Sine wave wani nau'in igiyar igiyar ruwa ne mai ci gaba da maimaita kansa kowane radiyo 2π, ko digiri 360, kuma ana iya amfani da shi don ƙira yawancin abubuwan al'ajabi. Hakanan ana kiran igiyar sine da sinusoid.
Kalmar sine wave ta samo asali ne daga aikin sine na lissafi, wanda shine tushen tsarin igiyar ruwa. Sine wave yana ɗaya daga cikin mafi sauƙi nau'ikan igiyoyin igiyar ruwa kuma ana amfani da su sosai a fagage da yawa.
A cikin wannan labarin, zan bayyana abin da sine wave yake da kuma dalilin da yasa yake da ƙarfi sosai.
Menene sine wave?
Sine Wave shine santsi, maimaituwar oscillation a cikin nau'in igiyar ruwa mai ci gaba. Yana da lanƙwan lissafi wanda aka ayyana cikin sharuddan aikin trigonometric sine, kuma ana wakilta ta a hoto azaman siffar igiyar ruwa. Wani nau'in igiyar igiyar ruwa ce mai ci gaba da ke da santsi, aiki na lokaci-lokaci, kuma ana samunsa a fannoni da yawa na lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina.
The mita na sine wave shine adadin oscillations ko zagayowar da ke faruwa a cikin wani adadin lokaci. Mitar angular, wanda ω ke nunawa, shine ƙimar canjin hujjar aikin, kuma ana auna shi cikin raka'a na radians a sakan daya. Ƙimar da ba ta sifili ba na ƙayyadaddun lokaci, wanda φ ke nuni da shi, yana wakiltar motsi a cikin dukan tsarin igiyar ruwa a cikin lokaci, tare da ƙima mara kyau na wakiltar jinkiri, da ƙima mai kyau yana wakiltar ci gaba a cikin daƙiƙa. Ana auna mitar kalaman sine a cikin hertz (Hz).
Ana amfani da igiyar sine don siffanta igiyar sauti, kuma ana siffanta ta da aikin sine, f(t) = A sin (ωt + φ). Hakanan ana amfani da ita don kwatanta tsarin ma'aunin bazara da ba a tauyewa ba a cikin ma'auni, kuma shi ne siffa mai mahimmanci a fannin kimiyyar lissafi yayin da yake riƙe da siffar igiyar igiyar sa idan aka ƙara shi zuwa wani igiyar igiyar ruwa mai mitar iri ɗaya da lokaci na sabani da girma. An san wannan kadarar da ƙa'idar babban matsayi, kuma dukiya ce ta lokaci-lokaci. Wannan kadarar tana kaiwa ga mahimmancin bincike na Fourier, saboda yana ba da damar iya bambanta madaidaicin sarari, x, wanda ke wakiltar matsayi a cikin girma ɗaya wanda igiyar ke yaduwa.
Siffar sifa ta igiyoyin igiyar ruwa ana kiranta lambar igiyar ruwa, k, wacce ita ce lambar igiyar angular kuma tana wakiltar daidaito tsakanin mitar angular, ω, da saurin yaduwa na layi, ν. Lambar igiyar ruwa tana da alaƙa da mitar angular da tsayin igiyar ruwa, λ, ta ma'auni λ = 2π/k. An ba da ƙididdiga don igiyar sine a cikin girma ɗaya ta y = A zunubi (ωt + φ). An ba da ƙarin ma'auni na gaba ɗaya ta y = A sin (kx – ωt + φ), wanda ke ba da ƙaurawar igiyar ruwa a matsayi x a lokaci t.
Hakanan za'a iya wakilta raƙuman raƙuman ruwa a wurare da yawa. An ba da ƙididdiga don igiyar jirgin sama mai tafiya ta y = A sin (kx – ωt + φ). Ana iya fassara wannan a matsayin ɗigo samfurin vector guda biyu, kuma ana amfani da shi don kwatanta hadadden igiyoyin ruwa, kamar igiyar ruwa a cikin tafki lokacin da aka jefa dutse. Ana buƙatar ƙarin hadaddun ma'auni don bayyana kalmar sinusoid, wanda ke bayyana halayen raƙuman ruwa na duka sine da raƙuman ruwa tare da canjin lokaci na π/2 radians, wanda ke ba wa igiyar cosine damar fara kan igiyar sine. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da na cosine tare da kashe lokaci.
Ana samun raƙuman ruwa a yanayi, gami da raƙuman ruwa, raƙuman sauti, da raƙuman haske. Kunnen mutum yana iya gane raƙuman sine guda ɗaya a matsayin sauti a sarari, kuma ana amfani da igiyoyin sine don wakiltar mitar guda ɗaya da jituwa. Kunnen mutum yana jin sauti a matsayin haɗuwa da raƙuman ruwa na sine tare da amplitudes daban-daban da mitoci daban-daban, kuma kasancewar mafi girma masu jituwa ban da mahimmancin mahimmanci yana haifar da bambanci a cikin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa tare da mita iri ɗaya da aka kunna akan kayan kida daban-daban ya bambanta.
Sautin tafa hannu yana ƙunshe da raƙuman ruwa na lokaci-lokaci, waɗanda ba su da maimaitawa a yanayi, kuma ba sa bin tsarin igiyar igiyar ruwa. Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffantawa da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci. Ana amfani da raƙuman ruwa don yaɗawa da canza tsari a cikin tsarin layi mai rarraba.
Menene tarihin raƙuman ruwa?
Gudun sine yana da dogon tarihi mai ban sha'awa. Masanin lissafi na Faransa Joseph Fourier ne ya fara gano shi a shekara ta 1822, wanda ya nuna cewa duk wani nau'in igiyar ruwa na lokaci-lokaci ana iya wakilta shi azaman jimlar raƙuman ruwa. Wannan binciken ya kawo sauyi a fannin lissafi da kimiyyar lissafi kuma tun daga lokacin ake amfani da shi.
• Masanin lissafi na Jamus Carl Friedrich Gauss ya ƙara haɓaka aikin Fourier a cikin 1833, wanda ya nuna cewa za a iya amfani da igiyoyin sine don wakiltar kowane nau'in motsi na lokaci-lokaci.
• A ƙarshen karni na 19, an yi amfani da sine wave don kwatanta halayen da'irar lantarki.
• A farkon karni na 20, an yi amfani da sine wave don kwatanta halayen raƙuman sauti.
• A cikin 1950s, an yi amfani da sine wave don kwatanta halayen raƙuman haske.
• A cikin 1960s, an yi amfani da sine wave don kwatanta halayen raƙuman rediyo.
• A cikin 1970s, an yi amfani da sine wave don kwatanta halayen siginar dijital.
• A cikin 1980s, an yi amfani da sine wave don kwatanta halayen igiyoyin lantarki.
• A cikin 1990s, an yi amfani da sine wave don kwatanta halayen tsarin injin ƙira.
• A yau, ana amfani da sine wave a fannoni daban-daban, ciki har da lissafi, kimiyyar lissafi, injiniyanci, sarrafa sigina, da sauransu. Kayan aiki ne mai mahimmanci don fahimtar halayen raƙuman ruwa kuma ana amfani dashi a aikace-aikace iri-iri, daga sarrafa sauti da bidiyo zuwa hoto na likita da na'ura mai kwakwalwa.
Sine Wave Mathematics
Zan yi magana ne game da raƙuman ruwa na sine, lanƙwan lissafin lissafi wanda ke bayyana santsi, maimaita oscillation. Za mu dubi yadda aka ayyana raƙuman ruwa, alakar da ke tsakanin mitar kusurwa da lambar igiyar ruwa, da menene bincike na Fourier. Za mu kuma bincika yadda ake amfani da raƙuman ruwa a cikin kimiyyar lissafi, injiniyanci, da sarrafa sigina.
Menene Sine Wave?
Sine wave wani santsi ne, maimaituwar oscillation wanda ke haifar da ci gaba da igiyar ruwa. Yana da lanƙwan lissafi, wanda aikin trigonometric sine ya siffanta, kuma galibi ana ganinsa a cikin jadawalai da sifofi. Wani nau'in igiyar ruwa ce mai ci gaba, ma'ana aiki ne mai santsi, aiki na lokaci-lokaci wanda ke faruwa a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina.
Sine wave yana da mitar talakawa, wanda shine adadin juzu'i ko zagayowar da ke faruwa a cikin ƙayyadadden lokaci. Ana wakilta wannan da mitar angular, ω, wanda yayi daidai da 2πf, inda f shine mitar a cikin hertz (Hz). Hakanan za'a iya canza igiyar sine a cikin lokaci, tare da ƙima mara kyau tana wakiltar jinkiri da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Ana amfani da igiyar sine sau da yawa don kwatanta igiyar sauti, kamar yadda aikin sine ke siffanta shi. Hakanan ana amfani da ita don wakiltar tsarin yawan ruwan bazara a ma'auni. Sine wave wani muhimmin ra'ayi ne a cikin ilimin kimiyyar lissafi, yayin da yake riƙe da siffar igiyar ruwa lokacin da aka ƙara shi zuwa wani sine na mita iri ɗaya da lokaci na sabani da girma. Wannan kadarorin, wanda aka sani da ƙa'idar babban matsayi, shine abin da ke haifar da mahimmancin bincike na Fourier, saboda yana ba da damar bambance tsakanin masu canjin sararin samaniya.
Ma'auni don igiyar sine a cikin nau'i ɗaya yana ba da y = A zunubi (ωt + φ), inda A shine girman girman, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Misalin layi daya, idan ana la'akari da darajar igiyar waya a matsayin waya, to, ana ba da ma'auni don igiyar sine a cikin ma'auni guda biyu ta y = A sin (kx - ωt + φ), inda k shine igiyar ruwa. lamba. Ana iya fassara wannan azaman samfurin vector biyu, samfurin digo.
Hadaddiyar raƙuman ruwa, kamar waɗanda aka ƙirƙira lokacin da aka jefa dutse a cikin tafki, suna buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don siffanta igiyar ruwa tare da halayen duka igiyoyin sine da igiyar cosine. Canjin lokaci na π/2 radians, ko farkon farawa, an ce yana ba da igiyar ruwan cosine, wanda ke jagorantar sine wave. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci.
Nuna kalaman cosine na iya taimakawa wajen nuna ainihin alaƙar da'irar da ƙirar jirgin sama mai rikitarwa na 3D, wanda zai iya taimakawa wajen hango fa'idar fa'idar igiyar ruwa a cikin fassarar tsakanin yanki. Wannan ƙirar igiyar ruwa tana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum yana iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma ana iya ganin alamun raƙuman raƙuman raƙuman ruwa na mitoci guda ɗaya.
Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girma masu jituwa ban da mahimmancin mahimmanci shine abin da ke haifar da bambancin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa da aka kunna akan kayan kida daban-daban ya bambanta.
Kunnen mutum yana jin sauti kamar na lokaci-lokaci da na lokaci-lokaci. Sautin lokaci-lokaci yana kunshe da raƙuman ruwa na sine, yayin da ake jin sautin lokaci a matsayin hayaniya. Ana siffanta surutu azaman lokaci mai tsawo, saboda yana da tsarin da ba ya maimaitawa.
Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffantawa da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina, da ƙididdigar ƙididdiga na jerin lokaci. Raƙuman raƙuman ruwa na iya yaduwa ta hanyar canza salo a cikin tsarin layin layi da aka rarraba.
Raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman ruwa masu girma da mitoci iri ɗaya. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa ta tsaye, kamar yadda ake gani lokacin da aka tsinke rubutu akan igiya. Raƙuman ruwa masu tsaka-tsaki waɗanda ke nunawa daga ƙayyadaddun wuraren ƙarshen kirtani suna haifar da raƙuman ruwa na tsaye, waɗanda ke faruwa a wasu mitoci da aka sani da mitoci masu faɗa. Waɗannan sun haɗa da mitar asali da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa, kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Ta yaya ake ayyana Sine Wave?
igiyar ruwa mai santsi mai santsi ce, maimaituwar jujjuyawar sifa mai ci gaba. An bayyana shi da lissafi azaman aikin trigonometric, kuma an zana shi azaman sinusoid. Sine wave wani muhimmin ra'ayi ne a ilimin kimiyyar lissafi, yayin da yake riƙe da siffar igiyar ruwa lokacin da aka ƙara shi zuwa wasu raƙuman ruwa iri ɗaya da girman lokaci na sabani. An san wannan kadarar a matsayin ka'idar babban matsayi, kuma tana kaiwa ga mahimmancinta a cikin bincike na Fourier.
Ana samun raƙuman ruwa a wurare da yawa na lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Ana siffanta su da mitar su, adadin oscillations ko zagayowar da ke faruwa a cikin wani lokaci da aka bayar. Mitar angular, ω, ita ce ƙimar canjin aikin muhawara a cikin radians a sakan daya. Ƙimar da ba ta sifili ba na φ, ƙayyadaddun lokaci, yana wakiltar motsi a cikin dukan tsarin raƙuman ruwa a cikin lokaci, tare da ƙima mara kyau yana wakiltar jinkiri, da ƙima mai kyau yana wakiltar gaba a cikin dakika.
A cikin sauti, ana siffanta igiyar sine ta equation f = ω/2π, inda f shine mitar oscillations, kuma ω shine mitar angular. Wannan ma'auni kuma ana amfani da shi ga tsarin ma'aunin bazara wanda ba shi da tushe a cikin ma'auni. Sine waves suma suna da mahimmanci a cikin acoustics, domin su ne kawai nau'in igiyar ruwa da kunnen ɗan adam ke ɗauka a matsayin mitar guda ɗaya. Sine igiyar ruwa guda ɗaya ta ƙunshi mitoci na asali da mafi girman jituwa, waɗanda duk ana fahimtar su azaman bayanin kula iri ɗaya.
Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girma masu jituwa ban da mahimmancin mahimmanci shine abin da ke haifar da bambancin timbre. Wannan shi ne dalilin da ya sa wannan bayanin kula na kiɗan da aka kunna akan kayan kida daban-daban ya bambanta. Tafa hannu, alal misali, yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, waɗanda ba su maimaituwa ba, ban da igiyoyin sine.
