I-sine wave yifom eqhubekayo ephinda-phinda yonke i-2π radians, okanye i-360 degrees, kwaye ingasetyenziselwa ukwenza umzekelo weziganeko ezininzi zendalo. I-sine wave ikwabizwa ngokuba yi-sinusoid.
Igama elithi sine wave lithatyathwe kumsebenzi wezibalo we-sine, osisiseko sokwakheka kwamaza. I-sine wave yenye yezona ndlela zilula zamaza kwaye isetyenziswa kakhulu kwiinkalo ezininzi.
Kweli nqaku, ndiza kuchaza ukuba yintoni i-sine wave kwaye kutheni inamandla kangaka.
Yintoni iliza elinesine?
I-sine Wave yi-oscillation egudileyo, ephinda-phindayo ngokohlobo lwamaza aqhubekayo. Ligophe lemathematika elichazwa ngokomsebenzi wesine trigonometric, kwaye imelwe ngokomzobo njengomaza. Luhlobo lwamaza aqhubekayo oluphawulwa ngokugudileyo, umsebenzi wamaxesha athile, kwaye lufumaneka kwiindawo ezininzi zemathematika, ifiziksi, ubunjineli, kunye nokusetyenzwa komqondiso.
The frequency of a sine wave linani lokujikeleza okanye imijikelo eyenzeka ngexesha elinikiweyo. I-angular frequency, echazwa ngu-ω, yireyithi yokutshintsha kwengxoxo yokusebenza, kwaye ilinganiswa ngeeyunithi zeeradians ngesekhondi. Ixabiso elingengo-zero lotshintsho lwesigaba, elichazwe ngu-φ, limele ukutshintshwa kwe-waveform yonke ngexesha, ngexabiso elibi elimele ukulibaziseka, kunye nexabiso elilungileyo elimele ukuqhubela phambili kwimizuzwana. Ubuninzi be-sine wave bulinganiswa nge-hertz (Hz).
I-sine wave isetyenziselwa ukuchaza isandi somsindo, kwaye ichazwa ngumsebenzi wesine, f (t) = Isono (ωt + φ). Ikwasetyenziswa ukuchaza inkqubo yentlakohlaza engaxitywanga kwi-equilibrium, kwaye iyimo yamaza ebalulekileyo kwifiziksi njengoko igcina imilo yayo yamaza xa idityaniswe kwelinye i-sine wave yophindaphindo olufanayo kunye nesigaba esingenasizathu kunye nobukhulu. Le propathi yaziwa ngokuba ngumgaqo-siseko, kwaye yipropathi yamaza ngamaxesha athile. Le propati ikhokelela ekubalulekeni kohlalutyo lwe-Fourier, njengoko yenza kube lula ukwahlula ngokuvakalayo i-acoustic variable, x, emele indawo kwindawo enye apho i-wave isasazeka.
Uphawu lweparamitha yomaza ibizwa ngokuba yinombolo yamaza, k, eyinombolo yamaza e-angular kwaye imele ulungelelwaniso phakathi kwamaza omoya, ω, kunye nesantya somgca sosasazo, ν. Inombolo yamaza inxulumene ne-angular frequency kunye ne-wavelength, λ, nge-equation λ = 2π/k. I-equation ye-sine wave kwi-dimensioni enye inikwa ngu-y = Isono (ωt + φ). I-equation ebanzi ngakumbi inikwa ngu y = Isono (kx - ωt + φ), enika ukufuduswa kwamaza kwindawo x ngexesha t.
Amaza eSine nawo anokumelwa kwimilinganiselo emininzi yendawo. I-equation ye-wave yenqwelomoya ehambayo inikwa ngu y = A isono (kx - ωt + φ). Oku kunokutolikwa njengemveliso yamachaphaza ee-vectors ezimbini, kwaye isetyenziselwa ukuchaza amaza antsonkothileyo, anje ngamaza amanzi echibini xa kuwiswa ilitye. Iiequations ezintsonkothileyo ngakumbi ziyafuneka ukuchaza igama elithi sinusoid, elichaza iimpawu zamaza omabini amaza e-sine kunye ne-cosine kunye nokutshintsha kwesigaba se-π/2 radians, enika i-cosine wave isiqalo sentloko phezu kwe-sine wave. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye ne-cosine anesigaba sokunciphisa.
Amaza esine afumaneka kwindalo, kuquka amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomntu iyakwazi ukubona amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine asetyenziselwa ukumela i-frequency kunye ne-harmonics. Indlebe yomntu ibona isandi njengendibaniselwano yamaza e-sine anee-amplitudes ezahlukeneyo kunye nee-frequencies, kunye nobukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukuhluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elinesandi esifanayo esidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Isandi sokuqhwaba ngesandla siqulathe amaza e-aperiodic, angaphindaphindiyo kwindalo, kwaye angalandeli ipateni yamaza e-sine. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwalo naluphi na uhlobo lwamaza olwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, afana nokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine asetyenziselwa ukusabalalisa kunye nokutshintsha ifom kwiinkqubo ezisasazwayo zomgca.
Yintoni imbali yamaza e-sine?
I-sine wave inembali ende nenomdla. Yafunyanwa okokuqala yingcali yezibalo yaseFransi uJoseph Fourier ngo-1822, owabonisa ukuba naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile lunokubonakaliswa njengesixa samaza esine. Oku kufunyenweyo kuguqule inkalo yezibalo kunye nefiziksi kwaye ibisetyenziswa ukusukela ngoko.
• Umsebenzi kaFourier waphuhliswa ngakumbi yingcali yezibalo yaseJamani uCarl Friedrich Gauss ngo-1833, owabonisa ukuba amaza e-sine anokusetyenziswa ukumela nayiphi na imo eyenzeka ngamaxesha athile.
• Ngasekupheleni kwenkulungwane ye-19, i-sine wave yasetyenziswa ukuchaza ukuziphatha kweesekethe zombane.
• Ekuqaleni kwenkulungwane ye-20, i-sine wave yayisetyenziselwa ukuchaza ukuziphatha kwamaza omsindo.
• Ngeminyaka yee-1950, i-sine wave yasetyenziswa ukuchaza ukuziphatha kwamaza okukhanya.
• Ngeminyaka yee-1960, i-sine wave yasetyenziswa ukuchaza ukuziphatha kwamaza erediyo.
• Ngeminyaka yee-1970, i-sine wave yasetyenziswa ukuchaza ukuziphatha kweempawu zedijithali.
• Ngeminyaka yoo-1980, i-sine wave yasetyenziswa ukuchaza ukuziphatha kwamaza ombane.
• Ngeminyaka yee-1990, iliza lesine lasetyenziswa ukuchaza indlela yokuziphatha kweenkqubo zoomatshini bequantum.
