kana system yacho pachayo.
Wave Propagation Inoongororwa Sei?
Sine waves imhando yekuenderera mberi waveform iyo inogona kushandiswa kuongorora wave kupararira. Iwo akatsetseka, anodzokorodza oscillation anogona kuwanikwa mumasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Sine masaisai anoratidzirwa nekuwanda kwawo (f), nhamba yeoscillations inoitika mune imwe nguva, uye yavo angular frequency (ω), inova chiyero icho basa nharo inochinja muzvikamu zve radians.
Sine masaisai anoshandiswa kutsanangura zvakasiyana-siyana zvezviitiko, kusanganisira masaisai eruzha, masaisai echiedza, uye kufamba kwechitubu. Iwo akakosha zvakare muFourier ongororo, izvo zvinoita kuti ive acoustically akasiyana. Sine wave inogona kumiririrwa muchikamu chimwe chete nemutsara mumwechete, ine kukosha kwesaisai pane yakapihwa nzvimbo munguva nenzvimbo. Muzviyero zvakawanda, equation ye sine wave inotsanangura mafungu endege inofamba, ine chinzvimbo (x), wave nhamba (k), uye angular frequency (ω).
Sinusoids imhando yewaveform inosanganisira ese sine uye cosine mafungu, pamwe nechero mafungu ane chikamu chekuchinja che π/2 radians (kutanga musoro). Izvi zvinotungamira kuhukama hwakakosha pakati pe sine uye cosine mafungu, ayo anogona kuoneswa mune 3D yakaoma ndege modhi. Iyi modhi inobatsira kushandura waveforms pakati penzvimbo dzakasiyana.
Mafungu eSinusoidal anogona kuwanikwa mune zvakasikwa, kusanganisira masaisai emhepo nemafungu emvura. Nzeve yemunhu inokwanisa kuziva mafungu ane sine imwe seinonzwika zvakajeka, asi ruzha runowanzo kuumbwa nemasaisai akawanda, anozivikanwa seharmonics. Kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency kunokonzera mutsauko wetimbre yekurira. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana.
Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekudzidza masaisai, uye chinoshandiswa mukuyerera kwekushisa uye kugadzirisa masaini. Inoshandiswawo mukuongorora kwenhamba yenguva dzakatevedzana.
Sine masaisai anogona kupararira chero divi muchadenga, uye anomiririrwa nemasaisai ane amplitude uye frequency anofamba achienda kwakapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Iyi ndiyo nzira imwe chete inogadzirwa kana chinyorwa chikabvutwa patambo, nekuda kwemasaisai anotaridzirwa pamagumo akagadziriswa etambo. Masaisai akamira anoitika pane mamwe ma frequency, anozivikanwa seresonant frequencies, ayo anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo maresonant frequencies etambo anoenzana nehurefu hwayo, uye zvakapesana nehupamhi hwayo pahurefu hwayo.
Sine Wave Spectrum
Ini ndichave ndichikurukura nezve sine wave spectrum, kusanganisira frequency yayo, wavelength, uye kuti ingashandiswa sei kugadzira akasiyana manzwi. Tichaongorora curve yemasvomhu inotsanangura kutsetseka, kudzokororwa kutenderera, uye mashandisirwo aanoitwa mundima dzemasvomhu, fizikisi, huinjiniya uye nemasaini. Tichatarisawo kuti sine wave yakakosha sei mufizikisi uye nei ichishandiswa mukuongorora kweFourier. Pakupedzisira, tichakurukura kuti sine wave inoshandiswa sei mukunzwika uye kuti inonzwisiswa sei nenzeve yemunhu.
Chii chinonzi Frequency yeSine Wave?
A sine wave chimiro chinoramba chichitenderera chinotenderera nenzira yakatsetseka, inodzokorora. Icho chinhu chakakosha chezvakawanda zvemuviri uye masvomhu zviitiko, senge ruzha, chiedza, uye magetsi masaini. Iyo frequency ye sine wave inhamba yeoscillations inoitika mune yakapihwa nguva yenguva. Inoyerwa muHertz (Hz) uye inowanzo ratidzwa maererano nematenderedzwa pasekondi. Hukama huri pakati pefrequency newavelength ndehwekuti iyo yakakwira frequency, ipfupi yewavelength.
Sine mafungu anoshandiswa kugadzira akasiyana siyana eruzha, kusanganisira vibrato, tremolo, uye chorus. Nekusanganisa akawanda sine mafungu emhando dzakasiyana, yakaoma waveforms inogona kugadzirwa. Izvi zvinozivikanwa seyekuwedzera synthesis, uye inoshandiswa mumhando dzakawanda dzekugadzira odhiyo. Pamusoro pezvo, mafungu ane sine anogona kushandiswa kugadzira akasiyana siyana, sekuchinja kwechikamu, kuputika, uye nhanho.
Mafungu eSine anoshandiswawo mukugadzirisa zviratidzo, senge muFourier ongororo, iyo inoshandiswa kudzidza kupararira kwemafungu uye kuyerera kwekushisa. Izvo zvinoshandiswawo mukuongorora kwenhamba uye nguva yekuongorora nguva.
Mukupfupisa, sine mafungu inoenderera mberi waveform iyo inotenderera mune yakatsetseka, inodzokorora fashoni. Izvo zvinoshandiswa kugadzira zvakasiyana-siyana zvinonzwika, uye zvinoshandiswawo mukugadzirisa zviratidzo uye kuongororwa kwenhamba. Iyo frequency ye sine wave inhamba yeoscillations inoitika mune imwe nguva yakatarwa, uye hukama pakati pe frequency uye wavelength ndeyekuti yakakwira frequency, ipfupi yewavelength.
Chii chinonzi Hukama pakati peFrequency uye Wavelength?
A sine wave inoenderera, yakatsetseka, inodzokorodza oscillation inowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Iyo inotsanangurwa neiyo trigonometric sine basa, uye inomiririrwa zvakajeka senge waveform. Iyo sine wave ine frequency, inova nhamba yekutenderera kana kutenderera kunoitika munguva yakatarwa. Angular frequency, inoratidzwa ne ω, chiyero cheshanduko yenharo yebasa, inoyerwa mumaradians pasekondi. Iyo yose waveform haioneki kamwechete, asi inoshandurwa munguva nechikamu chekuchinja, chinoratidzirwa ne φ, iyo inoyerwa mumasekondi. Kosi isina kunaka inomiririra kunonoka, uye kukosha kwakanaka kunomiririra kumberi mumasekonzi. Kuwanda kwe sine wave kunopimwa mu hertz (Hz), uye inhamba yekutenderera inoitika musekondi imwe.