A farkon karni na 19, masanin lissafin Faransa Joseph Fourier ya gano cewa ana iya amfani da raƙuman ruwa na sinusoidal azaman tubalan gini masu sauƙi don siffanta da kusan kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier shine kayan aikin nazari mai ƙarfi da ake amfani da shi don nazarin raƙuman ruwa a cikin kwararar zafi da sarrafa sigina, da kuma ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa ta kowace hanya a sararin samaniya, kuma ana wakilta su da raƙuman ruwa masu girma, mita, da tafiya ta wurare dabam-dabam. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan lamari ne guda ɗaya wanda ke faruwa lokacin da aka zazzage bayanin kula akan igiya, tare da raƙuman ruwa masu tsaka-tsaki suna nunawa a madaidaiciyar wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci masu faɗakarwa, waɗanda suka ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa, kuma sun yi daidai da tushen murabba'in ta kowace raka'a.
A taƙaice, ana amfani da kalmar sinusoid don bayyana halayen raƙuman ruwa na biyun sine da raƙuman ruwa, tare da jujjuyawar lokaci na π/2 radians, ma'ana igiyar igiyar ruwa tana da farkon farawa kuma igiyar sine tana baya. Kalmar sinusoidal ana amfani da ita gaba ɗaya don komawa ga raƙuman ruwa na sine da cosine tare da kashe lokaci. Ana misalta wannan ta hanyar kalaman cosine a cikin hoton da ke sama. Ana iya ganin wannan muhimmiyar alaƙar da ke tsakanin sine da cosine ta amfani da tsarin jirgin sama mai rikitarwa na 3D, wanda ke ƙara nuna fa'idar fassarar waɗannan ra'ayoyin a cikin yankuna daban-daban. Tsarin igiyar ruwa yana faruwa a yanayi, gami da iska, sauti, da raƙuman haske.
Menene Alakar Tsakanin Mitar Angular da Lambar Wave?
Sine wave wani lanƙwan lissafi ne wanda ke bayyana santsi, maimaituwar oscillation. Raƙuman ruwa ne mai ci gaba, wanda kuma aka sani da igiyar ruwa ta sinusoidal ko sinusoid, kuma an bayyana shi cikin sharuddan aikin sine na trigonometric. Jadawalin raƙuman ruwa na sine yana nuna sifar igiyar igiyar igiyar ruwa wacce ke jujjuyawa tsakanin matsakaicin matsakaici da mafi ƙarancin ƙima.
Matsakaicin angular, ω, shine ƙimar canjin hujjar aikin, wanda aka auna a cikin radians a sakan daya. Ƙimar da ba ta sifili ba na φ, canjin lokaci, tana wakiltar motsi a cikin dukkan sifofin igiyar ruwa ko dai gaba ko baya cikin lokaci. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa. Mitar, f, ita ce adadin oscillations ko zagayowar da ke faruwa a cikin daƙiƙa ɗaya, wanda aka auna a cikin hertz (Hz).
Sine wave yana da mahimmanci a ilimin kimiyyar lissafi domin yana riƙe da sifarsa ta igiyar ruwa idan aka ƙara shi zuwa wani sine mai mitar iri ɗaya da lokacin sabani da girma. Wannan kadara ta tsarin raƙuman ruwa na lokaci-lokaci ana kiranta da ƙa'idar superposition kuma shine abin da ke haifar da mahimmancin bincike na Fourier. Wannan ya sa ya zama na musamman na acoustically kuma shine dalilin da ya sa ake amfani da shi a sararin sararin samaniya x, wanda ke wakiltar matsayi a girma ɗaya. Taguwar igiyar ruwa tana yaduwa tare da siga mai siffa, k, da ake kira lambar igiyar ruwa ko lambar igiyar ruwa, wanda ke wakiltar daidaito tsakanin mitar angular, ω, da saurin yaduwa na layi, ν. Lambar igiyar ruwa, k, tana da alaƙa da mitar angular, ω, da tsayin igiyar ruwa, λ, ta ma'auni λ = 2π/k.
An ba da ƙididdiga don igiyar sine a girma ɗaya ta y = A zunubi (ωt + φ). Wannan ma'auni yana ba da sauyawar igiyar ruwa a kowane matsayi x a kowane lokaci t. Ana la'akari da misalin layi ɗaya, inda aka ba da ƙimar igiyar ta y = A sin (ωt + φ).
A cikin ma'auni biyu ko fiye, ma'auni yana kwatanta motsin jirgin sama mai tafiya. Matsayin x yana ba da x = A zunubi (kx – ωt + φ). Ana iya fassara wannan ma'auni a matsayin nau'i biyu, samfurin wanda samfurin ɗigo ne.
Hadaddiyar raƙuman ruwa, kamar waɗanda aka ƙirƙira lokacin da aka jefa dutse a cikin tafkin ruwa, suna buƙatar ƙarin hadaddun ma'auni don kwatanta su. Ana amfani da kalmar sinusoid don siffanta igiyar ruwa tare da halayen duka igiyoyin sine da igiyar cosine. Canjin lokaci na π/2 radians (ko 90°) yana ba wa igiyar cosine fara kai, don haka aka ce tana jagorantar igiyar sine. Wannan yana haifar da mahimmancin alaƙa tsakanin ayyukan sine da cosine, wanda za'a iya gani a matsayin da'irar a cikin ƙirar jirgin sama mai rikitarwa na 3D.
An kwatanta fa'idar fassarar wannan ra'ayi zuwa wasu yankuna ta hanyar gaskiyar cewa yanayin raƙuman ruwa iri ɗaya yana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum yana iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari. Raƙuman raƙuman raƙuman ruwa suna wakiltar mitar guda ɗaya da haɗin kai, kuma kunnen ɗan adam yana iya fitar da raƙuman ruwa tare da jitu masu iya fahimta. Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girma masu jituwa ban da mahimmancin mitar yana haifar da bambanci a cikin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa da aka kunna akan kayan kida daban-daban ya bambanta.
Sautin tafa hannu yana ƙunshe da raƙuman ruwa na lokaci-lokaci, waɗanda ba na lokaci-lokaci ba, ko kuma suna da tsarin mara maimaituwa. Masanin ilmin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal sune sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman ruwan raƙuman ruwa na iya yaɗuwa a cikin canjin tsari ta hanyar tsarin layin da aka rarraba. Ana buƙatar wannan don nazarin yaɗuwar igiyoyin ruwa a cikin girma biyu ko fiye. Raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman ruwa masu girma da mitoci iri ɗaya. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan yana kama da abin da ke faruwa lokacin da aka tsinke rubutu akan igiya; tãguwar ruwa masu tsangwama suna nunawa daga ƙayyadaddun wuraren ƙarshen kirtani, kuma raƙuman ruwa na tsaye suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa kuma sun yi daidai da tushen murabba'in ta kowace raka'a tsawon raka'a.
Menene Binciken Fourier?
Sine wave wani santsi ne, mai maimaituwar oscillation wanda aka siffanta da lissafi a matsayin igiyar ruwa mai ci gaba. Hakanan an san shi da igiyar sinusoidal, kuma an ayyana shi ta hanyar aikin sine na trigonometric. jadawali na igiyar ruwa mai santsi, lanƙwasa na lokaci-lokaci wanda ake amfani da shi a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina.
Mitar talakawa, ko adadin oscillations ko zagayowar da ke faruwa a cikin wani adadin lokaci, ana wakilta ta da harafin Helenanci ω (omega). Ana kiran wannan a matsayin mitar angular, kuma shine ƙimar da muhawarar aikin ke canzawa a cikin raka'a na radians.
Ana iya jujjuya igiyar igiyar ruwa a cikin lokaci ta hanyar canjin lokaci, wanda harafin Helenanci φ (phi) ke wakilta. Ƙimar mara kyau tana wakiltar jinkiri, kuma ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa. Ana auna mitar kalaman sine a cikin hertz (Hz).
Ana yawan amfani da igiyar sine don kwatanta raƙuman sauti, kuma ana siffanta su ta hanyar aikin sine f(t) = A sin (ωt + φ). Ana ganin jujjuyawar irin wannan nau'in a cikin tsarin bazara-ruwa mara nauyi a ma'auni.
Sine wave yana da mahimmanci a ilimin kimiyyar lissafi domin yana riƙe da siffar igiyar ruwa lokacin da aka ƙara shi zuwa wani sine na mita iri ɗaya da lokaci na sabani da girma. Wannan kadarorin, wanda ake kira ka'idar superposition, shine abin da ke haifar da mahimmancinta a cikin bincike na Fourier. Wannan ya sa ya zama na musamman a cikin sauti kuma shine dalilin da ya sa ake amfani da shi don kwatanta masu canjin sarari.
Misali, idan x yana wakiltar girman matsayi na igiyoyin igiyar ruwa da ke yaduwa, to, sigar sifa k (lambar kalaman) tana wakiltar daidaito tsakanin mitar angular ω da saurin yaduwa na layi ν. Lambar igiyar k tana da alaƙa da mitar angular ω da tsayin raƙuman ruwa λ (lambda) ta ma'auni k = 2π/λ. Mitar f da saurin layin v suna da alaƙa da ma'auni v = fλ.
Ma'auni don igiyar sine a cikin girma ɗaya shine y = A zunubi (ωt + φ). Ana iya haɗa wannan ma'auni don ma'auni masu yawa, kuma ga misalin layi ɗaya, ƙimar igiyar ruwa a kowane aya x a kowane lokaci t ana ba da shi ta y = A sin (kx - ωt + φ).
Hadaddiyar raƙuman ruwa, irin waɗanda ake gani lokacin da aka jefa dutse cikin tafki, suna buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don kwatanta igiyar ruwa tare da waɗannan sifofin, kuma ya haɗa da igiyoyin sine da raƙuman ruwa na cosine tare da kashe lokaci.
Misalin igiyar ruwa ta cosine, ainihin alakar dake tsakanin igiyar sine da igiyar igiyar ruwa iri daya ce da alakar da'irar da samfurin jirgin sama mai sarkakkiya na 3D. Wannan yana da amfani don ganin fa'idar fassarar raƙuman ruwa tsakanin yankuna daban-daban.
Tsarin igiyar ruwa yana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma galibi ana amfani da igiyoyin sine don wakiltar mitar guda ɗaya da jituwa.
Kunnen ɗan adam yana ganin sauti tare da haɗin raƙuman ruwa na sine da sauti na lokaci-lokaci, kuma kasancewar mafi girman jituwa baya ga mitar mahimmanci yana haifar da bambanci a cikin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa da aka kunna akan kayan kida daban-daban ya bambanta.
Tafa hannu, duk da haka, ya ƙunshi raƙuman ruwa na lokaci-lokaci, waɗanda ba masu maimaitawa ba. Masanin ilmin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal sune sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai.
Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina, da ƙididdigar ƙididdiga na jerin lokaci. Raƙuman raƙuman ruwa na iya yaduwa ba tare da canza tsarin su ba a cikin tsarin layin layi da aka rarraba, wanda shine dalilin da ya sa ake buƙatar su don nazarin yaduwar raƙuman ruwa.
Raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman ruwa masu girma da mitoci iri ɗaya. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Ana ganin wannan lokacin da aka zazzage bayanin kula akan kirtani, kuma raƙuman ruwa masu tsaka-tsaki suna nunawa a ƙayyadaddun wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci sun ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa, kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Sine da Cosine Waves
A cikin wannan sashe, zan yi magana game da bambance-bambancen tsakanin sine da cosine waves, menene canjin lokaci, da yadda igiyar sine ta bambanta da igiyar ruwa. Zan kuma bincika mahimmancin raƙuman ruwa a cikin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina.
Menene Bambanci Tsakanin Sine da Cosine Waves?
Sine da cosine taguwar ruwa na lokaci-lokaci, santsi, kuma ayyuka masu ci gaba waɗanda ake amfani da su don kwatanta al'amuran halitta da yawa, kamar sauti da raƙuman haske. Ana kuma amfani da su a aikin injiniya, sarrafa sigina, da lissafi.
Babban bambanci tsakanin igiyoyin sine da radiyon cosine shine cewa igiyar sine tana farawa da sifili, yayin da igiyar igiyar igiyar ruwa tana farawa a lokacin motsi na π/2 radians. Wannan yana nufin cewa kalaman cosine yana da farkon farawa idan aka kwatanta da sine wave.
Raƙuman raƙuman ruwa suna da mahimmanci a ilimin kimiyyar lissafi saboda suna riƙe da siffar igiyoyinsu idan aka haɗa su tare. Wannan kadarorin, wanda aka sani da ƙa'idar babban matsayi, shine abin da ke sa bincike na Fourier ya zama mai amfani sosai. Hakanan yana sanya raƙuman ruwa na sine su zama na musamman, saboda ana iya amfani da su don wakiltar mitoci ɗaya.
Raƙuman ruwa na Cosine suma suna da mahimmanci a ilimin kimiyyar lissafi, kamar yadda ake amfani da su don bayyana motsin taro a kan marmaro cikin daidaito. Ma'auni don igiyar sine shine f = oscillations/lokaci, inda f shine mitar kalaman kuma ω shine mitar angular. Wannan ma'auni yana ba da ƙaurawar igiyar ruwa a kowane matsayi x da lokaci t.
A cikin girma biyu ko fiye, za a iya siffanta igiyar sine ta igiyar jirgin mai tafiya. Lambar igiyar ruwa k sigar siffa ce ta igiyar ruwa, kuma tana da alaƙa da mitar angular ω da tsayin raƙuman λ. Ƙididdigar igiyar igiyar ruwa a cikin nau'i biyu ko fiye yana ba da sauyawar igiyoyin a kowane matsayi x da lokaci t.
Hadaddiyar raƙuman ruwa, irin waɗanda dutsen da aka jefa a cikin tafki ya ƙirƙira, suna buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don siffanta igiyar ruwa mai sifofi kama da igiyar ruwa ko igiyar ruwa, kamar canjin lokaci. Ana amfani da kalmar sinusoidal don haɗa kai zuwa raƙuman ruwa na sine da raƙuman ruwa na cosine tare da kashe lokaci.
Ana samun raƙuman ruwa a cikin yanayi, gami da raƙuman ruwa, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma yana iya gane kasancewar maɗaukakin jituwa ban da ainihin mitar. Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin.
Masanin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal su ne sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aiki ne mai ƙarfi da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina. Hakanan ana amfani dashi a cikin ƙididdigar ƙididdiga da jerin lokaci.
Raƙuman raƙuman ruwa na iya yaduwa ta kowace hanya a sararin samaniya, kuma ana wakilta su da raƙuman ruwa masu girma da mitar da ke tafiya ta saɓani. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan yana faruwa ne lokacin da aka tsinke bayanin kula akan kirtani, kamar yadda raƙuman ruwa ke nunawa a madaidaitan wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa ne a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Matsakaicin resonant na kirtani sun yi daidai da tsayinsa, kuma sun yi daidai da yawan adadin sa kowane tsayin raka'a.