• Namhlanje, i-sine wave isetyenziswa kwiinkalo ezahlukeneyo, kuquka imathematika, ifiziksi, ubunjineli, ukusetyenzwa komqondiso, nokunye. Sisixhobo esibalulekileyo sokuqonda ukuziphatha kwamaza kwaye sisetyenziswa kwizicelo ezahlukeneyo, ukusuka kwi-audio kunye nokulungiswa kwevidiyo ukuya kumfanekiso wezonyango kunye neerobhothi.
Sine Wave Mathematics
Ndizakube ndithetha ngamaza e-sine, igophe lezibalo elichaza i-oscillation egudileyo, ephindaphindayo. Siza kujonga indlela amaza e-sine achazwa ngayo, ubudlelwane phakathi kwe-angular frequency kunye nenani lamaza, kwaye yintoni uhlalutyo lwe-Fourier. Siza kuphonononga ukuba asetyenziswa njani amaza e-sine kwifiziksi, ubunjineli, kunye nokusetyenzwa kwemiqondiso.
Yintoni iSine Wave?
I-sine wave yi-oscillation egudileyo, ephindaphindayo eyenza iliza eliqhubekayo. Ligophe lemathematika, elichazwa ngumsebenzi wesine we-trigonometric, kwaye ibonwa rhoqo kwiigrafu kunye neefom zamaza. Ludidi lwamaza aqhubekayo, okuthetha ukuba lugudilo, lusebenza ngamaxesha athile olwenzeka kwimathematika, kwifiziksi, kubunjineli, nakwimimandla yokusetyenzwa komqondiso.
I-sine wave ine-frequency yesiqhelo, eli linani le-oscillation okanye imijikelo eyenzeka ngexesha elinikiweyo. Oku kumelwa yi-angular frequency, ω, elingana no-2πf, apho i-f yi-frequency kwi-hertz (Hz). I-sine wave nayo inokutshintshwa ngexesha, ngexabiso elingalunganga elimele ukulibaziseka kunye nexabiso elilungileyo elimele i-advance kwimizuzwana.
I-sine wave isoloko isetyenziselwa ukuchaza isandi somsindo, njengoko sichazwa ngumsebenzi wesine. Ikwasetyenziselwa ukumela inkqubo yentlakohlaza engenamda kwi-equilibrium. I-sine wave yingqikelelo ebalulekileyo kwifiziksi, njengoko igcina imilo yayo yamaza xa idityaniswe kwelinye i-sine wave yophindaphindo olufanayo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati, eyaziwa ngokuba ngumgaqo-siseko we-superposition, yinto ekhokelela ekubalulekeni kohlalutyo lwe-Fourier, njengoko yenza kube lula ukwahlula ngokuvakalayo phakathi kwezinto eziguquguqukayo zendawo.
I-equation ye-sine wave kumlinganiselo omnye inikwe ngu-y = Isono (ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, t lixesha, kwaye φ yi-phase shift. Kumzekelo womgca omnye, ukuba ixabiso le-wave lithathwa njengocingo, ngoko i-equation ye-sine wave kwimilinganiselo emibini yendawo inikwa ngu y = A isono (kx - ωt + φ), apho i-k iliza inani. Oku kunokutolikwa njengemveliso yeevektha ezimbini, imveliso yamachaphaza.
Amaza antsonkothileyo, afana nalawo adalwe xa ilitye liwiswa echibini, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu zombini i-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba se-π/2 radians, okanye isiqalo sentloko, kuthiwa kunika i-cosine wave, ekhokelela kwi-sine wave. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Ukubonisa i-cosine wave kunokunceda ukubonisa unxulumano olusisiseko phakathi kwesangqa kunye nemodeli ye-3D yenqwelomoya entsonkothileyo, enokunceda ukujonga ukuba luncedo kwamaza e-sine ekuguquleleni phakathi kwemimandla. Le pateni yamaza yenzeka kwindalo, kuqukwa namaza omoya, amaza esandi, kunye namaza okukhanya. Indlebe yomntu iyakwazi ukuqaphela amaza e-sine enye njengesandi esicacileyo, kwaye imiboniso yamaza e-sine ye-harmonics yefrikhwensi enye nayo iyaqondakala.
Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko yinto ebangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Indlebe yomntu ibona isandi njengamaxesha ngamaxesha kunye ne-aperiodic. Isandi se-periodic yenziwe ngamaza e-sine, ngelixa isandi se-aperiodic sibonwa njengengxolo. Ingxolo ibonakaliswe njenge-aperiodic, njengoko inepateni engaphindi.
Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwalo naluphi na uhlobo lwamaza olwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine nawo anokusasaza ngokutshintsha iifom kwiinkqubo ezisasaziweyo zomgca.
Amaza eSine ahamba kumacala ahlukeneyo esithubeni amelwa ngamaza anobukhulu obufanayo nokuphindaphinda. Xa la maza egqithisile, kwenziwa ipateni yokuma yamaza, njengoko kubonakala xa kuncothulwa inqaku ngomtya. Amaza aphazamisayo abonakaliswe kwiisiphelo ezisisigxina zomtya adala amaza amileyo, ayenzeka kwiifrikhwensi ezithile ezaziwa ngokuba zii-resonant frequencies. Ezi zenziwa ngamaza omoya asisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bawo, kwaye ngokuchanekileyo zihambelana nobunzima ngeyunithi yobude bomtya.
Ichazwa njani iSine Wave?
I-sine wave yi-oscillation egudileyo, ephinda-phindayo yeform yamaza eqhubekayo. Ichazwa ngokwemathematika njengomsebenzi we-trigonometric, kwaye igrafu njenge-sinusoid. I-sine wave yingqikelelo ebalulekileyo kwifiziksi, njengoko igcina imilo yayo yamaza xa idityaniswe kwamanye amaza e-sine amatyeli anjalo kunye nobukhulu besigaba esingenasizathu. Le propati yaziwa ngokuba ngumgaqo-siseko, kwaye ikhokelela ekubalulekeni kwayo kuhlalutyo lwe-Fourier.
Amaza e-Sine afumaneka kwiindawo ezininzi zemathematika, i-physics, ubunjineli, kunye nokulungiswa kwemiqondiso. Zibonakaliswa ngokuphindaphindiweyo kwazo, inani le-oscillations okanye imijikelo eyenzeka ngexesha elithile. I-angular frequency, ω, ngumyinge wotshintsho lwengxoxo yemisebenzi kwiiradians ngesekhondi. Ixabiso elingeyo-zero le-φ, i-shift yesigaba, imele utshintsho kwi-waveform yonke ngexesha, kunye nexabiso elibi elimele ukulibaziseka, kunye nexabiso elihle elimele ukuqhubela phambili kwimizuzwana.
Kwisandi, i-sine wave ichazwa yi-equation f = ω/2π, apho u-f yi-frequency of oscillations, kwaye ω yi-angular frequency. Le equation ikwasebenza kwinkqubo yobunzima bentwasahlobo engaxinzekiyo kwi-equilibrium. Amaza e-Sine nawo abalulekile kwi-acoustics, njengoko ikuphela kwendlela yamaza ebonwa njenge-frequency enye yindlebe yomntu. I-sine wave enye yenziwe ngokuphindaphindiweyo okusisiseko kunye ne-harmonics ephezulu, zonke zibonwa njengenqaku elifanayo.
Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko yinto ebangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku elifanayo lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo. Ukuqhwaba ngesandla, umzekelo, kukho amaza e-aperiodic, angaphindaphindiyo, ukongeza kumaza e-sine.
Ekuqaleni kwenkulungwane ye-19, isazi sezibalo esingumFrentshi uJoseph Fourier wafumanisa ukuba amaza e-sinusoidal anokusetyenziswa njengeebhloko zokwakha ezilula ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sohlalutyo esisetyenziselwa ukufunda amaza ekuqukuqeni kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasazeka kulo naliphi na icala esithubeni, kwaye amelwe ngamaza ane-amplitude, frequency, kunye nokuhamba kumacala achaseneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Le yinto efanayo eyenzekayo xa inqaku litsalwa kumtya, kunye namaza aphazamisayo abonakaliswe kwiisiphelo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies, ezenziwe ngamaza omoya asisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwekhwezi ze-resonant zomtya zihambelana nobude bawo, kwaye ngokuphambeneyo zihambelana nengcambu yobunzima bayo ngobude beyunithi nganye.
Isishwankathelo, igama elithi sinusoid lisetyenziselwa ukuchaza iimpawu zamaza omabini amaza e-sine kunye ne-cosine, kunye nokutshintshwa kwesigaba se-π/2 radians, oku kuthetha ukuba i-cosine wave inentloko kwaye i-sine wave ishiya ngasemva. Igama elithi sinusoidal lisetyenziswa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye ne-cosine anesigaba sokunciphisa. Oku kuboniswa ngamaza e-cosine kulo mfanekiso ungasentla. Obu budlelwane busisiseko phakathi kwe-sine kunye ne-cosine inokubonwa kusetyenziswa imodeli ye-3D yendiza entsonkothileyo, ebonisa ngakumbi ukuba luncedo koguqulo lwezi ngqikelelo kwimida eyahlukeneyo. Ipateni yamaza yenzeka kwindalo, kubandakanywa nomoya, isandi, kunye namaza okukhanya.
Buyintoni uBudlelwane phakathi kweAngular Frequency kunye neNombolo yamaza?
I-sine wave ligophe lemathematika elichaza i-oscillation egudileyo, ephindaphindayo. I-wave eqhubekayo, eyaziwa ngokuba yi-sinusoidal wave okanye i-sinusoid, kwaye ichazwa ngokwemigaqo ye-trigonometric sine function. Igrafu ye-sine wave ibonisa ifom yamaza ejikeleza phakathi kobuninzi kunye nexabiso eliphantsi.
I-angular frequency, ω, yireyithi yotshintsho lwengxoxo yokusebenza, elinganiselwa kwiiradians ngesekhondi. Ixabiso elingeyo-zero le-φ, inguqu yesigaba, imele ukutshintshwa kwi-waveform yonke okanye phambili okanye ngasemva ngexesha. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana. I-frequency, f, linani le-oscillations okanye imijikelo eyenzekayo kwisekhondi enye, elinganiselwa kwi-hertz (Hz).
I-sine wave ibalulekile kwifiziksi kuba igcina imilo yamaza xa idityaniswe kwelinye iliza le-sine yefrikhwensi efanayo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati yeefom zamaza ngamaxesha yaziwa ngokuba ngumgaqo-siseko we-superposition kwaye yiyo ekhokelela kukubaluleka kohlalutyo lwe-Fourier. Oku kuyenza ibe yodwa ngokuvakalayo kwaye yiyo loo nto isetyenziswa kuguquguquko lwesithuba x, emele indawo kumlinganiselo omnye. Amaza asasaza ngeparameter yophawu, k, ebizwa ngokuba yinombolo yamaza okanye inombolo ye-angular wave, emele ulungelelwaniso phakathi kwe-angular frequency, ω, kunye nesantya somgca sosasazo, ν. Inombolo yamaza, k, inxulumene ne-engular frequency, ω, kunye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave kumlinganiselo omnye inikwa ngu-y = A isono (ωt + φ). Le nxaki inika ukususwa kwamaza nakweyiphi na indawo x nangaliphi na ixesha t. Umzekelo womgca omnye uqwalaselwa, apho ixabiso le-wave linikezelwa ngu y = A isono (ωt + φ).
Kwimilinganiselo emibini okanye ngaphezulu yendawo, i-equation ichaza iliza lenqwelomoya ehambayo. Isikhundla x sinikwa ngu x = A isono (kx – ωt + φ). Le nxaki inokutolikwa njengeevekhtha ezimbini, imveliso yayo iyimveliso yamachaphaza.
Amaza antsonkothileyo, afana nalawo adalwe xa ilitye liwela echibini lamanzi, afuna iiequations ezintsonkothileyo ngakumbi ukuwachaza. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu zombini i-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba se-π/2 radians (okanye 90°) kunika i-cosine wave isiqalo, ngoko kuthiwa ikhokele i-sine wave. Oku kukhokelela kubudlelwane obusisiseko phakathi kwe-sine kunye nemisebenzi ye-cosine, enokuthi ibonwe njengesangqa kwimodeli ye-3D yendiza enzima.
Ukuba luncedo koguqulelo lwale ngcamango kweminye imimandla kubonakaliswa yinto yokuba ipateni efanayo yamaza yenzeka kwindalo, kubandakanywa amaza omoya, amaza esandi, namaza okukhanya. Indlebe yomntu iyakwazi ukubona amaza e-sine enye njengesandi esicacileyo. Amaza e-Sine abonisa ukuphindaphinda okukodwa kunye ne-harmonics, kwaye indlebe yomntu iyakwazi ukuvakala amaza e-sine kunye ne-harmonics ebonakalayo. Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukuhluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Isandi sokuqhwaba ngesandla siqulathe amaza e-aperiodic, angeyo-periodic, okanye anepateni engaphindi. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, afana nokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza ekutshintsheni ifom ngokusebenzisa iinkqubo ezisasaziweyo zomgca. Oku kuyafuneka ukuhlalutya ukwanda kwamaza kwimilinganiselo emibini okanye ngaphezulu. Amaza eSine ahamba kumacala ahlukeneyo esithubeni amelwa ngamaza anobukhulu obufanayo nokuphindaphinda. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Oku kuyafana nokwenzeka xa kutsalwa inowuthi emtya; amaza aphazamisayo abonakaliswa kwiindawo ezisisigxina zomtya, kwaye amaza amileyo avela kwiifrikhwensi ezithile, ezibizwa ngokuba yi-resonant frequencies. Ezi frikhwensi zenziwe ngokuphindaphindiweyo okusisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwekhwethe zeresonant zomtya zilingana nobude bawo kwaye zithelekiseka ngokuphambeneyo kwingcambu yobunzima bayo ngobude beyunithi.