A sine wave ndiyo yakakosha waveform mufizikisi, sezvo ichichengeta chimiro chayo kana yawedzerwa kune imwe sine wave yeakawanda ma frequency uye anopokana chikamu uye ukuru. Ichi chivakwa che periodic waveform chinozivikanwa se superposition musimboti, uye ndicho chivakwa ichi chinotungamira mukukosha kweFourier ongororo. Izvi zvinoita kuti ive acoustically yakasarudzika, sezvo iri iyo yega waveform inogona kushandiswa kugadzira chinja chepakati. Semuyenzaniso, kana x inomiririra chinzvimbo padivi pewaya, ipapo sine wave yenguva yakapihwa frequency uye wavelength inopararira pamwe newaya. Hunhu hweparamendi yefungu inozivikanwa senhamba yemafungu, k, inova nhamba yeangular wave uye inomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber ine hukama neangular frequency uye wavelength, λ, ne equation λ = 2π/k.
Equation ye sine wave mune imwe dimension inopiwa ne y = A chivi(ωt + φ), apo A ndiyo amplitude, ω ndiyo inotenderera, t inguva, uye φ ndiyo chikamu chekuchinja. Iyi equation inogona kuve yakajairwa kuti ipe kutamiswa kwemafungu panzvimbo yakapihwa, x, pane imwe nguva, t. Pamuenzaniso mumwechete wemutsara, kukosha kwesaisai panzvimbo yakapihwa kunopihwa ne y = A sin(kx - ωt + φ), uko k ndiyo nhamba yemafungu. Kana chiyero chenzvimbo chinopfuura chimwechete chikatariswa, imwe yakaoma equation inodiwa kutsanangura wave.
Izwi rekuti sinusoid rinoshandiswa kutsanangura waveform ine hunhu hwezvose sine wave uye cosine wave. A phase shift of π/2 radians inonzi inopa sine wave kutanga musoro, sezvo sine wave inoradzika cosine wave nehuwandu uhu. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa. Izvi zvinoratidzwa mugirafu riri pazasi, rinoratidza cosine wave ine phase shift ye π/2 radians.
Hukama hwakakosha pakati pe sine wave uye denderedzwa inogona kuoneswa uchishandisa 3D yakaoma ndege modhi. Izvi zvinobatsira kushandura waveform muzvikamu zvakasiyana, semafungu akafanana anoitika mumasikirwo, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai emwenje. Nzeve yemunhu inokwanisa kuona mafungu e sine imwe seinonzwika zvakajeka, uye mafungu ane sine anowanzo shandiswa seanomiririra manzwi emhando imwe chete. Harmonics iripowo mune ruzha, sezvo nzeve yemunhu inogona kuona harmonics mukuwedzera kune yakakosha frequency. Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kwepamusoro maharmonics mukuwedzera kune yakakosha frequency ndiko kunokonzera kusiyanisa kwetimbre. Ichi ndicho chikonzero nei chinyorwa chemumhanzi cheiyo frequency yakapihwa inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana.
Ruzha rwekuombera ruoko runewo masaisai eaperiodic, ari masaisai asiri enguva nenguva. Sine masaisai ari periodic, uye ruzha runonzwisiswa seruzha runoratidzwa neaperiodic masaisai, ine isingadzokorore pateni. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa uye kugadzirisa zviratidzo, uye kuongorora kwenhamba yenguva dzakatevedzana. Sine mafungu anogona zvakare kushandiswa kuparadzira kuburikidza nekuchinja mafomu mune akagoverwa mutsara masisitimu. Izvi zvinodikanwa kuti uongorore kupararira kwemafungu mumativi maviri muchadenga, sezvo masaisai ane amplitude yakafanana uye frequency anofamba akatarisana achizopfuura kugadzira wave wave pateni. Izvi ndizvo zvinonzwika kana chikwangwani chikabvutwa patambo, sezvo masaisai anoratidzwa panogumira tambo. Masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies etambo. Aya ma frequency anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo mazariro etambo anoenzana nehurefu hwetambo uye zvakapesana nehupamhi pahurefu hwechikamu chetambo.
Sei Sine Wave Inogona Kushandiswa Kugadzira Yakasiyana Manzwi Anoita?
A sine wave chimiro chinoramba chichitenderera chinotenderera nenzira yakatsetseka, inodzokorora. Ndiyo imwe yeakanyanya kukosha mafungu uye inoshandiswa munzvimbo dzakawanda dzemasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Sine mafungu anoratidzirwa nekuwanda kwawo, inova nhamba yekutenderera kana kutenderera kunoitika mune imwe nguva yakatarwa. Angular frequency, inova mwero weshanduko yenharo yebasa mumaradians pasekondi, ine hukama neyakajairwa frequency neiyo equation ω = 2πf.
Sine masaisai anowanzo shandiswa mukugadzira ruzha uye anogona kushandiswa kugadzira zvakasiyana-siyana zvinonzwika. Nekusanganisa akasiyana mafungu e sine ane akasiyana mafrequency, amplitudes, uye zvikamu, huwandu hwakasiyana hwekurira hunogona kugadzirwa. Sine wave ine imwe frequency inozivikanwa se "yakakosha" uye ndiyo hwaro hwese mimhanzi manotsi. Kana masaisai akawanda ane mafiridhi akasiyana asanganiswa, anoumba “harmonics” ari ma frequency epamusoro anowedzera kune timbre yeruzha. Nekuwedzera mamwe maharmonics, ruzha runogona kuitwa kuti runzwike rwakaoma uye runonakidza. Pamusoro pezvo, nekushandura chikamu chesine wave, ruzha runogona kuitwa kuti rwuite senge rwuri kubva kwakasiyana nzira.
Sine mafungu anoshandiswawo muacoustics kuyera kusimba kwemafungu eruzha. Nekuyera amplitude ye sine wave, kusimba kwenzwi kunogona kutsanangurwa. Izvi zvinobatsira pakuyera kukwira kweruzha kana kuona kuti ruzha rwakaita sei.
Mukupedzisa, sine mafungu akakosha waveform munzvimbo dzakawanda dzesainzi uye engineering. Izvo zvinoshandiswa kugadzira zvakasiyana-siyana zvinonzwika uye zvinoshandiswawo kuyera kusimba kwemafungu eruzha. Nekusanganisa akasiyana mafungu e sine ane akasiyana mafrequency, amplitudes, uye zvikamu, huwandu hwakasiyana hwekurira hunogona kugadzirwa.
Ko Sine Curve Inogona Kutsanangura Sei Wave?
Muchikamu chino, ndichave ndichikurukura kuti sine curve inogona kushandiswa sei kutsanangura wave, hukama pakati pe sine curve neplane wave, uye kuti sine curve inogona kushandiswa sei kuona masaisai. Tichaongorora kukosha kwemasaisai esine musvomhu, fizikisi, engineering, uye masaini kugadzirisa, uye mashandisirwo aanoitwa kumiririra masaisai eruzha uye mamwe masaisai.
Sei Sine Curve Inomiririra Wave?