Menene Canjin Mataki?
Sine igiyar ruwa wani santsi ne, maimaituwar oscillation wanda ke ci gaba a cikin lokaci da sarari. Yana da lanƙwan lissafi da aka ayyana ta aikin trigonometric sine kuma galibi ana amfani dashi don wakiltar raƙuman sauti, raƙuman haske, da sauran nau'ikan igiyoyin ruwa a cikin ilimin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Matsakaicin mitar (f) na sine wave shine adadin oscillations ko zagayowar da ke faruwa a cikin daƙiƙa ɗaya, kuma ana auna shi a cikin hertz (Hz).
Mitar angular (ω) ita ce ƙimar canjin aikin muhawara a cikin radians a cikin sakan daya, kuma yana da alaƙa da mitar talakawa ta ma'auni ω = 2πf. Ƙimar mara kyau ta φ tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar gaba a cikin daƙiƙa.
Sau da yawa ana amfani da raƙuman raƙuman raƙuman ruwa don bayyana raƙuman sauti, saboda suna iya riƙe siffar igiyoyinsu idan aka haɗa su tare. Wannan kadarorin yana haifar da mahimmancin bincike na Fourier, wanda ke ba da damar iya bambance mabanbantan sararin samaniya daban-daban. Misali, madaidaicin x yana wakiltar matsayi a cikin girma ɗaya, kuma kalaman yana yaduwa a cikin alkiblar sifa ta k, wanda ake kira lambar igiyar ruwa. Lambar kalaman angular tana wakiltar daidaito tsakanin mitar kusurwa (ω) da saurin yaduwa ta layi (ν). Lamba yana da alaƙa da mitar angular da tsayin raƙuman ruwa (λ) ta ma'auni λ = 2π/k.
Ma'auni na sine wave a cikin nau'i ɗaya ana ba da shi ta y = A sin (ωt + φ), inda A shine girman girman, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Ana iya haɗa wannan ma'auni don ba da ƙaurawar igiyar ruwa a kowane matsayi x a kowane lokaci t cikin layi ɗaya, misali, y = A sin (kx – ωt + φ). Lokacin yin la'akari da igiyar ruwa a cikin ma'auni biyu ko fiye, ana buƙatar ƙarin ma'auni masu rikitarwa.
Ana amfani da kalmar sinusoid sau da yawa don kwatanta igiyar ruwa mai halaye kama da igiyar sine. Wannan ya haɗa da raƙuman ruwa na cosine, waɗanda ke da motsin lokaci na π/2 radians, ma'ana suna da farkon farawa idan aka kwatanta da igiyoyin sine. Ana yawan amfani da kalmar sinusoidal gaba ɗaya don komawa ga raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci.
Misalin igiyar ruwa na cosine, ainihin alakar dake tsakanin igiyar ruwan sine da igiyar igiyar igiyar ruwa ana iya gani tare da da'irar a cikin tsarin jirgin sama mai sarkakkiya na 3D. Wannan yana da amfani don fassarar tsakanin yanki, kamar yadda yanayin raƙuman ruwa iri ɗaya ke faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum yana iya gane raƙuman raƙuman raƙuman raƙuman raƙuman raƙuman raƙuman raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma ana amfani da raƙuman raƙuman ruwa a matsayin wakilcin sautunan mitar guda ɗaya.
Harmonics kuma suna da mahimmanci a cikin sauti, kamar yadda kunnen ɗan adam ke fahimtar sauti azaman haɗuwa da raƙuman ruwa da mafi girman jituwa baya ga mitar asali. Kasancewar maɗaukakin jituwa baya ga ainihin abubuwan da ke haifar da bambance-bambance a cikin katako na sauti. Wannan shi ne dalilin da ya sa bayanin kula na kida da aka kunna akan kayan kida daban-daban zai yi sauti daban-daban. Koyaya, sautin da aka yi ta hanyar tafa hannu yana ƙunshe da taguwar ruwa na lokaci-lokaci, ma'ana ba ta ƙunshi igiyoyin igiya ba.
Za a iya kimanta raƙuman sauti na lokaci-lokaci ta amfani da sassauƙan tubalan ginin igiyoyin sinusoidal, kamar yadda masanin lissafin Faransa Joseph Fourier ya gano. Wannan ya haɗa da raƙuman murabba'i, waɗanda suka haɗa da mitar mahimmanci da mafi girman jituwa. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina, da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa suna iya yaduwa ba tare da canza tsari ba a cikin tsarin layin layi da aka rarraba, kuma ana buƙatar sau da yawa don nazarin yaduwar raƙuman ruwa. Raƙuman raƙuman ruwa na iya tafiya ta hanyoyi biyu a sararin samaniya, kuma ana wakilta su da raƙuman ruwa masu girma da mitoci. Lokacin da raƙuman ruwa biyu da ke tafiya a gaba da gaba suka yi girma, ana ƙirƙiri tsarin igiyar igiyar ruwa. Wannan yayi kama da lokacin da aka ɗebo bayanin kula akan kirtani, yayin da raƙuman ruwa masu tsaka-tsaki ke nunawa a madaidaitan wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci sun ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsayin kirtani, kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Ta yaya Sine Wave ya bambanta da Cosine Wave?
Sine wave wani nau'in igiyar igiyar ruwa ne mai ci gaba da gudana wanda ke jujjuyawa cikin santsi, mai maimaitawa. Aikin trigonometric ne da aka zana akan jirgin sama mai girman fuska biyu, kuma shine ainihin tsarin igiyar ruwa a cikin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Ana siffanta shi da mitar sa, ko yawan jujjuyawar da ke faruwa a cikin wani lokaci, da mitar ta angular, wanda shine yawan canjin hujjar aikin a cikin radians a cikin daƙiƙa guda. Ana iya canza igiyar sine a cikin lokaci, tare da ƙima mara kyau tana wakiltar jinkiri da ƙima mai kyau yana wakiltar ci gaba a cikin daƙiƙa.
Ana yawan amfani da igiyoyin ruwa don bayyana raƙuman sauti, kuma galibi ana kiran su sinusoids. Suna da mahimmanci a ilimin kimiyyar lissafi saboda suna riƙe da siffar igiyar igiyoyinsu idan aka haɗa su tare, kuma sune tushen bincike na Fourier, wanda ya sa su zama na musamman. Ana kuma amfani da su don bayyana sauye-sauye na sarari, tare da lambar igiyar ruwa tana wakiltar daidaito tsakanin mitar angular da saurin yaɗuwar layi.
Hakanan ana amfani da sine wave don kwatanta igiyar ruwa mai girma ɗaya, kamar waya. Lokacin da aka haɗa shi zuwa nau'i biyu, ƙididdiga ta bayyana motsin jirgin sama mai tafiya. Ana fassara lambar kalaman a matsayin vector, kuma ɗigon ɗigon igiyoyin ruwa biyu shine hadadden igiyar ruwa.
Hakanan ana amfani da igiyoyin igiyar ruwa don kwatanta tsayin igiyar ruwa a cikin tafki lokacin da aka jefa dutse. Ana buƙatar ƙarin hadaddun ma'auni don kwatanta kalmar sinusoid, wanda ke bayyana halayen igiyoyin ruwa, gami da sine da raƙuman ruwa tare da motsi lokaci. Sine wave yana yin la'akari da kalaman cosine ta π/2 radians, ko farkon farawa, don haka aikin cosine yana jagorantar aikin sine. Ana amfani da kalmar sinusoidal don haɗa baki ɗaya zuwa igiyoyin sine da cosine tare da kashe lokaci.
Nuna igiyar ruwan cosine muhimmiyar alaƙa ce ga da'ira a cikin ƙirar jirgin sama mai rikiɗar 3D, wanda ke taimakawa wajen hango fa'idarsa a cikin wuraren fassara. Wannan ƙirar igiyar ruwa tana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, da kuma wakilcin raƙuman raƙuman ruwa na mitoci guda ɗaya da haɗin kai. Kunnen ɗan adam yana ganin sauti azaman igiyar sine tare da sauti na lokaci-lokaci, da kasancewar mafi girman jituwa baya ga mahimman abubuwan da ke haifar da bambancin timbre.
Wannan shine dalilin da ya sa bayanin kida na takamaiman mitar da aka kunna akan kayan kida daban-daban ya bambanta. Sautin tafa hannu, alal misali, yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, waɗanda ba masu maimaitawa ba ne, maimakon raƙuman ruwa na lokaci-lokaci. Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffanta da ƙayyadaddun tsarin igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne mai ƙarfi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina, da kuma ƙididdigar ƙididdiga na jerin lokaci. Hakanan raƙuman ruwa na iya yaduwa a cikin canza sifofi ta hanyar tsarin layin layi da aka rarraba, wanda ake buƙata don nazarin yaduwar igiyar ruwa. Raƙuman raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman raƙuman ruwa masu girma da mitarsu iri ɗaya, kuma lokacin da aka fi ƙarfinsu, an ƙirƙiri tsarin igiyar igiyar ruwa. Ana lura da wannan lokacin da aka zazzage bayanin kula akan kirtani, yayin da raƙuman ruwa masu tsaka-tsaki ke nunawa ta wurin kafaffen ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, ana magana da su a matsayin mitoci, kuma sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin maimaita kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Menene Sautin Sine Wave Kamar?
Na tabbata kun taba jin labarin sine waves a baya, amma kun san yadda suke sauti? A cikin wannan sashe, za mu bincika yadda igiyoyin igiyar ruwa ke shafar sautin kiɗa, da yadda suke mu'amala da masu jituwa don ƙirƙirar katako na musamman. Za mu kuma tattauna yadda ake amfani da igiyoyin sine wajen sarrafa sigina da yaɗa igiyoyin ruwa. A ƙarshen wannan sashe, za ku sami kyakkyawar fahimtar raƙuman ruwa da yadda suke shafar sauti.
Ta yaya Sine Wave ke Sauti?
Sine igiyar ruwa ci gaba ne, santsi, maimaita oscillation wanda ake samu a yawancin al'amuran halitta, gami da raƙuman sauti, raƙuman haske, har ma da motsin taro a kan marmaro. Yana da lanƙwan lissafi da aka ayyana ta aikin trigonometric sine, kuma galibi ana zana shi azaman sifa.
Menene sautin kalaman sine? Wave na sine mai ci gaba ne, ma'ana ba shi da karyewa a sigar igiyar igiyar ruwa. Yana da santsi, aiki na lokaci-lokaci tare da mitar, ko adadin murɗawar da ke faruwa a cikin wani lokaci da aka bayar. Mitar ta na kusurwa, ko ƙimar canjin aikin gardama a cikin radians a sakan daya, ana wakilta ta alamar ω. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Ana auna mitar kalaman sine a cikin hertz (Hz), kuma shine adadin oscillations a sakan daya. A sine wave wani sauti ne da aka kwatanta ta hanyar aikin sine, f(t) = A sin (ωt + φ), inda A shine girma, ω shine mitar angular, kuma φ shine canjin lokaci. Canjin lokaci na π/2 radians yana ba da igiyar ruwa ta fara kai, don haka galibi ana kiranta da aikin cosine.
Ana amfani da kalmar "sinusoid" don bayyana halayen igiyoyin igiyar ruwa na sine, da kuma igiyar cosine tare da kashe lokaci. Ana kwatanta wannan ta hanyar igiyar ruwa, wanda ke bayan igiyar sine ta hanyar canjin lokaci na π/2 radians. Wannan muhimmiyar alaƙar tsakanin igiyoyin sine da cosine ana wakilta ta da'irar a cikin tsarin jirgin sama mai rikitarwa na 3D, wanda ke taimakawa wajen hango fa'idar fassarar tsakanin yanki.
Tsarin igiyar igiyar igiyar ruwa tana faruwa a yanayi, gami da raƙuman iska, raƙuman sauti, da raƙuman haske. Kunnen mutum yana iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma ana amfani da wakilcin igiyoyin igiyar igiyar ruwa na mitar mitar guda ɗaya don ƙirƙirar bayanin kula na kiɗa. Kasancewar manyan masu jituwa ban da ainihin mitar yana haifar da bambance-bambance a cikin timbre na sauti. Wannan shine dalilin da ya sa bayanin kida iri ɗaya da aka kunna akan kayan kida daban-daban zai zama daban.
Duk da haka, sautin da hannun ɗan adam ke samarwa ba ya haɗa da igiyoyin igiyar ruwa kawai ba, domin kuma yana ɗauke da igiyar ruwa. Raƙuman ruwa na lokaci-lokaci ba su da maimaitawa kuma ba su da tsari, yayin da raƙuman ruwa na lokaci-lokaci. Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffantawa da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne mai ƙarfi da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa a cikin canza salo ta hanyar tsarin layin layi da aka rarraba, kuma ana buƙata don nazarin yaduwar igiyoyin ruwa. Raƙuman raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman raƙuman ruwa masu girma da mitoci iri ɗaya, kuma lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙiri tsarin igiyar igiyar ruwa. Wannan yana kama da abin da ke faruwa lokacin da aka tsinke rubutu akan igiya; An ƙirƙiri raƙuman ruwa masu shiga tsakani, kuma lokacin da waɗannan raƙuman ruwa suka bayyana ta wurin kafaffen ƙarshen igiyoyin, igiyoyin igiyoyin tsaye suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci masu faɗakarwa sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa, kuma sun yi daidai da tushen murabba'in ta kowace raka'a.
Menene Matsayin Harmonics a Sauti?
Sine igiyar ruwa ci gaba ne, santsi, maimaita oscillation da ake samu a yawancin fannonin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Wani nau'in igiyar igiyar ruwa ce mai ci gaba wacce aka siffanta ta da aikin trigonometric, yawanci sine ko cosine, kuma ana wakilta ta da jadawali. Yana faruwa a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina.
Matsakaicin mitar igiyar sine, ko adadin oscillations da ke faruwa a cikin ƙayyadaddun lokaci, ana wakilta ta da mitar angular ω, wanda yayi daidai da 2πf, inda f shine mitar a cikin hertz. Ƙimar mara kyau ta φ tana wakiltar jinkiri a cikin daƙiƙa, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Sau da yawa ana amfani da igiyoyin igiyar ruwa don kwatanta raƙuman sauti, saboda sune mafi mahimmancin nau'in igiyar sauti. An kwatanta su ta hanyar aikin sine, f = A sin (ωt + φ), inda A shine girman girman, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Sauye-sauyen lokaci na π/2 radians yana ba da igiyar ruwa ta fara farawa, don haka an ce aikin cosine ne, wanda ke jagorantar aikin sine. Kalmar “sinusoidal” ana amfani da ita gabaɗaya zuwa ga raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci.