Yintoni uHlahlelo lweFourier?
I-sine wave yi-oscillation egudileyo, ephinda-phindayo echazwa ngokwemathematika njengeliza eliqhubekayo. Ikwabizwa ngokuba ngamaza e-sinusoidal, kwaye ichazwa ngumsebenzi wesine we-trigonometric. Igrafu ye-sine wave yigophe eligudileyo, lamaxesha athile elisetyenziswa kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokusetyenzwa komqondiso.
I-frequency eqhelekileyo, okanye inani le-oscillations okanye imijikelo eyenzeka kwixesha elinikiweyo, limelwe ngunobumba wesiGrike ω (omega). Oku kwaziwa njenge-angular frequency, kwaye ngumyinge apho ingxabano yomsebenzi itshintsha kwiiyunithi zeeradians.
I-sine wave inokutshintshwa ngexesha ngokutshintsha kwesigaba, esimelwe ngunobumba wesiGrike φ (phi). Ixabiso elilambathayo limele ukulibaziseka, kwaye ixabiso elivumayo limele kwangaphambili kwimizuzwana. Ubuninzi be-sine wave bulinganiswa nge-hertz (Hz).
I-sine wave isoloko isetyenziselwa ukuchaza amaza omsindo, kwaye ichazwa ngumsebenzi wesine f (t) = Isono (ωt + φ). Ii-oscillations zolu hlobo zibonwa kwi-spring-mass system engapheliyo ngokulingana.
I-sine wave ibalulekile kwifiziksi kuba igcina imilo yamaza xa idityaniswe kwelinye i-sine wave yamaza aphindaphindiweyo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati, ebizwa ngokuba ngumgaqo we-superposition, yiyo ekhokelela ekubalulekeni kwayo kuhlalutyo lwe-Fourier. Oku kuyenza ibe yodwa ngokuvakalayo kwaye yiyo loo nto isetyenziselwa ukuchaza iinguqu zesithuba.
Umzekelo, ukuba u-x umele indawo yomlinganiselo wamaza asasazayo, ngoko uphawu lweparameter k (inani lamaza) imele ulungelelwaniso phakathi kwe-engular frequency ω kunye nesantya somgca sosasazo ν. Inombolo yamaza u-k inxulumene ne-engular frequency ω kunye ne-wavelength λ (lambda) nge-equation k = 2π/λ. I-frequency f kunye nesantya somgca v zihambelana ne-equation v = fλ.
I-equation ye-sine wave kumlinganiselo omnye ngu-y = Isono (ωt + φ). Olu ngqamaniso lungenziwa ngokubanzi kwimilinganiselo emininzi, kunye nomzekelo womgca omnye, ixabiso le-wave nakweyiphi na indawo x nangaliphi na ixesha t inikwe ngu y = A isono (kx - ωt + φ).
Amaza antsonkothileyo, afana nalawo abonwa xa kuwiswa ilitye echibini, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza anezi mpawu, kwaye ibandakanya amaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Ukubonisa i-cosine wave, ubudlelwane obusisiseko phakathi kwe-sine wave kunye ne-cosine wave iyafana nobudlelwane phakathi kwesangqa kunye nemodeli ye-3D yenqwelomoya entsonkothileyo. Oku kuluncedo ekuboneni ukuba luncedo koguqulelo lwamaza anesine phakathi kwemimandla eyahlukeneyo.
Ipateni yamaza yenzeka kwindalo, kubandakanywa amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziselwa ukumela amaza omoya kunye neeharmonics.
Indlebe yomntu ibona isandi kunye nendibaniselwano yamaza e-sine kunye nesandi sexesha, kunye nobukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Ukuqhwaba ngesandla, nangona kunjalo, kuqulethe amaza e-aperiodic, angaphindaphindiyo. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere.
Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine anokusasaza ngaphandle kokutshintsha uhlobo lwawo kwiinkqubo ezisasazwayo zomgca, yiyo loo nto zifuneka ukuhlalutya ukusasazwa kwamaza.
Amaza eSine ahamba kumacala ahlukeneyo esithubeni amelwa ngamaza anobukhulu obufanayo nokuphindaphinda. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Oku kubonakala xa inqaku lihluthwa kumtya, kwaye amaza aphazamisayo abonakaliswe kwiindawo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Ezi frikhwensi zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bawo, kwaye ngokuchanekileyo zihambelana nobunzima ngeyunithi yobude bomtya.
Amaza eSine kunye neCosine
Kweli candelo, ndiza kube ndixoxa ngomahluko phakathi kwamaza e-sine kunye ne-cosine, yintoni ukutshintshwa kwesigaba, kwaye i-sine wave yahluke njani kwi-cosine wave. Ndizakube ndiphonononga ukubaluleka kwamaza esine kwimathematika, fiziksi, ubunjineli, kunye nokusetyenzwa komqondiso.
Uthini umahluko phakathi kwamaza eSine kunye neCosine?
Amaza e<em>sine kunye ne<em>cosine asebenza ngamaxesha athile, agudileyo, kwaye aqhubekayo asetyenziswa ukuchaza izinto ezininzi zendalo, ezifana nesandi kunye namaza okukhanya. Zikwasetyenziswa kubunjineli, ukusetyenzwa kwemiqondiso, nakwimathematika.
Owona mahluko ophambili phakathi kwamaza e-sine kunye ne-cosine kukuba i-sine wave iqala ku-zero, ngelixa i-cosine wave iqala kwi-shift yesigaba sika-π/2 weradians. Oku kuthetha ukuba i-cosine wave inentloko yokuqala xa ithelekiswa ne-sine wave.
Amaza eSine abalulekile kwifiziksi kuba agcina imilo yamaza xa edityanisiwe. Le propati, eyaziwa ngokuba ngumgaqo-siseko, yiyo eyenza uhlalutyo lwe-Fourier lube luncedo. Yenza kwakhona amaza e-sine acoustically awodwa, njengoko enokusetyenziselwa ukumela amaza omoya omnye.
Amaza eCosine nawo abalulekile kwifiziksi, njengoko asetyenziswa ukuchaza intshukumo yobunzima kwintwasahlobo ngokulingana. I-equation ye-sine wave ngu-f = i-oscillations/ixesha, apho u-f kukuphindaphinda kwamaza kwaye ω yi-angular frequency. Le nxaki inika ukususwa kwamaza nakweyiphi na indawo x kunye nexesha t.
Kwimilinganiselo emibini okanye ngaphezulu, i-sine wave inokuchazwa ngamaza endiza ehambayo. Inombolo yamaza u-k luphawu lweparameter yomaza, kwaye inxulumene ne-angular frequency ω kunye nobude bobude λ. Inxaki ye-sine iliza kwimilinganiselo emibini okanye ngaphezulu inika ukufuduswa kwamaza nakwesiphi na isikhundla x kunye nexesha t.