A sine wave inotsvedzerera, inodzokorodza oscillation inoenderera uye ine waveform inotsanangurwa ne sine trigonometric basa. Iyo imhando yekuenderera mberi wave yakatsetseka uye nguva nenguva, uye inowanikwa mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda. Iyo inoratidzirwa ne frequency, inova nhamba ye oscillations kana ma cycles anoitika mune yakapihwa huwandu hwenguva. Angular frequency, ω, ndiyo mwero wekuti gakava rebasa rinochinja mumayuniti emaradians pasekondi. Iyo isiri-yose waveform inoratidzika yakashandurwa munguva nechikamu chekuchinja, φ, iyo inoyerwa mumasekonzi. A negative value inomiririra kunonoka, ukuwo value yakanaka inomiririra kumberi mumasekonzi.
Sine wave inowanzoshandiswa kurondedzera ruzha rwekutinhira, uye inotsanangurwa neine basa, f = A chivi (ωt + φ). Oscillations inowanikwawo mune isina kuvharwa chitubu-mass system pakuenzana, uye sine wave yakakosha mufizikisi nekuti inochengeta wave wave chimiro kana yawedzerwa kune imwe sine wave yenguva yakafanana uye inopokana chikamu uye ukuru. Iyi periodic waveform pfuma ndiyo inotungamira mukukosha kwayo mukuongororwa kweFourier, izvo zvinoita kuti ive yakasarudzika.
Kana masaisai achipararira muchikamu chimwe chete, shanduko yenzvimbo, x, inomiririra nzvimbo umo masaisai ari kupararira, uye chimiro chechimiro, k, chinonzi nhamba yemasaisai. Angular wave nhamba inomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber ine hukama neangular frequency, λ (lambda) ndiyo yavelength, uye f ndiyo frequency. Equation v = λf inopa sine wave mune imwe dimension. A generalized equation inopiwa kupa kubviswa kwemafungu panzvimbo, x, panguva, t.
Kana muenzaniso wemutsara mumwe chete uchitariswa, kukosha kwemafungu pane imwe nzvimbo munzvimbo inopiwa ne equation x = A chivi (kx - ωt + φ). Pazvikamu zviviri zvenzvimbo, equation inotsanangura masaisai endege inofamba. Kana ichidudzirwa semavekita, chigadzirwa chemavekita maviri idoti chigadzirwa.
Kune masaisai akaoma, akadai semafungu emvura mudziva kana dombo radonhedzwa, equations yakaoma inodiwa. Izwi rokuti sinusoid rinoshandiswa kutsanangura mafungu emhando ye sine wave uye cosine wave. A phase shift of π/2 radians inonzi inopa cosine wave kutanga, sezvo ichitungamira sine wave. Sine wave inokandira cosine wave. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa, kuratidza hukama hwakakosha pakati pezviviri izvi. Denderedzwa mune 3D yakaoma plane modhi inogona kushandiswa kuona kukosha kweshanduro pakati pemadomasi maviri.
Mafungu akafanana anoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anomiririra imwe chete frequency uye harmonics. Nzeve yemunhu inoona ruzha senge sine wave ine inonzwisisika harmonics mukuwedzera kune yakakosha frequency. Kuwedzerwa kwemasaisai akasiyana-siyana kunoguma mune imwe waveform, iyo inoshandura timbre yekurira. Kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kukonzeresa mutsauko wetimbre. Ichi ndicho chikonzero nei rwiyo rwemhanzi rweimwe frequency inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana.
Ruzha rwekuombera ruoko rune mafungu aperiodic, asiri enguva nenguva, uye sine mafungu ari periodic. Inzwi rinonzwisiswa seruzha rinoratidzwa seaperiodic, riine maitiro asina kudzokorora. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvaka ari nyore kutsanangura uye kuita fungidziro ye periodic waveform, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana.
Sine masaisai anogona kupararira mukuchinja fomu kuburikidza akagoverwa mutsara masisitimu, uye inodiwa kuongorora wave kupararira. Masaisai eSine anofamba akapesana muchadenga anogona kumiririrwa semasaisai ane maamplitude akafanana uye frequency achifamba akapesana. Kana masaisai maviri ari pamusoro, patani yemafungu akamira inogadzirwa. Izvi zvakafanana nepanodonhedzwa katsamba patambo, apo masaisai ari kupindira anoratidzwa panoperera tambo. Masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Ruzha rwakaumbwa rwenoti yakadonhedzwa patambo inoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo mazariro etambo anoenzana nehurefu hwetambo uye zvakapesana nehupamhi pahurefu hwechikamu chetambo.
Chii chiri Hukama pakati peSine Curve uye Plane Wave?
A sine wave inotsvedzerera, inodzokorodza oscillation yeinoenderera mberi waveform. Iro curve yemasvomhu inotsanangurwa maererano nesine trigonometric basa, uye inowanzoitwa graphed seyakatsetseka, sinusoidal curve. Sine masaisai anowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, engineering, uye masignal processing fields.
Sine wave inoratidzwa neyakajairwa frequency, nhamba yeoscillations kana matenderedzwa anoitika munguva yakatarwa. chinguva. Angular frequency, ω, mwero wekushanduka kwenharo yebasa, uye inoyerwa mumayuniti emaradians pasekondi. Iyo isiri-yakazara waveform inoratidzika yakachinjika munguva, ine chikamu chekuchinja, φ, ye ωt masekonzi. A negative value inomiririra kunonoka, ukuwo value yakanaka inomiririra kumberi mumasekonzi.
A sine wave inoshandiswawo kutsanangura masaisai eruzha. Inotsanangurwa nesine basa, f (t) = Chivi (ωt + φ), apo A ndiyo amplitude, ω ndiyo frequency yeangular, uye φ ndiyo chikamu chekuchinja. Oscillations inoonekwa zvakare mune isina kuvharwa chitubu-mass system pakuenzanisa.
Sine masaisai akakosha mufizikisi nekuti anochengeta masaisai awo kana awedzerwa pamwechete. Ichi chivakwa, chinozivikanwa se superposition musimboti, chinotungamira mukukosha kweFourier ongororo, iyo inoita kuti zvikwanise kusiyanisa zvine ruzha pakati penzvimbo dzakasiyana. Semuyenzaniso, kana x achimiririra chinzvimbo mune imwe dimension, saka masaisai anopararira aine hunhu parameter, k, inodaidzwa kuti wave number. Angular wave nhamba, k, inomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber, k, ine hukama neangular frequency, ω, uye wavelength, λ, ne equation λ = 2π/k.
Equation ye sine wave mune imwe dimension inopiwa na y = A chivi(ωt + φ). Iyi equation inopa kutamiswa kwesaisai panzvimbo yakapihwa, x, pane imwe nguva, t. Kune imwechete mutsara muenzaniso, kana kukosha kwesaisai kuchionekwa sewaya, ipapo mumativi maviri enzvimbo, iyo equation inotsanangura inofamba ndege wave. Iyo chinzvimbo, x, uye wavenumber, k, inogona kududzirwa semavheji, uye chigadzirwa chezviviri idoti chigadzirwa.