Misalin wannan, igiyar ruwan cosine muhimmiyar alaƙa ce tsakanin da'irar da ƙirar jirgin sama mai rikitarwa na 3D, wanda ke taimakawa wajen hango fa'idarsa a cikin fassarar zuwa wasu yankuna. Wannan ƙirar igiyar ruwa tana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske.
Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma galibi ana amfani da igiyoyin igiyar ruwa azaman wakilcin daidaitawar mitoci guda ɗaya. Kunnen mutum yana jin sauti a matsayin haɗuwa da raƙuman ruwa na sine da jituwa, tare da ƙarin raƙuman ruwa daban-daban suna haifar da nau'i daban-daban da canje-canje a cikin timbre. Kasancewar mafi girman jituwa ban da mahimmancin mitar yana haifar da bambance-bambance a cikin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa tare da mita iri ɗaya da aka kunna akan kayan kida daban-daban ya bambanta.
Duk da haka, sauti ba wai kawai ya ƙunshi raƙuman ruwa na sine da haɗin kai ba, kamar yadda sautin da aka yi da hannu ya ƙunshi raƙuman ruwa na lokaci-lokaci. Raƙuman ruwa na lokaci-lokaci ba na lokaci-lokaci ba ne kuma suna da tsari mara maimaitawa. Masanin ilimin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal tubalan gini ne masu sauƙi waɗanda za a iya amfani da su don siffanta da kusan kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa ta hanyar canzawa ta hanyar tsarin layin layi da aka rarraba, kuma ana buƙata don nazarin yaduwar igiyoyin ruwa. Raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya na iya wakiltar raƙuman raƙuman ruwa masu girma da mitoci iri ɗaya, kuma idan sun girma, ana ƙirƙiri tsarin igiyar igiyar ruwa. Wannan shi ne abin da ke faruwa lokacin da aka zazzage bayanin kula akan kirtani: raƙuman ruwa masu shiga tsakani suna nunawa a madaidaiciyar wuraren ƙarshen kirtani, kuma raƙuman ruwa na tsaye suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci masu faɗakarwa sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsawonsa, kuma sun yi daidai da tushen murabba'in taro kowace raka'a na kirtani.
Ta yaya Sine Wave ke shafar Timbre na Sauti?
Sine igiyar ruwa ci gaba ne, santsi, maimaita oscillation wanda shine ainihin sashe na lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Wani nau'in igiyar igiyar ruwa ce mai ci gaba da ke da santsi, aiki na lokaci-lokaci kuma yana faruwa a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Matsakaicin mitar igiyar igiyar igiyar ruwa ita ce adadin girgiza ko zagayawa da ke faruwa a cikin raka'a na lokaci. Ana nuna wannan ta ω = 2πf, inda ω shine mitar angular kuma f shine mitar talakawa. Mitar angular ita ce ƙimar canjin aikin hujja kuma ana auna shi a cikin radians a sakan daya. Ƙimar da ba ta sifili ba na ω tana wakiltar motsi a cikin gabaɗayan sifili a cikin lokaci, wanda φ ke nunawa. Ƙimar mara kyau ta φ tana wakiltar jinkiri kuma ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Ana yawan amfani da igiyar sine don kwatanta raƙuman sauti, kuma ana siffanta su ta hanyar aikin sine f = sin(ωt). Hakanan ana ganin motsin motsi a cikin tsarin ma'aunin bazara da ba a daɗe ba a ma'auni, kuma raƙuman ruwa suna da mahimmanci a cikin ilimin kimiyyar lissafi saboda suna riƙe da siffar igiyoyinsu idan aka haɗa su tare. Wannan kadarorin sine tãguwar ruwa yana kaiwa ga mahimmancinta a cikin bincike na Fourier, wanda ya sa ya zama na musamman.
Lokacin da aka wakilta igiyar sine a cikin girman sarari ɗaya, lissafin yana ba da sauyawar igiyar a matsayi x a lokaci guda t. Ana la'akari da misalin layi ɗaya, inda ƙimar igiyar ruwa a ma'ana x aka ba da ƙima. A cikin ma'auni masu yawa, lissafin lissafin yana kwatanta motsin jirgin sama mai tafiya, inda matsayi x ke wakilta ta hanyar vector kuma lambar igiyar k shine vector. Ana iya fassara wannan azaman ɗigo samfurin vector biyu.
Hadaddiyar igiyoyin ruwa, kamar igiyar ruwa a cikin tafki lokacin da aka jefa dutse, suna buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don siffanta igiyar ruwa tare da halayen duka igiyoyin sine da igiyar cosine. An ce canjin lokaci na π/2 radians yana ba wa igiyar cosine fara kai, yayin da take jagorantar igiyar sine. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci, kamar yadda igiyar ruwa ta nuna.
Ana iya ganin wannan muhimmiyar alaƙar tsakanin sine da raƙuman ruwa na cosine tare da da'irar a cikin ƙirar jirgin sama mai rikiɗar 3D. Wannan samfurin yana da amfani don fassarar tsakanin yankuna daban-daban, kamar yadda tsarin raƙuman ruwa ke faruwa a yanayi, ciki har da raƙuman iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman raƙuman raƙuman ruwa guda ɗaya, suna sauti a sarari da tsabta. Sine taguwar ruwa kuma wakilci ne na daidaitattun mita guda ɗaya, wanda kunnen ɗan adam zai iya fahimta.
Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girman jituwa ban da mahimmancin mitar yana haifar da bambance-bambance a cikin timbre. Wannan shine dalilin da ya sa bayanin kida na takamaiman mitar da aka kunna akan kayan kida daban-daban ya bambanta. Sautin tafa hannu yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, maimakon raƙuman ruwa, saboda sauti ne na lokaci-lokaci. Da aka tsinkayi a matsayin hayaniya, ana siffanta amo a matsayin lokaci-lokaci, tare da yanayin da ba maimaituwa ba.
Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffantawa da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci. Hakanan raƙuman ruwa na iya yaduwa ta hanyar canza salo a cikin tsarin layin layi da aka rarraba, wanda ake buƙata don nazarin yaduwar igiyoyin ruwa. Raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya suna wakiltar raƙuman ruwa masu girma da mitoci iri ɗaya. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa ta tsaye, kamar yadda ake gani lokacin da aka tsinke rubutu akan igiya. Raƙuman ruwa masu tsaka-tsaki waɗanda ke nunawa daga ƙayyadaddun wuraren ƙarshen kirtani suna haifar da raƙuman ruwa na tsaye waɗanda ke faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci masu faɗakarwa sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin maimaita kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Sine Waves azaman Kayan Aikin Nazari
Zan yi magana game da igiyoyin ruwa na sine da kuma yadda ake amfani da su azaman kayan aikin nazari wajen sarrafa sigina, nazarin jerin lokaci da yaɗa igiyoyin ruwa. Za mu bincika yadda ake amfani da igiyoyin igiyar ruwa don bayyana santsi, maimaituwar motsi da kuma yadda ake amfani da su a fannin lissafi, kimiyyar lissafi, injiniyanci da sauran fannoni. Za mu kuma duba yadda za a iya amfani da igiyoyin sine don nazarin yaɗuwar igiyar ruwa da yadda ake amfani da su a cikin bincike na Fourier. A ƙarshe, za mu tattauna yadda ake amfani da igiyoyin ruwa don ƙirƙirar sauti da kuma yadda ake amfani da su a cikin kiɗa.
Menene Sarrafa Sigina?
Raƙuman ruwa sune kayan aiki na asali da ake amfani da su wajen sarrafa sigina da nazarin jerin lokaci. Su nau'in nau'in nau'in motsi ne mai ci gaba, wanda ke da santsi, maimaituwar oscillation tare da mitar guda ɗaya. Ana amfani da raƙuman raƙuman ruwa don kwatanta al'amuran zahiri iri-iri, gami da raƙuman sauti, raƙuman haske, da motsin taro a kan marmaro.
sarrafa sigina shine tsarin nazari da sarrafa sigina. Ana amfani da shi a fannoni daban-daban, ciki har da lissafi, kimiyyar lissafi, injiniyanci, da samar da sauti da bidiyo. Ana amfani da dabarun sarrafa sigina don nazarin sigina, gano alamu, da fitar da bayanai daga cikinsu.
Binciken jerin lokaci shine tsarin nazarin bayanan da aka tattara na tsawon lokaci. Ana amfani da shi don gano abubuwan da ke faruwa a cikin bayanai, da kuma yin tsinkaya game da abubuwan da za su faru nan gaba. Ana amfani da nazarin jerin lokaci a fannoni daban-daban, gami da tattalin arziki, kuɗi, da injiniyanci.
Yada igiyar igiyar ruwa shine tsarin da igiyar ruwa ke motsawa ta hanyar matsakaici. Ana nazarinta ta amfani da ma'auni na lissafi iri-iri, gami da ma'auni na igiyar ruwa da ma'aunin sine wave. Ana amfani da yaɗuwar igiyar ruwa don tantance halayen raƙuman sauti, raƙuman haske, da sauran nau'ikan raƙuman ruwa.
Menene Binciken Tsarin Lokaci?
Raƙuman raƙuman ruwa wani muhimmin kayan aiki ne don nazarin al'amuran jiki iri-iri, daga raƙuman sauti zuwa raƙuman haske. Binciken jerin lokaci hanya ce ta nazarin bayanan da aka tattara na tsawon lokaci, don gano alamu da abubuwan da ke faruwa. Ana amfani da shi don nazarin halayen tsarin a kan lokaci, da kuma yin tsinkaya game da halayen gaba.
Ana iya amfani da nazarin jerin lokaci don nazarin raƙuman ruwa. Ana iya amfani da shi don gano mita, girma, da lokaci na igiyoyin sine, da kuma gano duk wani canje-canje a cikin tsarin igiyar ruwa a kan lokaci. Hakanan za'a iya amfani da shi don gano kowane nau'i na asali a cikin tsarin raƙuman ruwa, kamar su lokaci-lokaci ko yanayi.
Hakanan za'a iya amfani da nazarin jerin lokaci don gano duk wani canje-canje a cikin girman ko lokacin igiyar ruwa na tsawon lokaci. Ana iya amfani da wannan don gano duk wani canje-canje a cikin tsarin wanda zai iya haifar da canjin yanayin motsi, kamar canje-canje a cikin yanayi ko tsarin kanta.
Hakanan za'a iya amfani da bincike na jerin lokaci don gano duk wani tsari mai tushe a cikin tsarin igiyar ruwa, kamar lokaci-lokaci ko abubuwan da ke faruwa. Ana iya amfani da wannan don gano kowane tsarin da ke cikin tsarin wanda zai iya haifar da canjin yanayin motsi, kamar canje-canje a cikin yanayi ko tsarin kanta.
Hakanan za'a iya amfani da nazarin jerin lokaci don gano duk wani canje-canje a mitar igiyar sine akan lokaci. Ana iya amfani da wannan don gano duk wani canje-canje a cikin tsarin wanda zai iya haifar da canjin yanayin motsi, kamar canje-canje a cikin yanayi ko tsarin kanta.
Hakanan za'a iya amfani da bincike na jerin lokaci don gano duk wani tsari mai tushe a cikin tsarin igiyar ruwa, kamar lokaci-lokaci ko abubuwan da ke faruwa. Ana iya amfani da wannan don gano kowane tsarin da ke cikin tsarin wanda zai iya haifar da canjin yanayin motsi, kamar canje-canje a cikin yanayi ko tsarin kanta.
Binciken jerin lokaci kayan aiki ne mai ƙarfi don nazarin raƙuman ruwa kuma za'a iya amfani da su don gano alamu da abubuwan da ke faruwa a cikin yanayin motsi na tsawon lokaci. Hakanan za'a iya amfani da shi don gano duk wani tsari mai tushe a cikin tsarin wanda zai iya haifar da canjin yanayin motsi, kamar canje-canje a cikin muhalli ko tsarin kansa.
Yaya ake nazarin Yada Wave?
Sine taguwar ruwa nau'in nau'in nau'in igiyar igiyar ruwa ce mai ci gaba da za a iya amfani da ita don tantance yaduwar igiyar ruwa. Su ne santsi, maimaita oscillation da za a iya samu a cikin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Sine taguwar ruwa ana siffanta su da mita (f), adadin oscillations da ke faruwa a cikin wani lokaci da aka ba da, da kuma mitar su na angular (ω), wanda shine adadin da hujjar aikin ke canzawa a cikin raka'a na radians.
Ana amfani da raƙuman raƙuman ruwa don kwatanta al'amura iri-iri, gami da raƙuman sauti, raƙuman haske, da motsin taro a kan marmaro. Hakanan suna da mahimmanci a cikin bincike na Fourier, wanda ke sa su zama na musamman. Za a iya wakilta igiyar sine a cikin girma ɗaya ta hanyar layi ɗaya, tare da ƙimar igiyar ruwa a wani wuri da aka ba da lokaci da sarari. A cikin nau'i-nau'i masu yawa, ma'auni don igiyoyin sine yana kwatanta igiyar jirgin sama mai tafiya, tare da matsayi (x), lambar igiyar ruwa (k), da mitar angular (ω).
Sinusoids wani nau'in nau'in igiyar igiyar ruwa ne wanda ya ƙunshi duka sine da raƙuman ruwa na cosine, da kuma kowane nau'in igiyar ruwa tare da canjin lokaci na π/2 radians (farkon kai). Wannan yana haifar da mahimmancin alaƙa tsakanin sine da raƙuman ruwa na cosine, wanda za'a iya gani a cikin ƙirar jirgin sama mai rikitarwa na 3D. Wannan samfurin yana da amfani don fassara nau'ikan raƙuman ruwa tsakanin yankuna daban-daban.
Ana iya samun raƙuman ruwa na sinusoidal a cikin yanayi, gami da igiyoyin iska da raƙuman ruwa. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, amma yawanci sauti yana kunshe da raƙuman ruwa da yawa, waɗanda aka sani da jituwa. Kasancewar manyan masu jituwa ban da ainihin mitar yana haifar da bambance-bambance a cikin timbre na sauti. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa da aka kunna akan kayan kida daban-daban ya bambanta.