Amaza antsonkothileyo, afana nalawo adalwe lilitye eliwiswe echibini, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu ezifana ne-sine wave okanye i-cosine wave, njengokutshintsha kwesigaba. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kumaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Amaza esine afumaneka kwindalo, kubandakanywa amaza omoya, amaza omsindo, kunye namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye inokuqonda ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko. Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi.
Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso. Ikwasetyenziswa kuhlalutyo lwamanani kunye nochungechunge lwexesha.
Amaza ane-Sine anokusasaza kulo naliphi na icala esithubeni, kwaye amelwe ngamaza ane-amplitude kunye ne-frequency ehamba kumacala ahlukeneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Oku kwenzeka xa inqaku litsalwa kumtya, njengoko amaza ebonakaliswa kwiindawo ezisisigxina zomtya. Amaza okuma ayenzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bawo, kwaye ngokuchanekileyo ngokuhambelana nobunzima bayo ngeyunithi yobude.
Yintoni i-Phase Shift?
I-sine wave yi-oscillation egudileyo, ephindaphindayo eqhubekayo kuzo zombini ixesha nakwindawo. Ligophe lemathematika elichazwa ngumsebenzi wesine we-trigonometric kwaye isoloko isetyenziselwa ukumela amaza esandi, amaza okukhanya, kunye nezinye iimo zamaza kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokusetyenzwa komqondiso. I-frequency frequency (f) ye-sine wave linani lokujikeleza okanye imijikelo eyenzeka ngomzuzwana omnye, kwaye ilinganiswa nge-hertz (Hz).
I-angular frequency (ω) yireyithi yokutshintsha kwengxoxo yokusebenza kwiiradians ngesekhondi, kwaye inxulumene nesiqhelo esiqhelekileyo nge-equation ω = 2πf. Ixabiso elilambathayo lika φ limela ulibaziseko, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
Amaza e-Sine ahlala esetyenziselwa ukuchaza amaza omsindo, njengoko ekwazi ukugcina imilo yawo yamaza xa edibene kunye. Le propati ikhokelela kukubaluleka kohlalutyo lwe-Fourier, okwenza kube lula ukwahlula ngokuvakalayo iinguqu ezahlukeneyo zesithuba. Umzekelo, i-variable x imele indawo kumlinganiselo omnye, kwaye i-wave isasazeke kwicala le-parameter yempawu k, ebizwa ngokuba yinombolo yamaza. Inombolo yamaza e-angular imele ulungelelwaniso phakathi kwe-engular frequency (ω) kunye nesantya somgca sosasazo (ν). Inombolo yamaza inxulumene ne-angular frequency kunye ne-wavelength (λ) nge-equation λ = 2π/k.
I-equation ye-sine wave kumlinganiselo omnye inikwa ngu-y = A isono (ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, t lixesha, kunye no-φ yi-phase shift. Le nxaki ingenziwa ngokubanzi ukunika ukufuduswa kwamaza nakweyiphi na indawo x nangaliphi na ixesha t kumgca omnye, umzekelo, y = Isono (kx – ωt + φ). Xa kuqwalaselwa amaza kumacala amabini okanye ngaphezulu, iiequations ezinzima ngakumbi ziyafuneka.
Igama elithi sinusoid lidla ngokusetyenziswa ukuchaza amaza aneempawu ezifana ne-sine wave. Oku kuquka amaza e-cosine, anesigaba sokutshintsha kwe-π/2 radians, okuthetha ukuba banesiqalo sentloko xa kuthelekiswa namaza e-sine. Igama elithi sinusoidal lihlala lisetyenziswa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anenqanaba lokuphelisa.
Ukubonisa i-cosine wave, ubudlelwane obusisiseko phakathi kwe-sine wave kunye ne-cosine wave inokubonwa ngesangqa kwimodeli ye-3D yenqwelomoya entsonkothileyo. Oku kuluncedo kuguqulelo phakathi kwemimandla, njengoko ipateni efanayo yamaza isenzeka kwindalo, kuquka amaza omoya, amaza esandi, namaza okukhanya. Indlebe yomntu iyakwazi ukuqaphela amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziswa njengokubonisa iithowuni eziphindaphindiweyo.
I-Harmonics nayo ibalulekile kwisandi, njengoko indlebe yomntu ibona isandi njengomxube wamaza e-sine kunye ne-harmonics ephezulu ukongeza kwi-frequency esisiseko. Ubukho be-harmonics ephezulu ngaphezu kwezizathu ezisisiseko ukuhluka kwi-timbre yesandi. Esi sizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo liya kuvakala ngokwahlukileyo. Nangona kunjalo, isandi esiveliswa kukuqhwaba kwezandla siqulathe amaza e-aperiodic, okuthetha ukuba asenziwanga ngamaza e-sine.
Amaza esandi ngamaxesha athile anokuqikelelwa kusetyenziswa iibhloko zokwakha ezilula zamaza e-sinusoidal, njengoko kufunyenwe yingcali yezibalo yaseFransi uJoseph Fourier. Oku kubandakanya amaza asisikwere, akhiwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine ayakwazi ukusasaza ngaphandle kokutshintsha ifom kwiinkqubo ezisasazwayo zomgca, kwaye zihlala zifuneka ukuhlalutya ukusasazwa kwamaza. Amaza ane-Sine anokuhamba kumacala amabini esithubeni, kwaye amelwe ngamaza ane-amplitude kunye ne-frequency. Xa amaza amabini ehamba kumacala ahlukeneyo egqitha, kwenziwa ipateni yokuma yamaza. Oku kufana naxa inqaku litsalwa kumtya, njengoko amaza aphazamisayo ebonakala kwiindawo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Ezi frikhwensi zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwekhwethe zeresonant zomtya zilingana nobude bomtya, kwaye ngokuphambeneyo zilinganisa ubunzima ngeyunithi yobude bomtya.
I-Sine Wave yohluke njani kwiCosine Wave?
I-sine wave yindlela eqhubekayo yamaza ejikeleza ngendlela egudileyo, ephinda-phindayo. Ngumsebenzi wetrigonometric owenziwe ngegrafu kwinqwelo-moya enamacala amabini, kwaye yeyona ndlela ingundoqo yamaza kwimathematika, ifiziksi, ubunjineli, kunye nokusetyenzwa komqondiso. Ibonakaliswa ngokuphindaphindiweyo kwayo, okanye inani le-oscillations eyenzeka ngexesha elinikiweyo, kunye ne-angular frequency, elizinga lokutshintsha kwengxabano yomsebenzi kwi-radians ngomzuzwana. I-sine wave inokutshintshwa ngexesha, ngexabiso elingalunganga elimele ulibaziseko kunye nexabiso elilungileyo elimele i-advanced kwimizuzwana.