Masaisai akaoma kunzwisisa, seaya anoonekwa mudziva panodonhedzwa dombo, anoda maequation akaoma kunzwisisa kuti aatsanangure. Izwi rekuti sinusoid rinoshandiswa kutsanangura masaisai akafanana neine wave. A cosine wave yakafanana nesine wave, asi nechikamu chekuchinja che π/2 radians, kana kutanga musoro. Izvi zvinotungamira kune sine wave inomira iyo cosine wave. Izwi rokuti sinusoidal rinoshandiswa pamwe chete kureva zvose sine mafungu uye cosine masaisai ane phase offset.
Kufananidzira cosine wave hukama hwakakosha kune denderedzwa mune 3D yakaoma plane modhi, iyo inogona kushandiswa kuona kukosha kwe sine mafungu mukududzira pakati penzvimbo. Iyi wave wave inoitika mumasikirwo, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anomiririra imwe chete frequency uye harmonics. Nzeve yemunhu inoona ruzha senge sine wave ine harmonics mukuwedzera kune yakakosha frequency. Izvi zvinokonzeresa mutsauko wetimbre. Chikonzero chinoridzwa mumhanzi pazviridzwa zvakasiyana chinonzwika zvakasiyana ndechekuti ruzha rwune mafungu aperiodic kuwedzera kune sine mafungu. Ruzha rweAperiodic runoonekwa seruzha, uye ruzha runoratidzwa nekuva nemaitiro asingadzokorore.
Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal zvivharo zvekuvaka zviri nyore kutsanangura uye kuita fungidziro ye periodic waveform, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana. Sine mafungu anogona zvakare kupararira pasina kushandura fomu mune akagoverwa mutsara masisitimu. Izvi zvinodikanwa kuongorora kupararira kwemafungu mumativi maviri muchadenga, uye inomiririrwa nemasaisai ane amplitude yakafanana uye frequency, asi achifamba akapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Izvi zvinoonekwa kana chinyorwa chikabvutwa patambo, uye masaisai anopindira anoratidzwa pamagumo etambo. Mafungu akamira anoitika pane mamwe mafrequency, anonzi resonant frequencies, uye anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo mazariro etambo anoenzana nehurefu hwetambo uye zvakapesana nehupamhi pahurefu hwechikamu chetambo.
Sei Sine Curve Inogona Kushandiswa Kuona Wave Pateni?
Sine wave inoenderera, yakatsvedzerera, inodzokorodza oscillation iyo inotsanangurwa nemasvomhu curve. Iyo imhando yekuenderera mberi wave inotsanangurwa neiyo trigonometric sine basa, iro rakadhindwa senge waveform. Izvo zvinoitika mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda.
Iyo sine wave ine yakajairwa frequency, inova nhamba yekutenderera kana kutenderera kunoitika mune yakapihwa huwandu hwenguva. Izvi zvinomiririrwa neangular frequency, ω, iyo yakaenzana ne 2πf, apo f iri frequency mu hertz (Hz). Sine wave inogona kuchinjwa nekufamba kwenguva, ine kukosha kwakashata kunomiririra kunonoka uye kukosha kwakanaka kunomiririra kumberi mumasekonzi.
Sine wave inowanzo shandiswa kutsanangura mafungu eruzha, sekutsanangurwa kwaanoitwa nesine function. Iyo frequency ye sine wave, f, ndiyo nhamba yekutenderera pasekondi. Izvi zvakafanana nekudzungaira kwechitubu-mass system isina kuvharwa pakuenzanisa.
Iyo sine wave yakakosha mufizikisi nekuti inochengeta chimiro chayo chewave kana yawedzerwa kune imwe sine wave yenguva imwechete uye inopokana chikamu uye ukuru. Ichi chivakwa che sine wave inozivikanwa seyo superposition musimboti uye inguva yenguva waveform pfuma. Ichi chivakwa chinotungamira mukukosha kweFourier ongororo, izvo zvinoita kuti zvikwanise kusiyanisa zvine hunyoro pakati pezvakasiyana zvenzvimbo.
Semuyenzaniso, kana x achimiririra chiyero chenzvimbo umo masaisai ari kupararira, ipapo chimiro chechimiro k, chinodaidzwa kuti wave nhamba, chinomiririra kuenzana pakati peangular frequency, ω, uye mutsara wekumhanya kwekuparadzira, ν. Wavenumber ine hukama neangular frequency uye wavelength, λ, ne equation λ = 2π/k.
Equation ye sine wave mune imwe dimension inopiwa ne y = A chivi (ωt + φ), apo A ndiyo amplitude, ω ndiyo inotenderera, t ndiyo nguva, uye φ ndiyo chikamu chekuchinja. Kana muenzaniso mumwechete wemutsara uchitariswa, ipapo kukosha kwemafungu pane chero nguva x chero nguva t inopiwa ne y = A chivi (kx - ωt + φ).
Munzvimbo dzakawanda dzenzvimbo, equation ye sine wave inopiwa ne y = A chivi (kx – ωt + φ), apo A ndiyo amplitude, k inhamba yemasaisai, x ndiyo nzvimbo, ω inguva yeangular, t. inguva, uye φ ndiyo danho rekuchinja. Iyi equation inotsanangura masaisai endege inofamba.
Kubatsira kwe sine wave hakugumiri pakududzira mumatunhu enyama. Mafungu akafanana anoitika muzvisikwa, kusanganisira mumafungu emhepo, masaisai eruzha, uye masaisai echiedza. Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anowanzo shandiswa kumiririra imwechete frequency harmonics.
Nzeve yemunhu inogona zvakare kuziva ruzha rwunoumbwa neakakosha frequency uye yakakwirira harmonics. Aya mafambiro anorira etambo anoenzana nehurefu hwetambo uye anopesana nehupamhi pahurefu hwechikamu chetambo.
Muchidimbu, izwi rekuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwe sine wave uye cosine wave. Sine wave inonzi ine phase shift ye π/2 radians, iyo yakaenzana nekutanga musoro, ukuwo cosine wave ichinzi inotungamira sine wave. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine, ane chikamu chekubvisa. Izvi zvinoratidzwa necosine wave, inova hukama hwakakosha mudenderedzwa mumhando ye 3D yakaoma plane iyo inoshandiswa kuona kubatsira kwe sine wave mukuturikira munzvimbo dzenyama.
Sine Waves uye Phase
Muchikamu chino, ini ndichave ndichiongorora hukama pakati pe sine mafungu uye chikamu. Ini ndichakurukura kuti chikamu chinokanganisa sei sine wave uye kuti inogona kushandiswa sei kugadzira akasiyana waveform. Ini ndichapawo mimwe mienzaniso kuratidza kuti chikamu chinogona kushandiswa sei mumashandisirwo akasiyana siyana.
Chii chiri Hukama pakati peSine Wave nePhase?
A sine wave inotsvedzerera, inodzokorora oscillation inoenderera uye ine imwe frequency. Iro curve yemasvomhu inotsanangurwa netrigonometric sine function, uye inowanzomiririrwa negirafu. Sine masaisai anowanikwa munzvimbo dzakawanda dzemasvomhu, fizikisi, mainjiniya, uye masaini kugadzirisa.