Masanin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal su ne sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aiki ne mai ƙarfi don nazarin raƙuman ruwa, kuma ana amfani dashi a cikin kwararar zafi da sarrafa sigina. Hakanan ana amfani dashi a cikin ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa ta kowace hanya a sararin samaniya, kuma ana wakilta su da raƙuman ruwa masu girma da mitar da ke tafiya a gaba da gaba. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan shi ne irin tsarin da ake ƙirƙira lokacin da aka zazzage rubutu a kan igiya, saboda raƙuman ruwa da ke nunawa a kafaffen wuraren ƙarshen kirtani. Tsayewar igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda aka sani da mitoci masu faɗakarwa, waɗanda suka haɗa da mahimman mitoci da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsayinsa, kuma sun yi daidai da yawan adadin sa kowane tsayin raka'a.
Sine Wave Spectrum
Zan yi magana game da sine wave bakan, gami da mitar sa, tsayinsa, da kuma yadda za a yi amfani da shi don ƙirƙirar tasirin sauti daban-daban. Za mu bincika lanƙwan lissafin da ke bayyana santsi, maimaituwar motsi, da yadda ake amfani da shi a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Za mu kuma duba yadda igiyar sine ke da mahimmanci a kimiyyar lissafi da kuma dalilin da ya sa ake amfani da ita a cikin bincike na Fourier. A ƙarshe, za mu tattauna yadda ake amfani da igiyar sine a cikin sauti da kuma yadda kunnen ɗan adam ke gane shi.
Menene Mitar Sine Wave?
Sine wave wani nau'in igiyar igiyar ruwa ne mai ci gaba da gudana wanda ke juyawa cikin santsi, mai maimaitawa. Abu ne mai mahimmanci na yawancin al'amura na zahiri da na lissafi, kamar sauti, haske, da siginar lantarki. Mitar kalaman sine shine adadin muryoyin da ke faruwa a cikin wani ɗan lokaci. Ana auna shi a cikin Hertz (Hz) kuma yawanci ana bayyana shi ta hanyar hawan keke a cikin daƙiƙa guda. Dangantakar da ke tsakanin mita da tsayin raƙuman ruwa shine cewa mafi girman mitar, shine guntu tsawon zangon.
Ana amfani da raƙuman ruwa don ƙirƙirar tasirin sauti iri-iri, gami da vibrato, tremolo, da ƙungiyar mawaƙa. Ta hanyar haɗa raƙuman ruwa masu yawa na mitoci daban-daban, za a iya ƙirƙira hadaddun igiyoyin igiyoyin ruwa. Ana kiran wannan da ƙari hadawa, kuma ana amfani dashi a cikin nau'ikan samar da sauti da yawa. Bugu da ƙari, za a iya amfani da igiyoyin sine don ƙirƙirar tasiri iri-iri, kamar jujjuyawar lokaci, flanging, da kuma lokaci.
Hakanan ana amfani da igiyoyin igiyar ruwa don sarrafa sigina, kamar a cikin bincike na Fourier, wanda ake amfani da shi don nazarin yaduwar igiyar ruwa da kwararar zafi. Ana kuma amfani da su a cikin ƙididdigar ƙididdiga da nazarin jerin lokaci.
A taƙaice, raƙuman ruwa na sine wani nau'in igiyar igiyar ruwa ce mai ci gaba da gudana a cikin santsi, mai maimaitawa. Ana amfani da su don ƙirƙirar tasirin sauti iri-iri, kuma ana amfani da su wajen sarrafa sigina da ƙididdigar ƙididdiga. Mitar sine wave shine adadin muryoyin da ke faruwa a cikin wani ɗan lokaci, kuma alaƙar da ke tsakanin mita da tsayin igiyar ruwa ita ce mafi girman mitar, mafi guntu tsawon zangon.
Menene Alakar Tsakanin Mitoci da Tsawon Wave?
Sine igiyar ruwa ci gaba ne, santsi, maimaita oscillation da ake samu a yawancin fannonin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. An bayyana shi ta hanyar aikin sine na trigonometric, kuma ana wakilta ta da hoto azaman siffar igiyar ruwa. Sine wave yana da mitar, wanda shine adadin juzu'i ko zagayowar da ke faruwa a cikin ƙayyadaddun lokaci. Matsakaicin angular, wanda ω ke nunawa, shine ƙimar canjin hujjar aikin, wanda aka auna a cikin radians a sakan daya. Gabaɗayan tsarin igiyar ruwa ba ya bayyana a lokaci ɗaya, amma ana jujjuya shi cikin lokaci ta hanyar juzu'i, wanda ake nuna shi ta φ, wanda aka auna cikin daƙiƙa. Ƙimar mara kyau tana wakiltar jinkiri, kuma ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa. Ana auna mitar kalaman sine a cikin hertz (Hz), kuma shine adadin oscillations da ke faruwa a cikin dakika ɗaya.
Sine wave wani muhimmin igiyar igiyar ruwa ce a fannin kimiyyar lissafi, kamar yadda yake riƙe da sifarsa idan aka ƙara shi zuwa wani igiyar igiyar ruwa na mitar lokaci ɗaya da sabani da girma. Wannan kadara ta tsarin motsi na lokaci-lokaci ana kiranta da ƙa'idar superposition, kuma wannan kadarar ce ta haifar da mahimmancin bincike na Fourier. Wannan ya sa ya zama na musamman na acoustically, domin shi ne kawai nau'in igiyar ruwa da za a iya amfani da shi don ƙirƙirar m sarari. Misali, idan x yana wakiltar matsayi tare da waya, to, igiyar sine na mitar da aka bayar da tsayin tsayin za su yaɗu tare da waya. Siffar siffa ta igiyar ruwa ana saninta da lambar igiyar ruwa, k, wacce ita ce lambar igiyar angular kuma tana wakiltar daidaito tsakanin mitar angular, ω, da saurin yaduwa, ν. Lambar igiyar ruwa tana da alaƙa da mitar angular da tsayin igiyar ruwa, λ, ta ma'auni λ = 2π/k.
Ƙididdigar sine wave a cikin girma ɗaya ana ba da ita ta y = A sin(ωt + φ), inda A shine girman girman, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Wannan ma'auni na iya zama gama gari don ba da ƙaurawar igiyar ruwa a wani wuri da aka ba, x, a wani lokaci, t. Don misalin layi ɗaya, ƙimar igiyar ruwa a wurin da aka ba da ita ana bada ta y = A sin(kx – ωt + φ), inda k shine lambar igiyar ruwa. Lokacin da aka yi la'akari da girma fiye da ɗaya, ana buƙatar ma'auni mai rikitarwa don kwatanta igiyar ruwa.
Ana amfani da kalmar sinusoid don siffanta nau'in igiyar ruwa wanda ke da halayen duka igiyoyin sine da igiyar cosine. Canjin lokaci na π/2 radians an ce zai ba wa wave sine farkon farawa, yayin da igiyar sine ta yi la'akari da kalaman cosine da wannan adadin. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci. An kwatanta wannan a cikin jadawali da ke ƙasa, wanda ke nuna raƙuman ruwa na cosine tare da canjin lokaci na π/2 radians.
Ana iya ganin ainihin alaƙar da ke tsakanin igiyar igiyar ruwa da da'irar ta amfani da ƙirar jirgin sama mai rikitarwa na 3D. Wannan yana da amfani don fassara tsarin igiyar ruwa zuwa yankuna daban-daban, kamar yadda tsarin igiyar ruwa iri ɗaya ke faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma galibi ana amfani da raƙuman raƙuman ruwa azaman wakilcin sautunan mitoci ɗaya. Harmonics kuma suna nan a cikin sauti, kamar yadda kunnen ɗan adam zai iya fahimtar jituwa ban da ainihin mitar. Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girma masu jituwa ban da mahimmancin mahimmanci shine abin da ke haifar da bambancin timbre. Wannan shine dalilin da yasa bayanin kida na mitar da aka bayar akan kayan kida daban-daban zai zama daban.
Har ila yau, sautin tafa hannu yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, waɗanda raƙuman ruwa ne waɗanda ba na lokaci-lokaci ba. Raƙuman raƙuman ruwa na lokaci-lokaci, kuma sautin da ake ɗauka a matsayin hayaniya ana siffanta shi da raƙuman ruwa na lokaci-lokaci, tare da yanayin da ba mai maimaitawa ba. Masanin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal su ne sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aiki ne mai ƙarfi na nazari wanda ake amfani dashi don nazarin raƙuman ruwa, kamar kwararar zafi da sarrafa sigina, da ƙididdigar ƙididdiga na jerin lokaci. Hakanan za'a iya amfani da raƙuman ruwa don yaduwa ta hanyar canza salo a cikin tsarin layin layi da aka rarraba. Ana buƙatar wannan don nazarin yaɗuwar igiyoyin ruwa zuwa wurare biyu a cikin sararin samaniya, saboda raƙuman ruwa masu girma iri ɗaya da mitar tafiya a wurare dabam-dabam za su yi girma don ƙirƙirar ƙirar igiyar igiyar ruwa. Wannan shi ne abin da ake ji lokacin da aka zazzage rubutu a kan igiya, yayin da raƙuman ruwa ke nunawa a kafaffen wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci masu resonant na kirtani. Waɗannan mitoci sun ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin maimaita kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Ta yaya Za a Yi Amfani da Sine Wave don Ƙirƙirar Tasirin Sauti daban-daban?
Sine wave wani nau'in igiyar igiyar ruwa ne mai ci gaba da gudana wanda ke juyawa cikin santsi, mai maimaitawa. Yana ɗaya daga cikin mafi mahimmancin raƙuman raƙuman ruwa kuma ana amfani dashi a wurare da yawa na lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. Sine taguwar ruwa ana siffanta su da mita, wanda shine adadin oscillations ko zagayowar da ke faruwa a cikin wani adadin lokaci. Mitar angular, wanda shine adadin canjin gardamar aikin a cikin radians a sakan daya, yana da alaƙa da mitar talakawa ta ma'auni ω = 2πf.
Ana yawan amfani da igiyoyin igiyar ruwa wajen samar da sauti kuma ana iya amfani da su don ƙirƙirar tasirin sauti iri-iri. Ta hanyar haɗa raƙuman ruwa daban-daban tare da mitoci daban-daban, amplitudes, da matakai daban-daban, ana iya ƙirƙira kewayon sautuka. Ana kiran igiyoyin sine tare da mitar guda ɗaya a matsayin "masu mahimmanci" kuma shine tushen duk bayanin kula na kiɗa. Lokacin da aka haɗu da raƙuman sine da yawa tare da mitoci daban-daban, suna samar da “harmonics” waɗanda suke mafi girman mitoci waɗanda ke ƙara ƙarar sautin. Ta hanyar ƙara ƙarin jituwa, za a iya sanya sautin don yin sauti mai rikitarwa da ban sha'awa. Bugu da ƙari, ta hanyar canza yanayin igiyoyin sine, za a iya yin sautin sauti kamar yana fitowa daga wurare daban-daban.
Hakanan ana amfani da igiyoyin sine a cikin sauti don auna ƙarfin raƙuman sauti. Ta hanyar auna girman igiyoyin sine, ana iya tantance ƙarfin sautin. Wannan yana da amfani don auna ƙarar sauti ko don tantance yawan sautin.
A ƙarshe, raƙuman ruwa mai mahimmancin igiyoyin ruwa ne mai mahimmanci a fagage da yawa na kimiyya da injiniyanci. Ana amfani da su don ƙirƙirar tasirin sauti iri-iri kuma ana amfani da su don auna ƙarfin raƙuman sauti. Ta hanyar haɗa raƙuman ruwa daban-daban tare da mitoci daban-daban, amplitudes, da matakai daban-daban, ana iya ƙirƙira kewayon sautuka.
Ta yaya Sine Curve zai iya kwatanta kalaman?
A cikin wannan sashe, zan tattauna yadda za a iya amfani da lanƙwan sine don kwatanta igiyar ruwa, alakar da ke tsakanin lanƙwan sine da igiyar jirgin sama, da kuma yadda za a iya amfani da lanƙwan sine don hango alamun igiyar ruwa. Za mu bincika mahimmancin raƙuman ruwa a cikin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina, da yadda ake amfani da su don wakiltar raƙuman sauti da sauran nau'ikan igiyoyin igiyar ruwa.
Ta yaya Sine Curve ke wakiltar igiyar ruwa?
Sine wave wani santsi ne, maimaituwar oscillation wanda ke ci gaba kuma yana da sifar igiyar igiyar ruwa wacce aikin trigonometric sine ya siffanta. Wani nau'in igiyar ruwa ce mai ci gaba mai santsi kuma na lokaci-lokaci, kuma ana samunsa a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Ana siffanta shi da mitar, wanda shine adadin oscillations ko zagayawa da ke faruwa a cikin wani adadin lokaci. Mitar angular, ω, ita ce ƙimar da gardamar aiki ke canzawa a raka'a na radians a sakan daya. Siffar igiyar igiyar ruwa gabaɗaya tana bayyana tana canzawa a cikin lokaci ta hanyar canjin lokaci, φ, wanda aka auna cikin daƙiƙa. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Sau da yawa ana amfani da igiyar sine don kwatanta igiyar sauti, kuma ana siffanta ta da aikin sine, f = A sin (ωt + φ). Hakanan ana samun juzu'i a cikin tsarin ma'aunin bazara da ba a daɗe ba a ma'auni, kuma igiyar igiyar ruwa tana da mahimmanci a ilimin kimiyyar lissafi domin tana riƙe da sifar kalaman sa idan aka ƙara zuwa wani sine mai mitar iri ɗaya da kuma lokaci na sabani da girma. Wannan kadarar sifa ta lokaci-lokaci ita ce abin da ke haifar da mahimmancinta a cikin bincike na Fourier, wanda ya sa ya zama na musamman.
Lokacin da igiyar ruwa ke yaduwa a cikin girma ɗaya, madaidaicin sararin samaniya, x, yana wakiltar girman matsayi wanda igiyar ke yaduwa, kuma ma'aunin sifa, k, ana kiran lambar igiyar ruwa. Lambar kalaman angular tana wakiltar daidaito tsakanin mitar kusurwa, ω, da saurin yaduwa, ν. Lamba yana da alaƙa da mitar angular, λ (lambda) shine tsayin raƙuman ruwa, kuma f shine mitar. Ma'auni v = λf yana ba da igiyoyin sine a cikin girma guda. An ba da ma'auni na gaba ɗaya don ba da ƙaurawar igiyoyin a wuri, x, a lokaci guda, t.