Amaza e-Sine asetyenziswa ngokuqhelekileyo ukuchaza amaza omsindo, kwaye ahlala ebizwa ngokuba sinusoids. Zibalulekile kwifiziksi kuba zigcina imilo yazo yamaza xa zidityaniswe kunye, kwaye zisisiseko sohlalutyo lweFourier, oluzenza zibe zizodwa ngokuvakalayo. Zikwasetyenziselwa ukuchaza izinto eziguquguqukayo zendawo, kunye nenombolo yamaza emele ukulingana phakathi kwe-angular frequency kunye nesantya somgca wokusasaza.
I-sine wave ikwasetyenziswa ukuchaza i-single-dimension wave, efana nocingo. Xa i-generalized to two-dimensions, i-equation ichaza i-wave yenqwelomoya ehambayo. Inombolo yamaza itolikwa njenge-vector, kwaye imveliso yechaphaza yamaza amabini ngamaza antsonkothileyo.
Amaza e-Sine nawo asetyenziselwa ukuchaza ukuphakama kwamaza amanzi echibini xa ilitye liwa. Iiequations ezintsonkothileyo ngakumbi ziyafuneka ukuchaza igama elithi sinusoid, elichaza iimpawu zamaza, kubandakanywa amaza e-sine kunye ne-cosine anesigaba sokutshintsha. I-sine wave ibeka iliza i-cosine ngo-π/2 radians, okanye isiqalo sentloko, ngoko ke umsebenzi we-cosine ukhokela umsebenzi wesine. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kumaza e-sine kunye ne-cosine kunye nesigaba sokunciphisa.
Ukubonisa i-cosine wave lubudlelwane obusisiseko kwisangqa kwimodeli ye-3D yenqwelomoya entsonkothileyo, enceda ukubona ukuba luncedo kwayo kwimimandla yoguqulo. Le pateni yamaza yenzeka kwindalo, kuquka amaza omoya, amaza esandi, namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kunye nokubonakaliswa kwamaza okuphindaphinda kunye nokuhambelana kwawo. Indlebe yomntu ibona isandi njengezandi ezinesandi esinesandi sexesha, kunye nobukho be-harmonics ephezulu ukongeza kwezona zizathu zibalulekileyo zokwahluka kwi-timbre.
Esi sisizathu sokuba inqaku lomculo lefrikhwensi ethile edlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo. Isandi sokuqhwaba kwesandla, umzekelo, siqulathe amaza e-aperiodic, angaphindaphindiyo, kunamaza e-sine periodic. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sokufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine nawo anokusasaza kwiifom eziguqukayo ngokusasazwa kweenkqubo zomgca, ezifunekayo ukuhlalutya ukusasazwa kwamaza. Amaza e-Sine ahamba kumacala achaseneyo esithubeni amelwe ngamaza ane-amplitude efanayo kunye nokuphindaphinda, kwaye xa ebekwe phezulu, ipateni yokuma yamaza yenziwa. Oku kubonwa xa inqaku lihluthwa kumtya, njengoko amaza aphazamisayo abonakaliswa ngamanqaku amisiweyo omtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies, kwaye zenziwe ngamaza omoya asisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo kubunzima ngeyunithi yobude bomtya.
Ingaba iSine Wave ivakala njani?
Ndiqinisekile ubukhe weva ngamaza e-sine ngaphambili, kodwa uyawazi ukuba avakala njani? Kweli candelo, siza kuphonononga ukuba amaza e-sine asichaphazela njani isandi somculo, kunye nendlela anxibelelana ngayo nee-harmonics ukwenza ii-timbres ezizodwa. Siza kuxoxa kwakhona ukuba amaza e-sine asetyenziswa njani ekusetyenzweni komqondiso kunye nokusasazwa kwamaza. Ekupheleni kweli candelo, uya kuba nokuwaqonda ngcono amaza e-sine kunye nendlela asichaphazela ngayo isandi.
Ivakala njani iSine Wave?
I-sine wave yi-oscillation eqhubekayo, egudileyo, ephindaphindwayo efumaneka kwizinto ezininzi zendalo, kubandakanywa amaza omsindo, amaza okukhanya, kunye nokuhamba kobunzima entwasahlobo. Lijiko lemathematika elichazwa ngumsebenzi wesine we-trigonometric, kwaye ihlala igrafu njengefomo yamaza.
Ingaba iliza elinesine livakala njani? I-sine wave iliza eliqhubekayo, elithetha ukuba alinakhefu kwi-waveform. Ngumsebenzi ogudileyo, owenziwe ngamaxesha athile, okanye inani lee-oscillations ezenzeka ngexesha elithile. Ubuninzi bayo be-angular, okanye ireyithi yotshintsho lwengxoxo yokusebenza kwiiradians ngomzuzwana, imelwe luphawu ω. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
Ubuninzi be-sine wave bulinganiswa nge-hertz (Hz), kwaye linani lokujikeleza ngesekhondi. I-sine wave lizandi zomsindo ochazwa ngumsebenzi wesine, f (t) = Isono (ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, kwaye φ lutshintsho lwesigaba. Ukutshintsha kwesigaba sika π/2 seeradians kunika amaza isiqalo sentloko, ngoko kaninzi kubhekiselwa kuwo njengomsebenzi wecosine.
Igama elithi "sinusoid" lisetyenziselwa ukuchaza iimpawu zamaza amaza e-sine wave, kunye ne-cosine wave ene-phase offset. Oku kuboniswa ngamaza e-cosine, athi ashiyeke ngasemva kwe-sine wave ngesigaba sokutshintsha kwe-π/2 radians. Obu budlelwane busisiseko phakathi kwamaza e-sine kunye ne-cosine imelwe sisangqa kwimodeli ye-3D yendiza enzima, enceda ukubona ukuba luncedo koguqulelo phakathi kwemimandla.
Ipateni yamaza e-sine yenzeke kwindalo, kubandakanywa namaza omoya, amaza omoya, kunye namaza okukhanya. Indlebe yomntu iyakwazi ukubona amaza e-sine enye njengesandi esicacileyo, kwaye imiboniso yamaza e-sine ye-harmonics yefrikhwensi enye isetyenziselwa ukwenza amanqaku omculo. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre yesandi. Esi sizathu sokuba inqaku elifanayo lomculo elidlalwa kwizixhobo ezahlukeneyo liya kuvakala ngokwahlukileyo.
Nangona kunjalo, isandi esiveliswa sisandla somntu asenziwanga ngamaza e-sine kuphela, njengoko sikwanayo namaza e-aperiodic. Amaza e-Aperiodic awaphindaphindi kwaye akanapatheni, ngelixa amaza e-sine eyenzeka ngamaxesha athile. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwalo naliphi na imo eyenzeka ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza kwiifom eziguqukayo ngokusasazwa kweenkqubo zomgca, kwaye ziyafuneka ukuhlalutya ukusasazwa kwamaza. Amaza eSine ahamba kumacala achaseneyo esithubeni amelwe ngamaza ane-amplitude efanayo kunye nokuphindaphinda, kwaye xa la maza egqithisile, ipateni yokuma yamaza yenziwa. Oku kuyafana nokwenzeka xa kutsalwa inowuthi emtya; amaza aphazamisayo adalwe, kwaye xa la maza ebonakaliswe ngamanqaku asisigxina esigxina somtya, amaza amileyo avela kwiifrikhwensi ezithile, ezibizwa ngokuba yi-resonant frequencies. Ezi frikhwensi zeresonant zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwekhwezi ze-resonant zomtya zihambelana nobude bawo, kwaye ngokuphambeneyo zihambelana nengcambu yobunzima bayo ngobude beyunithi nganye.