Iyo frequency ye sine wave inhamba yekutenderera kana kutenderera kunoitika munguva yakatarwa, uye inofananidzwa nerechigiriki vara ω (omega). Angular frequency ndiyo mwero weshanduko yenharo yebasa, uye inoyerwa mumayuniti emaradians pasekondi. Iyo isiri-yose waveform inogona kuoneka yakachinjika munguva, nechikamu chekuchinja che φ (phi) mumasekondi. A negative value inomiririra kunonoka, ukuwo value yakanaka inomiririra kumberi mumasekonzi. Kuwanda kwe sine wave kunoyerwa ne hertz (Hz).
Sine wave inowanzo shandiswa kutsanangura mafungu eruzha, sekutsanangurwa kwaanoitwa nesine function. Semuenzaniso, f = 1/T, apo T ndiyo nguva ye oscillation, uye f ndiyo frequency ye oscillation. Izvi zvakangofanana neisina kuvharwa chitubu-mass system muequilibrium.
Iyo sine wave yakakosha mufizikisi nekuti inochengeta chimiro chayo chewave kana yawedzerwa kune imwe sine wave yenguva imwechete uye inopokana chikamu uye ukuru. Ichi chivakwa chekuve periodic chivakwa chinotungamira mukukosha kwacho mukuongororwa kweFourier, izvo zvinoita kuti ive yakasarudzika.
Kana masaisai achipararira muchadenga, mutsauko wenzvimbo x unomiririra nzvimbo mune imwe dimension. Masaisai ane hunhu paramende k, inodaidzwa kuti wave nhamba, inomiririra kuenzana pakati peangular frequency ω uye mutsara wekumhanya kwekuparadzira ν. Wavenumber k ine hukama neangular frequency ω uye wavelength λ (lambda) ne equation λ = 2π/k. Iyo frequency f uye mutsara kumhanya v zvine hukama neiyo equation v = λf.
Equation ye sine wave mune imwe dimension inopiwa na y = A chivi(ωt + φ), apo A ndiyo amplitude, ω ndiyo inotenderera, t ndiyo nguva, uye φ ndiyo chikamu chekuchinja. Iyi equation inopa kutamiswa kwesaisai panzvimbo yakapihwa x uye nguva t. Muenzaniso wemutsara mumwechete unotariswa, uine kukosha kwe y = A chivi(ωt + φ) kune ese x.
Munzvimbo dzakawanda dzenzvimbo, equation yemafungu endege inofamba inopiwa ne y = A sin(kx – ωt + φ). Equation iyi inogona kududzirwa semavekita maviri mundege yakaoma kunzwisisa, uye chigadzirwa chemavekita maviri chiri chigadzirwa chedoti.
Masaisai akaomarara, semasaisai emvura mudziva kana dombo radonhedzwa, anoda mamwe maequation akaoma kunzwisisa. Izwi rokuti sinusoid rinoshandiswa kutsanangura masaisai ane hunhu hwezvose sine wave uye cosine wave. A phase shift of π/2 radians inopa cosine wave kutanga musoro, uye inonzi inotungamira sine wave. Izvi zvinoreva kuti sine wave inokandira cosine wave. Izwi rekuti sinusoidal rinowanzo shandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine, ane kana asina chikamu chinobvisa.
Kuratidzira cosine wave, hukama hwakakosha pakati pe sine wave uye cosine wave inogona kuoneswa ne 3D yakaoma plane modhi. Uyu modhi unobatsira pakuturikira wave pateni inoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai emwenje.
Nzeve yemunhu inogona kuziva masaisai eine imwe chete, inonzwika zvakajeka uye yakachena. Sine masaisai anowanzo shandiswa sezviratidziro zveimwe frequency toni, pamwe neharmonics. Nzeve yemunhu inoona ruzha senge musanganiswa wemasaisai e sine, nekuvapo kweakakwirira maharmonics mukuwedzera kune yakakosha frequency inokonzera mutsauko mutimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chine frequency yakafanana inoridzwa pazviridzwa zvakasiyana ichinzwika zvakasiyana.
Kuombera neruoko, zvisinei, kune masaisai enguva nenguva, asiri enguva nenguva uye ane maitiro asingadzokorore. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero nguva yemasaisai, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba dzenguva dzakatevedzana.
Mafungu eSine anogona kupararira mukuchinja fomu kuburikidza neakagoverwa mutsara masisitimu, uye anodiwa kuti uongorore wave wave kuparadzira. Sine masaisai anogona kufamba nemativi maviri muchadenga, uye anomiririrwa nemasaisai ane amplitude yakafanana uye frequency asi achifamba akapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Izvi zvakafanana nenoti inobvutwa patambo, apo masaisai anoratidzwa panogumira tambo. Masaisai akamira anoitika pane mamwe mafrequency, ayo anonzi maresonant frequencies. Aya ma frequency anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Iwo ma frequency eresonant etambo anoenzana nehurefu hwetambo, uye anopesana nehupamhi pahurefu hwechikamu chetambo.
Chikamu Chinobata Sei Sine Wave?
A sine wave imhando yeinoenderera mberi waveform iyo inoratidzwa nekutsetseka, inodzokorodza oscillation. Imasvomhu curve inotsanangurwa netrigonometric basa uye inoshandiswa mumasvomhu, fizikisi, mainjiniya, uye masignal processing fields. Iyo yakajairwa frequency ye sine wave nhamba yekutenderera kana kutenderera kunoitika mune yakapihwa huwandu hwenguva, kazhinji kuyerwa mumasekonzi. Angular frequency, inoratidzwa ne ω, chiyero cheshanduko yenharo yebasa, inowanzoyerwa mumaradians. Iyo isiri-yakazara waveform inoratidzika yakachinjika munguva nehuwandu φ, yakayerwa mumasekonzi. Iyo unit of frequency is hertz (Hz), iyo yakaenzana neoscillation imwe pasekondi.
Sine wave inowanzoshandiswa kurondedzera ruzha rwemasaisai, uye inotsanangurwa neine basa, f(t) = Chivi (ωt + φ). Iri rudzi rwe waveform rinoonekwa zvakare mune isina kuvharwa chitubu-mass system pakuenzanisa. Sine masaisai akakosha mufizikisi nekuti anochengeta wave wave shape kana awedzerwa pamwechete, inova pfuma inozivikanwa se superposition musimboti. Ichi chivakwa chinotungamira mukukosha kweFourier ongororo, iyo inoita kuti zvikwanise kusiyanisa zvine ruzha kusiyanisa inzwi kubva kune rimwe.
Muchidimbu chimwe chete, sine wave inogona kumiririrwa nemutsara mumwechete. Semuenzaniso, kukosha kwemafungu patambo kunogona kumiririrwa nemutsara mumwe chete. Pamatanho akawanda enzvimbo, equation yakajairika inodiwa. Iyi equation inotsanangura kutamiswa kwemafungu pane imwe nzvimbo, x, pane imwe nguva, t.