Lokacin da aka yi la'akari da misalin layi ɗaya, ƙimar igiyar ruwa a kowane wuri a sararin samaniya ana ba da shi ta hanyar equation x = A sin (kx - ωt + φ). Don ma'auni biyu na sararin samaniya, ma'aunin yana kwatanta motsin jirgin sama mai tafiya. Lokacin da aka fassara shi azaman vectors, samfurin vector biyu samfurin ɗigo ne.
Don hadaddun raƙuman ruwa, kamar igiyar ruwa a cikin tafki lokacin da aka jefa dutse, ana buƙatar daidaita daidaito. Ana amfani da kalmar sinusoid don bayyana halayen igiyoyin igiyar ruwa na sine da igiyar cosine. An ce canjin lokaci na π/2 radians yana ba wa igiyar cosine fara kai, yayin da take jagorantar igiyar sine. Sine kalaman yana yin la'akari da kalaman cosine. Kalmar sinusoidal ana amfani da ita gabaɗaya zuwa ga raƙuman ruwa da raƙuman ruwa na cosine tare da ɓata lokaci, yana nuna ainihin alaƙar da ke tsakanin su biyun. Za a iya amfani da da'irar a cikin hadadden tsarin jirgin sama na 3D don ganin fa'idar fassarar tsakanin sassan biyu.
Irin wannan nau'in igiyar ruwa yana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma raƙuman ruwa suna wakiltar mitar guda ɗaya da jituwa. Kunnen ɗan adam yana ganin sauti azaman igiyar sine tare da jitu masu iya fahimta ban da ainihin mitar. Ƙarin raƙuman ruwa na sine daban-daban yana haifar da wani nau'i na nau'i daban-daban, wanda ke canza sautin sautin. Kasancewar mafi girman jituwa ban da mahimmancin mitar yana haifar da bambance-bambance a cikin timbre. Wannan shine dalilin da ya sa bayanin kida na takamaiman mitar da aka kunna akan kayan kida daban-daban ya bambanta.
Sautin tafa hannu yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, waɗanda ba na lokaci-lokaci ba, kuma igiyoyin sine na lokaci-lokaci. Sautin da aka tsinkayi a matsayin mai hayaniya ana siffanta shi azaman lokaci-lokaci, yana da tsarin da ba ya maimaitawa. Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal sune sassauƙan tubalan gini don siffanta da ƙayyadaddun tsarin igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aiki ne na nazari da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa ta hanyar canzawa ta hanyar tsarin layin layi da aka rarraba, kuma ana buƙata don nazarin yaduwar raƙuman ruwa. Raƙuman raƙuman ruwa da ke tafiya a wurare dabam-dabam a sararin samaniya ana iya wakilta su azaman raƙuman ruwa masu girma iri ɗaya da mitar tafiya a gaba da gaba. Lokacin da raƙuman ruwa biyu suka yi girma, ana ƙirƙiri tsarin igiyar igiyar ruwa. Wannan yayi kama da lokacin da aka zazzage bayanin kula akan kirtani, inda tãguwar ruwa ke nuna tsangwama a madaidaitan wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Ƙunƙarar sautin bayanin kula da aka ɗora akan kirtani ya ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin maimaita kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Menene Alakar Tsakanin Lantarki na Sine da Kalaman Jirgin Sama?
igiyar ruwa mai santsi mai santsi ce, maimaituwar jujjuyawar sifa mai ci gaba. Yana da lanƙwan lissafi da aka ayyana cikin sharuddan aikin trigonometric sine, kuma galibi ana zana shi azaman santsi, lanƙwan sinusoidal. Ana samun raƙuman ruwa a wurare da yawa na lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina.
Sine wave ana siffanta shi da mitarsa na yau da kullun, adadin oscillations ko zagayowar da ke faruwa a cikin wani lokaci da aka bayar. lokaci lokaci. Mitar angular, ω, shine adadin canjin gardamar aikin, kuma ana auna shi cikin raka'a na radians a sakan daya. Siffar igiyar igiyar ruwa gabaɗaya tana bayyana tana canzawa cikin lokaci, tare da canjin lokaci, φ, na ωt seconds. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa.
Hakanan ana amfani da igiyar sine don kwatanta raƙuman sauti. An kwatanta shi ta hanyar aikin sine, f(t) = A sin (ωt + φ), inda A shine girman girman, ω shine mitar angular, kuma φ shine canjin lokaci. Hakanan ana ganin jujjuyawa a cikin tsarin ruwan bazara da ba a daɗe ba a ma'auni.
Raƙuman raƙuman ruwa suna da mahimmanci a ilimin kimiyyar lissafi saboda suna riƙe da siffar igiyoyinsu idan aka haɗa su tare. Wannan kadarorin, wanda aka sani da ƙa'idar babban matsayi, tana kaiwa ga mahimmancin bincike na Fourier, wanda ke ba da damar yin bambance tsakanin masu canjin sararin samaniya. Misali, idan x yana wakiltar matsayi a cikin girma ɗaya, to, igiyar ruwa tana yaduwa tare da ma'auni, k, wanda ake kira lambar igiyar ruwa. Lambar kalaman angular, k, tana wakiltar daidaito tsakanin mitar angular, ω, da kuma saurin yaduwa, ν. Lambar igiyar ruwa, k, tana da alaƙa da mitar angular, ω, da tsayin igiyar ruwa, λ, ta ma'auni λ = 2π/k.
An ba da ƙididdiga don igiyar sine a cikin girma ɗaya ta y = A zunubi (ωt + φ). Wannan ma'auni yana ba da ƙaurawar igiyar ruwa a wani wuri da aka ba, x, a wani lokaci, t. Misalin layi daya, idan ana ganin darajar igiyar igiyar waya ce, to a cikin ma'auni guda biyu, ma'auni yana kwatanta igiyar jirgin mai tafiya. Matsayi, x, da lambar igiyar ruwa, k, ana iya fassara su azaman vectors, kuma samfurin biyun samfurin ɗigo ne.
Hadaddiyar raƙuman ruwa, irin waɗanda ake gani a cikin tafki lokacin da aka jefa dutse, suna buƙatar hadaddun ma'auni don kwatanta su. Ana amfani da kalmar sinusoid don bayyana halayen raƙuman ruwa waɗanda suke kama da igiyar ruwa. Kalaman cosine yana kama da igiyar ruwa, amma tare da canjin lokaci na π/2 radians, ko farkon farawa. Wannan yana haifar da sine wave yana raguwar kalaman cosine. Ana amfani da kalmar sinusoidal gaba ɗaya don komawa ga raƙuman ruwa na sine da raƙuman ruwa tare da kashe lokaci.
Misalin igiyar ruwa ta cosine muhimmiyar alaƙa ce zuwa da'irar a cikin ƙirar jirgin sama mai rikiɗar 3D, wanda za'a iya amfani dashi don hango fa'idar fa'idar igiyar ruwa a cikin fassarar tsakanin yanki. Wannan ƙirar igiyar ruwa tana faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma raƙuman ruwa suna wakiltar mitar guda ɗaya da jituwa. Kunnen mutum yana ganin sauti azaman igiyar sine tare da jituwa ban da ainihin mitar. Wannan yana haifar da bambanci a cikin timbre. Dalilin da yasa bayanin kida da aka kunna akan kayan kida daban-daban ke yin sauti daban-daban shine saboda sautin yana dauke da raƙuman ruwa na lokaci baya ga igiyar ruwa. Ana tsinkayar sauti na lokaci-lokaci a matsayin hayaniya, kuma ana siffanta amo da samun yanayin da ba maimaituwa ba.
Masanin lissafin Faransa Joseph Fourier ya gano cewa raƙuman ruwa na sinusoidal tubalan gini ne masu sauƙi don siffantawa da kuma ƙayyadaddun tsarin igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'i. Binciken Fourier kayan aikin nazari ne mai ƙarfi da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci. Raƙuman raƙuman ruwa na iya yaduwa ba tare da canza tsari ba a cikin tsarin layin da aka rarraba. Ana buƙatar wannan don nazarin yaduwar igiyoyin ruwa zuwa wurare biyu a cikin sararin samaniya, kuma ana wakilta ta da raƙuman ruwa masu girma da mita iri ɗaya, amma suna tafiya ta hanyoyi daban-daban. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Ana ganin wannan lokacin da aka tsinke bayanin kula akan kirtani, kuma raƙuman ruwa masu tsaka-tsaki suna nunawa a ƙayyadaddun wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, ana magana da su a matsayin mitoci masu sake sauti, kuma sun ƙunshi ainihin mitoci da mafi girman jituwa. Matsakaicin maimaita kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Ta yaya Za'a Yi Amfani da Sine Curve don Hana Hanyoyi Na Wave?
Sine igiyar ruwa ci gaba ne, santsi, maimaita oscillation wanda aka kwatanta ta hanyar lanƙwasa na lissafi. Wani nau'in igiyar igiyar ruwa ce mai ci gaba wanda aka siffanta ta hanyar aikin sine na trigonometric, wanda aka zana azaman sifa. Yana faruwa a fannin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina.
Sine wave yana da mitar talakawa, wanda shine adadin juzu'i ko zagayowar da ke faruwa a cikin ƙayyadadden lokaci. Ana wakilta wannan da mitar angular, ω, wanda yayi daidai da 2πf, inda f shine mitar a cikin hertz (Hz). Ana iya canza igiyar sine a cikin lokaci, tare da ƙima mara kyau tana wakiltar jinkiri da ƙima mai kyau yana wakiltar ci gaba a cikin daƙiƙa.
Ana amfani da igiyar sine sau da yawa don kwatanta igiyar sauti, kamar yadda aikin sine ke siffanta shi. Mitar sine wave, f, shine adadin oscillations a cikin daƙiƙa guda. Wannan daidai yake da jujjuyawar tsarin yawan ruwan bazara a ma'auni.
Sine wave yana da mahimmanci a ilimin kimiyyar lissafi domin yana riƙe da siffar igiyar ruwa lokacin da aka ƙara shi zuwa wani sine na mita iri ɗaya da lokaci na sabani da girma. Wannan kadara ta igiyar igiyar ruwa ana kiranta da ƙa'idar babban matsayi kuma dukiya ce ta lokaci-lokaci. Wannan kadarorin yana haifar da mahimmancin bincike na Fourier, wanda ke ba da damar yin bambance tsakanin masu canjin sararin samaniya daban-daban.
Misali, idan x yana wakiltar girman matsayin da igiyar ruwa ke yaduwa, to, sifa mai siffa k, wacce ake kira lambar igiyar ruwa, tana wakiltar daidaito tsakanin mitar angular, ω, da saurin yaduwa, ν. Lambar igiyar ruwa tana da alaƙa da mitar angular da tsayin igiyar ruwa, λ, ta ma'auni λ = 2π/k.
Ma'auni na sine wave a cikin nau'i ɗaya yana ba da y = A zunubi (ωt + φ), inda A shine girma, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Idan an yi la'akari da misalin layi ɗaya, to, ƙimar igiyar ruwa a kowane lokaci x a kowane lokaci t yana ba da y = A sin (kx - ωt + φ).
A cikin ma'auni masu yawa, ana ba da ƙididdiga don igiyar sine ta y = A sin (kx - ωt + φ), inda A shine girman girman, k shine lambar kalaman, x shine matsayi, ω shine mitar angular, t shine lokacin, kuma φ shine canjin lokaci. Wannan ma'auni yana kwatanta motsin jirgin sama mai tafiya.
Amfanin igiyar sine bai iyakance ga fassarar a cikin sassan jiki ba. Irin wannan nau'in igiyar ruwa yana faruwa a yanayi, ciki har da raƙuman iska, raƙuman sauti, da raƙuman haske. Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma galibi ana amfani da igiyoyin ruwa don wakiltar jituwar mitar mitoci ɗaya.
Kunnen mutum kuma zai iya gane sautin da ya ƙunshi mitoci na asali da mafi girman jituwa. Waɗannan mitoci masu ɗorewa na kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
A taƙaice, ana amfani da kalmar sinusoid don siffanta igiyar ruwa da ke da sifofi na igiyar sine da igiyar igiyar ruwa. An ce sine wave yana da motsin lokaci na π/2 radians, wanda yayi daidai da farkon farawa, yayin da aka ce igiyar cosine tana jagorantar igiyar sine. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da raƙuman ruwa, tare da kashe lokaci. Ana kwatanta wannan ta hanyar igiyar ruwa, wanda shine ainihin alaƙa a cikin da'irar a cikin rikitaccen tsarin jirgin sama na 3D wanda ake amfani da shi don ganin fa'idar igiyar igiyar ruwa a cikin fassarar a cikin sassan jiki.
Sine Waves da Mataki
A cikin wannan sashe, zan bincika alaƙar da ke tsakanin igiyoyin sine da lokaci. Zan tattauna yadda lokaci ke shafar igiyar ruwa da kuma yadda za a iya amfani da shi don ƙirƙirar nau'ikan igiyoyin ruwa daban-daban. Zan kuma ba da wasu misalai don nuna yadda za a iya amfani da lokaci a aikace-aikace daban-daban.
Menene Alakar Tsakanin Sine Wave da Fase?
Sine wave wani santsi ne, maimaituwar oscillation wanda ke ci gaba kuma yana da mitoci guda ɗaya. Yana da lanƙwan lissafi wanda aka ayyana ta aikin sine na trigonometric, kuma galibi ana wakilta shi da jadawali. Ana samun raƙuman ruwa a wurare da yawa na lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina.
Mitar sine wave shine adadin oscillations ko zagayowar da ke faruwa a cikin ƙayyadaddun lokaci, kuma ana nuna shi da harafin Helenanci ω (omega). Mitar angular ita ce ƙimar canji na gardamar aiki, kuma ana auna ta cikin raka'a na radians a sakan daya. Tsarin igiyar igiyar ruwa gaba ɗaya na iya bayyana canzawa cikin lokaci, tare da canjin lokaci na φ (phi) a cikin daƙiƙa. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba a cikin daƙiƙa. Ana auna mitar kalaman sine a cikin hertz (Hz).
Ana amfani da igiyar sine sau da yawa don kwatanta igiyar sauti, kamar yadda aikin sine ke siffanta shi. Misali, f = 1/T, inda T shine lokacin oscillation, kuma f shine mitar oscillation. Wannan daidai yake da tsarin yawan bazara a cikin ma'auni.