Masaisai akaomarara, semafungu emvura mudziva mushure mekunge dombo radonhedzwa, anoda mamwe maequation akaomarara. Izwi rekuti sinusoid rinoshandiswa kutsanangura waveform ine hunhu hweese sine wave uye cosine wave. Kuchinja kwechikamu che π/2 radians kwakafanana nekutanga musoro, uye zvakangofanana nekutaura kuti basa re cosine rinotungamira basa resine, kana kuti sine inorasira cosine. Izwi rekuti sinusoidal rinoshandiswa kureva pamwe chete kune ese mafungu ane sine uye mafungu ecosine ane chikamu chekubvisa.
Kuenzanisira cosine wave, hukama hwakakosha pakati pesine wave uye cosine wave hunogona kuoneswa pachishandiswa denderedzwa mune ye3D yakaoma plane modhi. Izvi zvinobatsira pakuturikira pakati penzvimbo dzakasiyana, semasaisai akafanana anoitika muzvisikwa, kusanganisira masaisai emhepo, masaisai eruzha, uye masaisai echiedza.
Nzeve yemunhu inokwanisa kuona mafungu ane sine seanonzwika zvakajeka, uye sine mafungu anowanzo shandiswa kumiririra imwe chete ma frequency uye harmonics. Kana masaisai akasiyana-siyana akawedzerwa pamwe chete, iyo waveform inoguma inoshanduka, inoshandura timbre yeruzha. Kuvapo kweakakwira maharmonics mukuwedzera kune yakakosha frequency kukonzeresa mutsauko wetimbre. Ichi ndicho chikonzero nei chinyorwa chemimhanzi chinoridzwa pazviridzwa zvakasiyana chichinzwika zvakasiyana.
Ruzha rwekuombera ruoko rune masaisai aperiodic, asiri enguva nenguva, kusiyana neine masaisai, ayo ari periodic. Nyanzvi yemasvomhu yekuFrance Joseph Fourier akawana kuti masaisai e sinusoidal ndiwo mabhuroko ekuvakisa ari nyore anogona kushandiswa kutsanangura uye kufungidzira chero masaisai enguva nenguva, kusanganisira masikweya masaisai. Fourier ongororo chishandiso chine simba chekuongorora chinoshandiswa kudzidza masaisai, sekuyerera kwekushisa, uye chinowanzoshandiswa mukugadzirisa zviratidzo uye kuongororwa kwenhamba yenguva dzakatevedzana.
Sine masaisai anogona kupararira mukuchinja mafomu kuburikidza akagoverwa mutsara masisitimu. Kuongorora kupararira kwemafungu, masaisai esine anofamba nenzira dzakasiyana muchadenga anomiririrwa nemasaisai ane amplitude yakafanana uye frequency, asi achifamba akapesana. Kana masaisai aya akadarika, patani yemafungu akamira inogadzirwa. Iyi ndiyo patani imwe chete inogadzirwa kana chinyorwa chikabvutwa patambo. Kupindira masaisai anotaridzwa kubva kumagumo etambo anogadzira masaisai akamira anoitika pane mamwe mafrequency, anonzi maresonant frequencies. Aya ma frequency resonant anoumbwa neiyo yakakosha frequency uye yakakwirira harmonics. Mafambiro anoita tambo anoenzana nehurefu hwetambo uye anoenzana neskweya mudzi wehuremu pahurefu hwechikamu chetambo.
Chikamu Chinogona Kushandiswa Sei Kugadzira Akasiyana Waveforms?
Sine waves imhando yekuenderera mberi waveform iyo yakatsetseka uye inodzokororwa, uye inogona kushandiswa kutsanangura zvakasiyana-siyana zvezviitiko mumasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Iwo anotsanangurwa ne trigonometric basa, uye anogona kudhirowa seyakatsetseka, periodic curve. Iyo frequency ye sine wave inhamba yekutenderera kana kutenderera kunoitika munguva yakatarwa, kazhinji kuyerwa muHertz (Hz). Angular frequency, ω, chiyero chinoshanduka chiito nharo, yakayerwa mumaradians pasekondi. Sine wave inogona kuoneka yakachinjika munguva, nechikamu chekuchinja, φ, kuyerwa mumasekonzi. A negative value inomiririra kunonoka, ukuwo positive value inomiririra kumberi.
Phase chinhu chakakosha chesine wave, uye inogona kushandiswa kugadzira akasiyana waveform. Kana maviri sine mafungu ane frequency yakafanana uye nhanho yenhanho uye ukuru zvakabatanidzwa, iyo inoguma waveform ndeye periodic waveform ine chivakwa chimwe chete. Ichi chivakwa chinotungamira mukukosha kweFourier ongororo, iyo inoita kuti zvikwanise kuziva uye kuongorora masaini akasarudzika akasarudzika.
Phase inogona kushandiswa kugadzira akasiyana waveform nenzira dzinotevera:
• Nekushandura chikamu che sine wave, inogona kuitwa kuti itange pane imwe nzvimbo munguva. Izvi zvinozivikanwa sechikamu chekuchinja, uye chinogona kushandiswa kugadzira akasiyana waveform.
• Nekuwedzera sine wave ine frequency yakasiyana uye chikamu kune yakakosha sine wave, yakaoma waveform inogona kugadzirwa. Izvi zvinozivikanwa seharmonic, uye zvinogona kushandiswa kugadzira akasiyana siyana.
• Nekubatanidza sine mafungu ane mafrequency akasiyana uye zvikamu, chimiro chekumira chinogona kugadzirwa. Izvi zvinozivikanwa seresonant frequency, uye inogona kushandiswa kugadzira manzwi akasiyana.
• Nekubatanidza sine mafungu ane mafrequency akasiyana uye zvikamu, yakaoma waveform inogona kugadzirwa. Izvi zvinozivikanwa seFourier ongororo, uye inogona kushandiswa kuongorora wave kuparadzira.
Nekushandisa chikamu kugadzira akasiyana waveforms, zvinokwanisika kugadzira akasiyana manzwi uye kuongorora wave kupararira. Ichi chinhu chakakosha chesine mafungu, uye chinoshandiswa munzvimbo dzakasiyana siyana, kusanganisira acoustics, chiratidzo chekugadzirisa, uye fizikisi.
Ndiani Anoshandisa Sine Waves Mumisika?
Semunhu anodyara mari, ndine chokwadi chekuti wakanzwa nezve sine mafungu uye basa ravo mumisika yemari. Muchinyorwa chino, ndichave ndichiongorora kuti sine mafungu chii, mashandisirwo aanogona kuita kufanotaura, uye hukama pakati pemafungu e sine uye ongororo yehunyanzvi. Pakupera kwechinyorwa chino, iwe unenge wave nekunzwisisa zvirinani kuti sine mafungu anogona kushandiswa sei kune mukana wako mumisika.
Ndeipi Basa reSine Waves muMarike Marike?
Sine waves imhando yemasvomhu curve inotsanangura kutsvedzerera, kudzokororwa oscillations mune inoenderera mberi wave. Iwo anonziwo sinusoidal mafungu uye anoshandiswa mumasvomhu, fizikisi, mainjiniya, uye masaini ekugadzirisa minda. Sine mafungu akakosha mumisika yemari, sezvo anogona kushandiswa kufanotaura uye kuongorora maitiro.
Mumisika yemari, sine mafungu anoshandiswa kuona uye kuongorora mafambiro. Iwo anogona kushandiswa kuona tsigiro uye nhanho dzekupokana, pamwe nekuona anogona kupinda nekubuda mapoinzi. Sine masaisai anogonawo kushandiswa kuona uye kuongorora mapatani, akadai semusoro nemapfudzi, matop maviri uye pasi, uye mamwe machati mapatani.
Sine mafungu anoshandiswawo mukuongorora kwehunyanzvi. Kuongorora kwehunyanzvi ndiko kudzidza kwekufamba kwemitengo uye mapatani mumisika yemari. Vaongorori vehunyanzvi vanoshandisa sine mafungu kuona mafambiro, tsigiro uye mazinga ekupikisa, uye anogona kupinda nekubuda mapoinzi. Ivo zvakare vanoshandisa sine mafungu kuona mapatani, akadai semusoro nemapfudzi, maviri kumusoro uye pasi, uye mamwe machati mapatani.
Sine masaisai anogonawo kushandiswa kufanotaura. Nekuongorora zvakaitika kare uye zvazvino, vaongorori vehunyanzvi vanogona kuita kufanotaura nezvekufamba kwemitengo yeramangwana. Nekuongorora iyo sine mafungu, vanogona kuona inogona kupinda nekubuda mapoinzi, pamwe nerutsigiro rwunogoneka uye nhanho dzekuramba.
Sine mafungu chinhu chakakosha chevashandi vehunyanzvi mumisika yemari. Iwo anogona kushandiswa kuona uye kuongorora mafambiro, tsigiro uye nhanho dzekuramba, uye anogona kupinda nekubuda mapoinzi. Dzinogonawo kushandiswa kuita fungidziro pamusoro pekufamba kwemutengo mune ramangwana. Nekuongorora iyo sine mafungu, vaongorori vehunyanzvi vanogona kuwana kunzwisisa kuri nani kwemisika uye kuita sarudzo dzine ruzivo.
Sei Mafungu eSine Anogona Kushandiswa Kuita Kufanotaura?
Sine mafungu anoshandiswa mumisika yemari kuongorora mafambiro uye kufanotaura. Iwo rudzi rwemasaisai anotenderera pakati pemapoinzi maviri, uye anogona kushandiswa kuona mapatani uye maitiro mumisika. Sine mafungu anoshandiswa mukuongorora kwehunyanzvi uye anogona kushandiswa kufanotaura mafambiro emutengo wemangwana.
Heano dzimwe nzira idzo sine mafungu anogona kushandiswa mumisika:
• Kuziva tsigiro uye nhanho dzekupokana: Sine masaisai anogona kushandiswa kuona rutsigiro uye nhanho dzekupokana mumisika. Nekutarisa panhongonya uye zvimwiro zve sine wave, vatengesi vanogona kuona nzvimbo uko mutengo unogona kuwana rutsigiro kana kuramba.
• Kuziva maitiro ekudzokera shure: Nekutarisa kune sine wave, vatengesi vanogona kuona zvinogona kuitika maitiro ekuchinja. Kana iyo sine wave ichiratidza kudzikira, vatengesi vanogona kutsvaga nzvimbo dzinogona kutsigirwa uko maitiro anogona kudzoka.
• Kuziva maitiro emitengo: Mafungu eSine anogona kushandiswa kuona maitiro emitengo mumisika. Nekutarisa kune sine wave, vatengesi vanogona kuona dzingangove nzvimbo dzekutsigirwa uye kuramba, pamwe neangangove maitiro ekuchinja.
• Kuita kufanotaura: Nekutarisa kune sine wave, vatengesi vanogona kufanotaura nezvekufamba kwemutengo mune ramangwana. Nekutarisa panhongonya uye zvimwiro zve sine wave, vatengesi vanogona kuona nzvimbo dzinogona kutsigirwa uye kuramba, pamwe neangango chinja maitiro.
Sine mafungu anogona kuve chishandiso chinobatsira kune vatengesi vanotarisa kuita mafungidziro mumisika. Nekutarisa kune sine wave, vatengesi vanogona kuona dzingangove nzvimbo dzekutsigirwa uye kuramba, pamwe neangangove maitiro ekuchinja. Nekushandisa sine mafungu, vatengesi vanogona kuita sarudzo dzine ruzivo nezve kutengeserana kwavo uye kuwedzera mikana yavo yekubudirira.
Chii chiri Hukama pakati peSine Waves uye technical Analysis?
Sine mafungu anoshandiswa mumisika yemari kuongorora maitiro emitengo uye kufanotaura nezvekufamba kwemitengo kweramangwana. Iwo anoshandiswa nevaongorori vehunyanzvi kuona mafambiro, tsigiro uye nhanho dzekupikisa, uye kuona zvinogona kupinda nekubuda.
Sine waves imhando ye periodic waveform, zvichireva kuti anodzokorora nekufamba kwenguva. Iwo anoratidzirwa nekutsvedzerera, kudzokorora oscillation uye anoshandiswa kutsanangura zvakasiyana-siyana zvezviitiko mumasvomhu, fizikisi, engineering, uye chiratidzo chekugadzirisa. Mumisika yemari, sine mafungu anoshandiswa kuona kudzokorora mapatani mukufamba kwemitengo.
Hukama huri pakati pe sine mafungu uye ongororo yehunyanzvi ndeyekuti sine mafungu anogona kushandiswa kuona anodzokorora mapatani mukufamba kwemitengo. Vaongorori vehunyanzvi vanoshandisa sine mafungu kuona mafambiro, tsigiro uye nhanho dzekuramba, uye kuona zvinogona kupinda nekubuda.
Sine mafungu anogona zvakare kushandiswa kuita fungidziro nezve remangwana mutengo mafambiro. Nekuongorora maitiro ekare emitengo, vaongorori vehunyanzvi vanogona kuona kudzokorora mapatani uye kushandisa mapatani aya kuita fungidziro nezvekufamba kwemutengo mune ramangwana.
Sine masaisai anoshandiswawo kuona kutenderera mumisika. Nekuongorora maitiro emitengo nekufamba kwenguva, vaongorori vehunyanzvi vanogona kuona kudzokorora kutenderera uye kushandisa aya madhigirii kuita fungidziro pamusoro pekufamba kwemutengo mune ramangwana.
Muchidimbu, sine mafungu anoshandiswa mumisika yemari kuongorora maitiro emitengo uye kuita fungidziro pamusoro pekufamba kwemutengo mune ramangwana. Iwo anoshandiswa nevaongorori vehunyanzvi kuona mafambiro, tsigiro uye nhanho dzekupikisa, uye kuona zvinogona kupinda nekubuda. Mafungu eSine anogona zvakare kushandiswa kuita fungidziro pamusoro pekufamba kwemitengo yeramangwana nekuongorora maitiro ekare emitengo uye kuona kudzokorora mapatani nematenderedzwa.