Sine wave yana da mahimmanci a ilimin kimiyyar lissafi domin yana riƙe da siffar igiyar ruwa lokacin da aka ƙara shi zuwa wani sine na mita iri ɗaya da lokaci na sabani da girma. Wannan kadarorin zama na lokaci-lokaci dukiya ce wacce ke kaiwa ga mahimmancinta a cikin bincike na Fourier, wanda ya sa ta zama na musamman.
Lokacin da igiyar ruwa ke yaduwa a sarari, madaidaicin sarari x yana wakiltar matsayi a girma ɗaya. Taguwar ruwa tana da sifa mai siffa k, wanda ake kira lambar igiyar ruwa, wanda ke wakiltar daidaito tsakanin mitar kusurwa ω da saurin yaduwa na madaidaiciya ν. Lambar igiyar k tana da alaƙa da mitar angular ω da tsayin raƙuman ruwa λ (lambda) ta ma'auni λ = 2π/k. Mitar f da saurin layin v suna da alaƙa da ma'auni v = λf.
Ƙididdigar sine wave a cikin nau'i ɗaya yana ba da y = A sin(ωt + φ), inda A shine girman girman, ω shine mitar angular, t shine lokaci, kuma φ shine canjin lokaci. Wannan ma'auni yana ba da sauyawar igiyar ruwa a wani wuri da aka ba x da lokacin t. Ana ɗaukar misalin layi ɗaya, tare da ƙimar y = A sin(ωt + φ) ga duka x.
A cikin ma'auni masu yawa, ƙididdiga don igiyoyin jirgin sama mai tafiya yana ba da y = A sin (kx - ωt + φ). Ana iya fassara wannan ma'auni a matsayin nau'i biyu a cikin hadadden jirgin sama, tare da samfurin vector biyu shine samfurin digo.
Hadaddiyar igiyoyin ruwa, kamar igiyar ruwa a cikin tafki lokacin da aka jefa dutse, suna buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don siffanta igiyar ruwa tare da halayen duka igiyoyin sine da igiyar cosine. Canjin lokaci na π/2 radians yana ba wa igiyar cosine fara kai, kuma an ce tana jagorantar igiyar sine. Wannan yana nufin cewa sine wave yana yin la'akari da kalaman cosine. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa da raƙuman ruwa, tare da ko ba tare da ɓata lokaci ba.
Misalin igiyar ruwa na cosine, ainihin alakar dake tsakanin igiyar sine da igiyar igiyar ruwa za a iya gani tare da ƙirar jirgin sama mai sarƙaƙƙiya na 3D. Wannan samfurin yana da amfani don fassarar yanayin raƙuman ruwa da ke faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske.
Kunnen mutum na iya gane raƙuman raƙuman raƙuman ruwa guda ɗaya, suna sauti a sarari da tsabta. Ana amfani da igiyoyin sine sau da yawa azaman wakilcin sautunan mitar guda ɗaya, da kuma masu jituwa. Kunnen mutum yana jin sauti a matsayin haɗuwa da raƙuman ruwa na sine, tare da kasancewar mafi girma masu jituwa ban da mahimmancin mitar da ke haifar da bambanci a cikin katako. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa tare da mita iri ɗaya da aka kunna akan kayan kida daban-daban zai bambanta.
Tafa hannu, duk da haka, yana ƙunshe da raƙuman ruwa na lokaci-lokaci, waɗanda ba na lokaci-lokaci ba kuma suna da tsari mara maimaitawa. Masanin ilmin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal sune sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aikin nazari ne mai ƙarfi wanda ake amfani dashi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani dashi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman raƙuman ruwa na iya yaɗuwa ta hanyar canzawa ta hanyar tsarin layin layi da aka rarraba, kuma ana buƙata don nazarin yaduwar igiyoyin ruwa. Raƙuman raƙuman ruwa na iya tafiya ta hanyoyi biyu a sararin samaniya, kuma ana wakilta su da raƙuman ruwa masu girma da mita iri ɗaya amma suna tafiya ta saɓani. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan yayi kama da bayanin kula da ake ɗigo akan kirtani, inda raƙuman ruwa ke nunawa a madaidaitan wuraren ƙarshen kirtani. Tsayayyen igiyoyin ruwa suna faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci sun ƙunshi mahimman mitoci da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsayin kirtani, kuma sun yi daidai da yawan adadin kowane tsawon raka'a na kirtani.
Ta Yaya Matakin Ya Shafi Sine Wave?
Sine wave nau'in nau'in igiyar igiyar ruwa ce mai ci gaba wacce ke da santsi, maimaituwa. Yana da lanƙwan lissafi da aka ayyana ta hanyar aikin trigonometric kuma ana amfani dashi a cikin ilimin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Matsakaicin mitar igiyar igiyar igiyar ruwa ita ce adadin oscillations ko zagayowar da ke faruwa a cikin wani adadin lokaci, yawanci ana aunawa cikin daƙiƙa. Mitar angular, wanda ω ke nunawa, shine ƙimar canjin gardamar aiki, yawanci ana aunawa a cikin radians. Siffar igiyar igiyar ruwa gabaɗaya tana bayyana tana canzawa cikin lokaci ta adadin φ, wanda aka auna cikin daƙiƙa. Naúrar mitar ita ce hertz (Hz), wanda yayi daidai da oscillation ɗaya a sakan daya.
Ana yawan amfani da igiyar sine don siffanta igiyar sauti, kuma ana siffanta ta da aikin sine, f(t) = A sin (ωt + φ). Hakanan ana ganin irin wannan nau'in igiyar igiyar ruwa a cikin tsarin ruwan bazara da ba a tashe ba a ma'auni. Raƙuman raƙuman ruwa suna da mahimmanci a cikin ilimin kimiyyar lissafi saboda suna riƙe da siffar raƙuman ruwa lokacin da aka haɗa su tare, wanda shine dukiya da aka sani da ka'idar superposition. Wannan kadarorin yana haifar da mahimmancin bincike na Fourier, wanda ke ba da damar a iya bambanta sautin sauti daga wani.
A cikin girma ɗaya, za a iya wakilta igiyar sine ta hanyar layi ɗaya. Misali, darajar igiyar igiyar igiyar waya za a iya wakilta ta da layi daya. Don ma'auni na sarari da yawa, ana buƙatar ƙarin ma'auni na gaba ɗaya. Wannan ma'auni yana kwatanta ƙaurawar igiyar ruwa a wani matsayi, x, a wani lokaci, t.
Hadadden igiyar ruwa, kamar igiyar ruwa a cikin tafki bayan an jefar da dutse, yana buƙatar ƙarin hadaddun daidaito. Ana amfani da kalmar sinusoid don siffanta tsarin igiyar ruwa tare da halayen duka igiyoyin sine da igiyar cosine. Canjin lokaci na π/2 radians iri ɗaya ne da farkon farawa, kuma daidai yake da cewa aikin cosine yana jagorantar aikin sine, ko kuma sine ya kasance tsakanin cosine. Ana amfani da kalmar sinusoidal don haɗa kai zuwa duka raƙuman ruwa na sine da raƙuman ruwa tare da ɓangarorin lokaci.
Misalin igiyar ruwa na cosine, ainihin alaƙar da ke tsakanin igiyar sine da igiyar igiyar igiyar ruwa za a iya gani ta amfani da da'irar a cikin ƙirar jirgin sama mai rikiɗar 3D. Wannan yana da amfani don fassarar tsakanin yankuna daban-daban, kamar yadda yanayin raƙuman ruwa iri ɗaya ke faruwa a yanayi, gami da igiyoyin iska, raƙuman sauti, da raƙuman haske.
Kunnen mutum na iya gane raƙuman ruwa guda ɗaya a matsayin sauti a sarari, kuma galibi ana amfani da raƙuman ruwa don wakiltar mitoci guda ɗaya da jituwa. Lokacin da aka haɗa raƙuman ruwa daban-daban tare, yanayin raƙuman ruwa yana canzawa, wanda ke canza timbre na sauti. Kasancewar mafi girman jituwa ban da mahimmancin mitar yana haifar da bambance-bambance a cikin timbre. Wannan shi ne dalilin da ya sa bayanin kula na kiɗa da aka kunna akan kayan kida daban-daban ya bambanta.
Sautin tafa hannu yana ƙunshe da igiyoyin ruwa na lokaci-lokaci, waɗanda ba na lokaci-lokaci ba, sabanin raƙuman ruwa, waɗanda suke lokaci-lokaci. Masanin lissafin Faransa Joseph Fourier ya gano cewa igiyoyin ruwa na sinusoidal su ne sassauƙan tubalan ginin da za a iya amfani da su don siffanta da kusantar kowane nau'in igiyar ruwa na lokaci-lokaci, gami da raƙuman murabba'ai. Binciken Fourier kayan aikin nazari ne mai ƙarfi da ake amfani da shi don nazarin raƙuman ruwa, kamar kwararar zafi, kuma ana yawan amfani da shi wajen sarrafa sigina da ƙididdigar ƙididdiga na jerin lokaci.
Raƙuman ruwan raƙuman ruwa na iya yaduwa a cikin canza salo ta hanyar tsarin layin layi da aka rarraba. Don nazarin yaɗuwar igiyoyin igiyar ruwa, raƙuman raƙuman raƙuman ruwa da ke tafiya a wurare daban-daban a sararin samaniya suna wakilta da raƙuman ruwa masu girma da mitoci iri ɗaya, amma suna tafiya ta wurare dabam-dabam. Lokacin da waɗannan raƙuman ruwa suka yi girma, ana ƙirƙira ƙirar igiyar igiyar ruwa. Wannan shi ne tsarin da ake ƙirƙira lokacin da aka tsinke rubutu a kan igiya. Raƙuman ruwa masu tsaka-tsaki waɗanda ke nunawa daga ƙayyadaddun wuraren ƙarshen kirtani suna haifar da raƙuman ruwa na tsaye waɗanda ke faruwa a wasu mitoci, waɗanda ake magana da su a matsayin mitoci. Waɗannan mitoci masu faɗakarwa sun ƙunshi mitoci na asali da mafi girman jituwa. Matsakaicin resonant na kirtani sun yi daidai da tsayin kirtani kuma sun yi daidai da tushen murabba'in taro kowane tsawon raka'a na kirtani.
Ta yaya Za a Yi Amfani da Mataki don Ƙirƙirar Waveform daban-daban?
Sine taguwar ruwa nau'in nau'in nau'in igiyar igiyar ruwa ce mai ci gaba mai santsi da maimaituwa, kuma ana iya amfani da ita don bayyana al'amura iri-iri a cikin ilimin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. An bayyana su ta hanyar aikin trigonometric, kuma ana iya zana su azaman santsi, lanƙwasa na lokaci-lokaci. Mitar sine wave shine adadin oscillations ko zagayowar da ke faruwa a cikin ƙayyadadden lokaci, yawanci ana aunawa a Hertz (Hz). Mitar angular, ω, ita ce ƙimar da mahawarar aikin ke canzawa, wanda aka auna a cikin radians a sakan daya. Za a iya bayyana kalaman sine a cikin lokaci, tare da canjin lokaci, φ, wanda aka auna cikin daƙiƙa. Ƙimar mara kyau tana wakiltar jinkiri, yayin da ƙima mai kyau tana wakiltar ci gaba.
Mataki shine muhimmin abu na igiyar igiyar ruwa, kuma ana iya amfani da ita don ƙirƙirar nau'ikan igiyoyin ruwa daban-daban. Lokacin da aka haɗa igiyoyin sine guda biyu masu mitar iri ɗaya da lokaci na sabani da girma, sakamakon igiyoyin igiyar ruwa na lokaci-lokaci tare da dukiya iri ɗaya. Wannan kadarorin yana haifar da mahimmancin bincike na Fourier, wanda ke ba da damar ganowa da bincika sigina na musamman na acoustically.
Ana iya amfani da lokaci don ƙirƙirar nau'ikan igiyoyi daban-daban ta hanyoyi masu zuwa:
• Ta hanyar canza yanayin igiyar igiyar ruwa, ana iya sanya shi ya fara a wani lokaci daban. An san wannan a matsayin canjin lokaci, kuma ana iya amfani dashi don ƙirƙirar nau'ikan igiyoyi daban-daban.
• Ta ƙara igiyar igiyar ruwa tare da mitoci daban-daban da lokaci zuwa madaidaicin igiyar ruwa, za a iya ƙirƙira ƙaƙƙarfan igiyar igiyar ruwa. Wannan ana kiransa da jituwa, kuma ana iya amfani dashi don ƙirƙirar sautuna iri-iri.
• Ta hanyar haɗa raƙuman ruwa na sine tare da mitoci daban-daban da matakai, ana iya ƙirƙirar yanayin igiyar igiyar ruwa. Ana kiran wannan a matsayin mitar resonant, kuma ana iya amfani dashi don ƙirƙirar sautuna daban-daban.
• Ta hanyar haɗa raƙuman ruwa na sine tare da mitoci da matakai daban-daban, za a iya ƙirƙira ƙaƙƙarfan tsarin igiyar ruwa. An san wannan a matsayin bincike na Fourier, kuma ana iya amfani dashi don nazarin yaɗuwar igiyar ruwa.
Ta hanyar yin amfani da lokaci don ƙirƙirar nau'ikan igiyoyi daban-daban, yana yiwuwa a ƙirƙiri nau'ikan sautuka da nazarin yaduwar igiyar ruwa. Wannan muhimmiyar kadara ce ta igiyoyin ruwa, kuma ana amfani da su a fannoni daban-daban, gami da acoustics, sarrafa sigina, da kimiyyar lissafi.
Wanene Ke Amfani da Waves na Sine a cikin Kasuwanni?
A matsayin mai saka hannun jari, na tabbata kun ji labarin sine waves da rawar da suke takawa a kasuwannin hada-hadar kudi. A cikin wannan labarin, zan bincika menene raƙuman ruwa na sine, yadda za a iya amfani da su don yin tsinkaya, da dangantakar dake tsakanin igiyoyin sine da bincike na fasaha. A ƙarshen wannan labarin, za ku sami kyakkyawar fahimtar yadda za a iya amfani da igiyoyin sine don amfanin ku a cikin kasuwanni.
Menene Matsayin Sine Waves a cikin Kasuwannin Kudi?