Kusiyana
Sine wave vs simulated sine wave
Sine Wave vs Simulated Sine Wave:
• Sine wave ndiyo inoenderera mberi waveform inotevera sinusoidal pattern uye inoshandiswa mumasvomhu, physics, engineering, uye signal processing.
• Simulated sine wave is an artificial waveform yakagadzirwa nemagetsi inverter kutevedzera maitiro e sine wave.
• Sine masaisai ane kamwe chete frequency uye chikamu, nepo simulated sine mafungu ane akawanda frequencies uye zvikamu.
• Sine masaisai anoshandiswa kumiririra masaisai anonzwika uye mamwe marudzi esimba, nepo simulated mafungu emagetsi anoshandiswa kugonesa midziyo yemagetsi.
• Sine mafungu anogadzirwa neakasikwa masosi, nepo simulated sine mafungu anogadzirwa nemagetsi inverters.
• Sine masaisai anoshandiswa muFourier ongororo yekudzidza kuparadzirwa kwemasaisai, nepo simulated masaisai achishandiswa kugonesa midziyo yemagetsi.
• Sine masaisai anoshandiswa kumiririra mafungu eruzha, nepo simulated mafungu emagetsi anoshandiswa kugonesa midziyo yemagetsi.
FAQ nezve sine wave
Chadenga isimbi wave here?
Aiwa, chisiko chapose pose hachisi chine wave. A sine wave igoko remasvomhu rinotsanangura kutsetseka, kudzokororwa kudzokororwa, uye iine waveform inoenderera ine frequency imwe chete. Chadenga, zvisinei, igadziriro yakaomarara uye ine simba inogara ichichinja uye ichichinja.
Chadenga chinoumbwa nezvinhu zvakawanda zvakasiyana-siyana, zvinosanganisira zvinhu, simba, uye nguva yechadenga. Izvi zvikamu zvinopindirana nenzira dzakasiyana-siyana, zvichiita kuti pave nezviitiko zvakasiyana-siyana, kubva pakuumbwa kwemapoka enyeredzi kusvika pakushanduka kwehupenyu. Chadenga chinodzorwawo nemitemo yefizikisi, iyo yakavakirwa pakuenzanisa kwemasvomhu.
Chadenga hachisi chine wave, asi chine masaisai mazhinji. Inga muezaniso, masaisai eruzha isimbi masaisai, uye aripo muchadenga. Masaisai echiedza ndiwo mafungu ane simba, uye aripo muchadenga. Pamusoro pezvo, muchadenga mune mamwe marudzi mazhinji emasaisai, akadai semagetsi emagetsi, masaisai egiravhiti, uye masaisai equantum.
Chadenga chinoumbwawo nezvimedu zvakawanda zvakasiyana, zvakadai semapurotoni, manyuturoni, uye maerekitironi. Zvimedu izvi zvinodyidzana nenzira dzakasiyana-siyana, zvichiita kuti pave nezviitiko zvakasiyana-siyana, kubva pakuumbwa kwemaatomu kusvika pakushanduka kwenyeredzi.
Mukupedzisa, denga harisi sine wave, asi rine akawanda masaisai. Aya ma-sine mafungu aripo nenzira yemafungu eruzha, masaisai echiedza, uye mamwe marudzi emasaisai. Chadenga chinoumbwawo nezvimedu zvakawanda zvakasiyana zvinodyidzana nenzira dzakasiyana-siyana, zvichiita kuti pave nezviitiko zvakasiyana-siyana.
Hukama hwakakosha
Amplitude:
• Amplitude ndiyo yakanyanya kutamiswa ye sine wave kubva panzvimbo yayo yakaenzana.
• Inopimwa nezvikamu zvechinhambwe, semamita kana tsoka.
• Iyo inobatanawo nesimba remafungu, nepamusoro amplitudes ane simba rakawanda.
• The amplitude ye sine wave inoenzana neskweya mudzi we frequency yayo.
• Iyo amplitude ye sine wave inoenderanawo nechikamu chayo, nepamusoro amplitudes ine chikamu chikuru chekuchinja.
Frequency Response:
• Frequency mhinduro ndiyo chiyero chekuti system inopindura sei kune akasiyana mafrequency ekupinda.
• Inowanzoyerwa mumadecibels (dB) uye chiyero chekuwana kana kuderedzwa kwegadziriro panguva dzakasiyana-siyana.
• Iyo frequency mhinduro ye sine wave inotarwa neamplitude yayo uye chikamu.
• Sine wave ine amplitude yakakwirira ichava nepamusoro pefrequency mhinduro pane imwe ine yakaderera amplitude.
• Mhinduro yenguva yakawanda ye sine wave inobatwawo nechikamu chayo, nezvikamu zvepamusoro zvinoguma nepamusoro-soro mhinduro.
Sawtooth:
• Sawtooth wave imhando ye periodic waveform ine kusimuka kwakapinza uye kudonha zvishoma nezvishoma.
• Inowanzoshandiswa mumutauro wezwi uye inoshandiswawo mune mamwe marudzi ekugadzirisa zviratidzo zvemadhijitari.
• The sawtooth wave yakafanana nesine wave pakuti iri periodic waveform, asi ine chimiro chakasiyana.
• The sawtooth wave ine kukwira kwakanyanya uye kudonha zvishoma nezvishoma, nepo sine wave ine kusimuka zvishoma nezvishoma uye zvishoma nezvishoma kudonha.
• Iyo sawtooth wave ine yakakwirira frequency mhinduro kupfuura sine wave, uye inowanzo shandiswa mukuteerera synthesis kugadzira ruzha rwakanyanya.
• Iyo sawtooth wave inoshandiswawo mune mamwe marudzi edhijitari masaini ekugadzirisa, akadai se frequency modulation uye phase modulation.
mhedziso
Sine mafungu chikamu chakakosha chefizikisi, masvomhu, engineering, chiratidzo chekugadzirisa, uye mamwe akawanda minda. Iwo imhando yemafungu anoenderera ane kutsetseka, kudzokorodza oscillation, uye anowanzoshandiswa kutsanangura masaisai eruzha, masaisai emwenje, uye mamwe masaisai. Sine masaisai akakoshawo pakuongorora kweFourier, izvo zvinoita kuti ive acoustically akasiyana uye inobvumira kuti ishandiswe mukusiyana kwenzvimbo. Kunzwisisa sine mafungu kunogona kutibatsira kunzwisisa zviri nani kupararira kwemafungu, kugadzirisa chiratidzo, uye nguva yekuongorora.
Ini ndini Joost Nusselder, muvambi weNeaera uye mushambadzi wemukati, baba, uye ndinoda kuyedza michina mitsva ine gitare pamoyo pechido changu, uye pamwe nechikwata changu, ndanga ndichigadzira zvakadzama zvinyorwa zveblog kubva 2020. kubatsira vaverengi vakavimbika nekurekodha nemagitare.