Raƙuman raƙuman ruwa wani nau'i ne na lanƙwan lissafi wanda ke bayyana santsi, maimaituwar oscillations a ci gaba da kalaman. Ana kuma san su da igiyoyin sinusoidal kuma ana amfani da su a cikin ilimin lissafi, kimiyyar lissafi, injiniyanci, da filayen sarrafa sigina. Raƙuman ruwa suna da mahimmanci a kasuwannin kuɗi, saboda ana iya amfani da su don yin tsinkaya da kuma nazarin abubuwan da ke faruwa.
A cikin kasuwannin kuɗi, ana amfani da raƙuman ruwa don ganowa da kuma nazarin abubuwan da ke faruwa. Ana iya amfani da su don gano matakan tallafi da juriya, da kuma gano yiwuwar shigarwa da wuraren fita. Hakanan za'a iya amfani da igiyoyin igiyar ruwa don ganowa da tantance alamu, kamar kai da kafadu, sama da kasa biyu, da sauran sifofi.
Hakanan ana amfani da igiyoyin ruwa a cikin bincike na fasaha. Binciken fasaha shine nazarin motsin farashi da alamu a cikin kasuwannin kudi. Manazarta fasaha suna amfani da raƙuman ruwa don gano abubuwan da ke faruwa, tallafi da matakan juriya, da yuwuwar shigarwa da wuraren fita. Har ila yau, suna amfani da igiyoyin sine don gano alamu, kamar kai da kafadu, sama da kasa biyu, da sauran alamu.
Hakanan ana iya amfani da igiyoyin ruwa don yin tsinkaya. Ta hanyar nazarin abubuwan da suka gabata da na yanzu, masu nazarin fasaha na iya yin tsinkaya game da motsin farashin nan gaba. Ta hanyar nazarin raƙuman ruwa na sine, za su iya gano yuwuwar shigarwa da wuraren fita, da yuwuwar tallafi da matakan juriya.
Sine taguwar ruwa kayan aiki ne mai mahimmanci ga masu nazarin fasaha a cikin kasuwannin kuɗi. Ana iya amfani da su don ganowa da kuma nazarin abubuwan da ke faruwa, tallafi da matakan juriya, da yuwuwar shigarwa da wuraren fita. Hakanan ana iya amfani da su don yin tsinkaya game da motsin farashin nan gaba. Ta hanyar nazarin raƙuman ruwa na sine, manazarta fasaha za su iya samun kyakkyawar fahimta game da kasuwanni kuma su yanke shawara mai zurfi.
Ta yaya Za a Yi Amfani da Waves don Yin Hasashe?
Ana amfani da raƙuman ruwa a cikin kasuwannin kuɗi don nazarin yanayin da yin tsinkaya. Su nau'in nau'in igiyar igiyar ruwa ne da ke jujjuyawa tsakanin maki biyu, kuma ana iya amfani da su don gano alamu da abubuwan da ke faruwa a kasuwanni. Ana amfani da raƙuman ruwa a cikin bincike na fasaha kuma ana iya amfani da su don tsinkaya motsin farashin nan gaba.
Ga wasu hanyoyin da za a iya amfani da igiyar ruwa a cikin kasuwanni:
• Gano matakan tallafi da juriya: Ana iya amfani da raƙuman ruwa don gano matakan tallafi da juriya a cikin kasuwanni. Ta hanyar kallon kololuwa da raƙuman ruwa na sine, yan kasuwa na iya gano wuraren da farashin zai iya samun tallafi ko juriya.
• Gano jujjuyawar yanayi: Ta hanyar kallon igiyar ruwa, 'yan kasuwa na iya gano yiwuwar jujjuyawar yanayin. Idan sine igiyar ruwa yana nuna yanayin ƙasa, 'yan kasuwa na iya neman wuraren da za a iya tallafawa inda yanayin zai iya juyawa.
• Gano tsarin farashi: Za a iya amfani da igiyoyin ruwa don gano yanayin farashi a kasuwanni. Ta hanyar kallon sine, 'yan kasuwa za su iya gano wuraren da za a iya samun goyon baya da juriya, da kuma yiwuwar juyawa.
• Yin tsinkaya: Ta hanyar kallon igiyoyin sine, 'yan kasuwa na iya yin tsinkaya game da motsin farashi na gaba. Ta hanyar kallon kololuwa da raƙuman ruwa na sine, 'yan kasuwa za su iya gano wuraren da za a iya samun goyon baya da juriya, da kuma yiwuwar juyawa.
Sine taguwar ruwa na iya zama kayan aiki mai amfani ga yan kasuwa da ke neman yin tsinkaya a cikin kasuwanni. Ta hanyar kallon sine, 'yan kasuwa za su iya gano wuraren da za a iya samun goyon baya da juriya, da kuma yiwuwar juyawa. Ta hanyar amfani da igiyoyin ruwa na sine, 'yan kasuwa na iya yanke shawarar yanke shawara game da kasuwancin su kuma suna ƙara damar samun nasara.
Menene Alakar Tsakanin Waves Sine da Binciken Fasaha?
Ana amfani da raƙuman ruwa a cikin kasuwannin kuɗi don nazarin halin farashin da yin tsinkaya game da motsin farashin nan gaba. Ana amfani da su ta hanyar manazarta fasaha don gano abubuwan da ke faruwa, tallafi da matakan juriya, da kuma gano yuwuwar shigar da wuraren fita.
Sine taguwar ruwa nau'in nau'in nau'in igiyar ruwa ne na lokaci-lokaci, ma'ana suna maimaita kan lokaci. Ana siffanta su da santsi, maimaituwar oscillation kuma ana amfani da su don bayyana abubuwa da yawa a cikin ilimin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina. A cikin kasuwannin kuɗi, ana amfani da raƙuman ruwa na sine don gano maimaita alamu a cikin motsin farashin.
Dangantakar da ke tsakanin igiyoyin sine da bincike na fasaha shine cewa za a iya amfani da igiyoyin ruwa don gano maimaita alamu a cikin motsin farashin. Manazarta fasaha suna amfani da raƙuman ruwa don gano abubuwan da ke faruwa, tallafi da matakan juriya, da kuma gano yuwuwar shigarwa da wuraren fita.
Hakanan za'a iya amfani da igiyoyin ruwa don yin tsinkaya game da motsin farashin nan gaba. Ta hanyar nazarin halayen farashin da suka gabata, manazarta fasaha za su iya gano tsarin maimaitawa kuma suyi amfani da waɗannan alamu don yin tsinkaya game da motsin farashin nan gaba.
Hakanan ana amfani da igiyoyin ruwa don gano hawan keke a cikin kasuwanni. Ta hanyar nazarin halayen farashi akan lokaci, manazarta fasaha na iya gano maimaita hawan keke kuma suyi amfani da waɗannan zagayawa don yin tsinkaya game da motsin farashin nan gaba.
A taƙaice, ana amfani da raƙuman ruwa na sine a cikin kasuwannin kuɗi don nazarin halin farashin da yin tsinkaya game da motsin farashin nan gaba. Ana amfani da su ta hanyar manazarta fasaha don gano abubuwan da ke faruwa, tallafi da matakan juriya, da kuma gano yuwuwar shigar da wuraren fita. Hakanan za'a iya amfani da raƙuman ruwa don yin tsinkaya game da motsin farashin nan gaba ta hanyar nazarin halayen farashin da suka gabata da gano maimaita alamu da hawan keke.
bambance-bambancen
Sine wave vs simulated sine wave
Sine Wave vs Simulated Sine Wave:
• Sine wave wani nau'in igiyar igiyar ruwa ne mai ci gaba da bin tsarin sinusoidal kuma ana amfani dashi a cikin lissafi, kimiyyar lissafi, injiniyanci, da sarrafa sigina.
• Siminated sine wave siffa ce ta wucin gadi da aka ƙirƙira ta hanyar jujjuyawar wuta don kwaikwayi halayen igiyar igiyar ruwa.
• Raƙuman raƙuman ruwa suna da mitoci guda ɗaya da lokaci guda, yayin da raƙuman ruwa da aka kwaikwayi suna da mitoci da matakai masu yawa.
• Ana amfani da igiyoyin sine don wakiltar raƙuman sauti da sauran nau'ikan makamashi, yayin da ake amfani da igiyoyin sine da aka kwaikwayi don kunna na'urorin lantarki.
• Raƙuman raƙuman ruwa suna haifar da maɓuɓɓuka na halitta, yayin da igiyoyin sine da aka kwaikwayi ana haifar da su ta hanyar inverter.
• Ana amfani da igiyoyin sine a cikin bincike na Fourier don nazarin yaduwar igiyoyin ruwa, yayin da ake amfani da igiyoyin sine da aka yi amfani da su don kunna na'urorin lantarki.
• Ana amfani da igiyoyin sine don wakiltar raƙuman sauti, yayin da ake amfani da igiyoyin sine da aka kwaikwayi don kunna na'urorin lantarki.
FAQ game da sine wave
Shin sararin samaniya igiyar ruwa ce?
A'a, sararin samaniya ba igiyar ruwa ba ce. Sine wave wani lanƙwan lissafin lissafi ne wanda ke bayyana santsi, maimaituwar oscillation, kuma shine ci gaba da igiyar igiyar ruwa tare da mitoci ɗaya. Duk da haka, sararin samaniya wani tsari ne mai sarkakiya kuma mai jujjuyawa wanda kullum yana canzawa kuma yana tasowa.
Duniyar ta ƙunshi abubuwa daban-daban da suka haɗa da kwayoyin halitta, kuzari, da lokacin sarari. Wadannan sassan suna mu'amala da juna ta hanyoyi daban-daban, wanda ke haifar da al'amura iri-iri, tun daga samuwar taurari zuwa juyin halitta. Hakanan ana gudanar da sararin samaniya bisa ka'idojin kimiyyar lissafi, wadanda suka dogara akan ma'auni na lissafi.
Duniya ba igiyar ruwa ba ce, amma tana ƙunshe da igiyoyin sine da yawa. Misali, raƙuman sauti raƙuman ruwa ne, kuma suna nan a sararin samaniya. Raƙuman haske suma raƙuman ruwa ne, kuma suna nan a sararin samaniya. Bugu da kari, sararin samaniya yana dauke da wasu nau'ikan raƙuman ruwa da yawa, kamar igiyoyin lantarki na lantarki, raƙuman nauyi, da raƙuman ƙima.
sararin samaniya kuma yana kunshe da wasu barbashi daban-daban, kamar su protons, neutrons, da electrons. Wadannan kwayoyin halitta suna mu'amala da juna ta hanyoyi daban-daban, wanda ke haifar da al'amura iri-iri, tun daga samuwar kwayoyin halitta zuwa juyin halittar taurari.
A ƙarshe, sararin samaniya ba igiyar ruwa ba ce, amma tana ɗauke da raƙuman ruwa da yawa. Waɗannan raƙuman ruwa na sine suna kasancewa a cikin nau'ikan raƙuman sauti, raƙuman haske, da sauran nau'ikan raƙuman ruwa. Haka nan duniya tana kunshe da wasu barbashi daban-daban wadanda suke mu'amala da juna ta hanyoyi daban-daban, wanda ke haifar da al'amura iri-iri.
Muhimman dangantaka
Girma:
Amplitude shine matsakaicin matsayar igiyar ruwa daga ma'auni.
• Ana auna shi da raka'a ta nisa, kamar mita ko ƙafafu.
• Har ila yau, yana da alaƙa da makamashin igiyar ruwa, tare da ƙananan amplitudes suna da karin makamashi.
Girman kalaman sine ya yi daidai da tushen murabba'in mitarsa.
• Girman igiyoyin sine kuma yana da alaƙa da lokacinsa, tare da mafi girma amplitudes yana da babban motsi na lokaci.
Amsar Saurari:
Amsar mitar ita ce ma'aunin yadda tsarin ke amsa mitoci daban-daban na shigarwa.
• Yawancin lokaci ana auna shi a cikin decibels (dB) kuma ma'auni ne na riba ko attenuation na tsarin a mitoci daban-daban.
• Ana ƙayyade amsawar mitar igiyar sine ta girman girmansa da lokaci.
• igiyar sine tare da girman girman girma zai sami amsa mafi girma fiye da wanda ke da ƙananan girman.
• Amsar mitar igiyar igiyar ruwa ita ma tana shafar yanayin sa, tare da mafi girman matakan da ke haifar da martani mai girma.
Sawtooth:
• igiyar sawtooth nau'in nau'in igiyar igiyar ruwa ce ta lokaci-lokaci wacce ke da tsayin daka da faduwa a hankali.
Ana amfani da shi sau da yawa wajen haɗa sauti kuma ana amfani dashi a wasu nau'ikan sarrafa siginar dijital.
• igiyar sawtooth yayi kama da sine wave domin shi ne na lokaci-lokaci, amma yana da wata siffa ta daban.
• igiyar sawtooth tana da kaifi tashi da faduwa a hankali, yayin da igiyar sine ke tashi a hankali da faduwa a hankali.
• Kalaman sawtooth yana da mafi girman martani fiye da igiyar sine, kuma ana amfani dashi sau da yawa a cikin haɗin sauti don ƙirƙirar ƙarar sauti.
• Hakanan ana amfani da igiyar sawtooth a wasu nau'ikan sarrafa siginar dijital, kamar daidaitawar mita da daidaita yanayin lokaci.
Kammalawa
Sine taguwar ruwa wani muhimmin bangare ne na kimiyyar lissafi, lissafi, injiniyanci, sarrafa sigina, da sauran fannoni masu yawa. Wani nau'in igiyar igiyar ruwa ce mai ci gaba da ke da santsi, mai maimaituwa, kuma galibi ana amfani da su don kwatanta raƙuman sauti, raƙuman haske, da sauran nau'ikan igiyoyin motsi. Sine taguwar ruwa suma suna da mahimmanci a cikin bincike na Fourier, wanda ke sa su zama na musamman kuma suna ba su damar amfani da su a cikin masu canjin sarari. Fahimtar raƙuman raƙuman ruwa na iya taimaka mana da fahimtar yaduwar igiyar ruwa, sarrafa sigina, da kuma nazarin jerin lokaci.
Ni Joost Nusselder, wanda ya kafa Neaera kuma ɗan kasuwan abun ciki, uba, kuma ina son gwada sabbin kayan aiki tare da guitar a zuciyar sha'awara, kuma tare da ƙungiyara, Ina ƙirƙirar labaran labarai masu zurfi tun daga 2020. don taimakawa masu karatu masu aminci tare da rikodi da tukwici na guitar.