Yintoni indima yeHarmonics kwiSandi?
I-sine wave yinto eqhubekayo, egudileyo, ephindaphindayo i-oscillation efumaneka kwiindawo ezininzi zemathematika, fiziksi, ubunjineli, kunye nokusetyenzwa komqondiso. Luhlobo lwamaza aqhubekayo achazwa ngumsebenzi we-trigonometric, ngokuqhelekileyo i-sine okanye i-cosine, kwaye imelwe yigrafu. Iyenzeka kwimathematika, kwifiziksi, kubunjineli, nakwiindawo zokusetyenzwa kwemiqondiso.
Ubuninzi obuqhelekileyo be-sine wave, okanye inani le-oscillations eyenzeka kwixesha elinikiweyo, limelwe yi-angular frequency ω, elingana no-2πf, apho u-f yi-frequency kwi-hertz. Ixabiso elilambathayo lika φ limela ulibaziseko kwimizuzwana, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
Amaza e-Sine adla ngokusetyenziswa ukuchaza amaza omsindo, njengoko elolona hlobo lusisiseko lwamaza omsindo. Zichazwa ngumsebenzi we-sine, f = Isono (ωt + φ), apho i-A yi-amplitude, ω yi-frequency ye-angular, t lixesha, kwaye φ yinguqu yesigaba. Ukutshintsha kwesigaba sika π/2 radians kunika amaza isiqalo sentloko, ngoko kuthiwa ngumsebenzi wecosine, okhokela umsebenzi wesine. Igama elithi "sinusoidal" lisetyenziselwa ukubhekisa ngokudibeneyo kumaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Ukubonisa oku, i-cosine wave lunxulumano olusisiseko phakathi kwesangqa kunye nemodeli ye-3D yenqwelomoya entsonkothileyo, enceda ukubona ukubaluleka kwayo ekuguquleleni kwezinye iindawo. Le pateni yamaza yenzeka kwindalo, kuqukwa namaza omoya, amaza esandi, kunye namaza okukhanya.
Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziswa njengokubonisa i-harmonics yefrikhwensi enye. Indlebe yomntu ibona isandi njengendibaniselwano yamaza e-sine kunye ne-harmonics, kunye nokongezwa kwamaza e-sine ahlukeneyo okukhokelela kwifomu eyahlukileyo kunye notshintsho kwi-timbre. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elinesandi esifanayo esidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Nangona kunjalo, isandi asiqulunqwe kuphela ngamaza e-sine kunye neeharmonics, njengoko isandi esenziwe ngesandla siqulethe amaza e-aperiodic. Amaza eAperiodic awayo-periodic kwaye anepateni engaphindi. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esisetyenziselwa ukufunda amaza, afana nokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza ekutshintsheni ifom ngokusebenzisa iinkqubo ezisasaziweyo zomgca, kwaye ziyafuneka ukuhlalutya ukusasazwa kwamaza. Amaza e-Sine ahamba kumacala ahlukeneyo esithubeni anokumelwa ngamaza ane-amplitude efanayo kunye ne-frequency, kwaye xa edlulayo, ipateni yokuma yamaza yenziwa. Oku kwenzekayo xa inqaku lihluthwa kumtya: amaza aphazamisayo abonakaliswa kwiindawo ezisisigxina zomtya, kwaye amaza amileyo avela kwiifrikhwensi ezithile, ezibizwa ngokuba yi-resonant frequencies. Ezi frikhwensi zeresonant zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwekhwethe zeresonant zomtya zilingana nobude bayo, kwaye ngokuphambeneyo zihambelana nengcambu yobunzima ngeyunithi yobude bomtya.
I-Sine Wave iyichaphazela njani i-Tibre yesandi?
I-sine wave yi-oscillation eqhubekayo, egudileyo, ephinda-phindayo eyinxalenye yezibalo, i-physics, ubunjineli, kunye nokusetyenzwa komqondiso. Olu luhlobo lwamaza aqhubekayo anomsebenzi ogudileyo, ngamaxesha athile kwaye lwenzeka kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokusetyenzwa komqondiso. Isiqhelo esiqhelekileyo se-sine wave linani lokujikeleza okanye imijikelo eyenzeka kwiyunithi yexesha. Oku kuchazwa ngu-ω = 2πf, apho u-ω yi-angular frequency kunye no-f yi-frequency frequency. I-angular frequency yireyithi yotshintsho lwengxoxo yokusebenza kwaye ilinganiswa ngeeradians ngesekhondi. Ixabiso elingengo-zero lika-ω limele ukutshintshwa kwendlela yamaza ephela ngexesha, echazwa ngu-φ. Ixabiso elibi lika φ limela ulibaziseko kwaye ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
I-sine wave isoloko isetyenziselwa ukuchaza amaza omsindo, kwaye ichazwa ngumsebenzi wesine f = isono (ωt). Ii-oscillations zikwabonwa kwi-system ye-spring-mass engasebenziyo kwi-equilibrium, kwaye amaza e-sine abalulekile kwi-physics kuba agcina imilo yawo yamaza xa edityaniswe kunye. Le propati yamaza e-sine ikhokelela ekubalulekeni kwayo kuhlalutyo lwe-Fourier, eyenza ibe yodwa ngokuvakalayo.
Xa i-sine wave imelwe kumyinge wesithuba esinye, i-equation inika ukufuduswa kwamaza kwindawo x ngexesha t. Umzekelo womgca omnye uyaqwalaselwa, apho ixabiso lamaza kwindawo x linikezelwa yi-equation. Kwimilinganiselo emininzi yendawo, i-equation ichaza i-wave yenqwelomoya ehambayo, apho indawo x imelwe yi-vector kunye ne-wavenumber k yi-vector. Oku kunokutolikwa njengemveliso yamachaphaza yeevektha ezimbini.
Amaza antsonkothileyo, anje ngamaza amanzi echibini xa kuwiswa ilitye, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu zombini i-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba se-π/2 radians kuthiwa kunika i-cosine wave isiqalo, njengoko ikhokela i-sine wave. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anenqanaba lokuphelisa, njengoko kubonisiwe ngamaza e-cosine.
Obu budlelwane busisiseko phakathi kwamaza e-sine kunye ne-cosine inokubonwa ngesangqa kwimodeli ye-3D yendiza entsonkothileyo. Lo mzekelo uluncedo kuguqulelo phakathi kwemimandla eyahlukeneyo, njengoko ipateni yamaza isenzeka kwindalo, kubandakanywa amaza omoya, amaza esandi, kunye namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye, isandi esicacileyo kwaye sisulungekile. Amaza e-Sine nawo abonisa i-harmonics yefrikhwensi enye, enokuthi indlebe yomntu ibone.
Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo lefrikhwensi ethile edlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo. Isandi sokuqhwaba ngesandla siqulathe amaza e-aperiodic, kunamaza e-sine, njengoko sisandi sexesha. Ibonwa njengengxolo, ingxolo ibonakaliswe njenge-aperiodic, enepateni engaphindi.
Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwalo naluphi na uhlobo lwamaza olwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine nawo anokusasaza ngokutshintsha kweefom kwiinkqubo ezisasaziweyo zomgca, ezifunekayo ukuhlalutya ukusasazwa kwamaza. Amaza eSine ahamba kumacala ahlukeneyo esithubeni amelwa ngamaza anobukhulu obufanayo nokuphindaphinda. Xa la maza egqithisile, kwenziwa ipateni yamaza emileyo, njengoko ibonwa xa kuncothulwa inowuthi emtya. Amaza aphazamisayo abonakaliswe kwiisiphelo ezisisigxina zomtya adala amaza amileyo avela kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Ezi frikhwensi zeresonant zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo kubunzima ngeyunithi yobude bomtya.
Amaza eSine njengeZixhobo zokuHlalutya
Ndiza kuthetha ngamaza e-sine kunye nendlela asetyenziswa ngayo njengezixhobo zokuhlalutya ekusetyenzweni komqondiso, uhlalutyo lwexesha kunye nokusasazwa kwamaza. Siza kuphonononga indlela asetyenziswa ngayo amaza e-sine ukuchaza agudileyo, ukuphinda-phinda oscillations kunye nendlela asetyenziswa ngayo kwimathematika, fiziksi, ubunjineli kunye namanye amacandelo. Siza kujonga kwakhona indlela amaza e-sine anokusetyenziswa ngayo ukuhlalutya ukwanda kwamaza kunye nendlela asetyenziswa ngayo kuhlalutyo lwe-Fourier. Okokugqibela, siza kuxoxa ngendlela amaza e-sine asetyenziswa ngayo ukwenza isandi kunye nendlela asetyenziswa ngayo emculweni.
Yintoni iNkqubo yoMqondiso?
Amaza e-Sine sisixhobo esisisiseko esisetyenziselwa ukusetyenzwa komqondiso kunye nohlalutyo lwexesha. Ziluhlobo lwe-waveform eqhubekayo, ebonakaliswe nge-oscillation egudileyo, ephindaphindiweyo kunye ne-frequency eyodwa. Amaza e-sine asetyenziselwa ukuchaza izinto ezahlukeneyo ezibonakalayo, kubandakanywa amaza omsindo, amaza okukhanya, kunye nokuhamba kobunzima entwasahlobo.
Ukulungiswa komqondiso yinkqubo yokuhlalutya kunye nokulawula iimpawu. Isetyenziswa kwiinkalo ezahlukeneyo, kubandakanya imathematika, ifiziksi, ubunjineli, kunye nokuveliswa kweaudio kunye nevidiyo. Ubuchule bokusebenza kwemiqondiso busetyenziselwa ukuhlalutya imiqondiso, ukubona iipateni, kunye nokukhupha ulwazi kubo.
Uhlalutyo lwenkqubo yexesha yinkqubo yokuhlalutya amanqaku edatha aqokelelwe ngexesha elithile. Isetyenziselwa ukuchonga iintsingiselo kunye neepateni kwidatha, kunye nokwenza uqikelelo malunga neziganeko zexesha elizayo. Uhlalutyo loluhlu lwexesha lusetyenziswa kwiinkalo ezahlukeneyo, kubandakanya ezoqoqosho, ezemali, kunye nobunjineli.
Ukusasazwa kwamaza yinkqubo apho iliza lihamba ngesiphakathi. Icazululwa kusetyenziswa iintlobo ngeentlobo zeeequation zemathematika, kubandakanywa ukulingana kwamaza kunye ne-sine wave equation. Ukusasazwa kwamaza kusetyenziselwa ukuhlalutya ukuziphatha kwamaza esandi, amaza okukhanya, kunye nezinye iindidi zamaza.
Yintoni Time Series Analysis?
Amaza e-Sine sisixhobo esibalulekileyo sokuhlalutya iintlobo ezahlukeneyo zezinto ezibonakalayo, ukusuka kumaza omsindo ukuya kumaza okukhanya. Uhlalutyo lwenkqubo yexesha yindlela yokuhlalutya amanqaku edatha aqokelelwe kwixesha elithile, ukwenzela ukuchonga iipateni kunye neendlela. Isetyenziselwa ukufunda indlela yokuziphatha kwenkqubo ekuhambeni kwexesha, kunye nokwenza uqikelelo malunga nokuziphatha kwexesha elizayo.
Uhlalutyo loluhlu lwexesha lunokusetyenziswa ukuhlalutya amaza e-sine. Ingasetyenziselwa ukuchonga ukuphindaphinda, i-amplitude, kunye nesigaba se-sine wave, kunye nokuchonga naluphi na utshintsho kwi-waveform ngokuhamba kwexesha. Isenokusetyenziswa ukuchonga naziphi na iipateni ezisisiseko kwi-waveform, efana ne-periodicities okanye iintsingiselo.
Uhlalutyo lwechungechunge lwexesha lungasetyenziselwa ukuchonga naluphi na utshintsho kwi-amplitude okanye isigaba se-sine wave ngokuhamba kwexesha. Oku kungasetyenziselwa ukuchonga naluphi na utshintsho kwinkqubo enokubangela ukuba i-waveform itshintshe, njengokutshintsha kokusingqongileyo okanye inkqubo ngokwayo.
Uhlalutyo loluhlu lwexesha lunokusetyenziselwa ukuchonga naziphi na iipateni ezisisiseko kuhlobo lwamaza, njengamaxesha athile okanye iintsingiselo. Oku kungasetyenziselwa ukuchonga naziphi na iipatheni ezisisiseko kwinkqubo enokubangela ukuba i-waveform itshintshe, njengokutshintsha kokusingqongileyo okanye inkqubo ngokwayo.
Uhlalutyo loluhlu lwexesha lunokusetyenziselwa ukuchonga naluphi na utshintsho kwi-frequency ye-sine wave ngokuhamba kwexesha. Oku kungasetyenziselwa ukuchonga naluphi na utshintsho kwinkqubo enokubangela ukuba i-waveform itshintshe, njengokutshintsha kokusingqongileyo okanye inkqubo ngokwayo.
Uhlalutyo loluhlu lwexesha lunokusetyenziselwa ukuchonga naziphi na iipateni ezisisiseko kuhlobo lwamaza, njengamaxesha athile okanye iintsingiselo. Oku kungasetyenziselwa ukuchonga naziphi na iipatheni ezisisiseko kwinkqubo enokubangela ukuba i-waveform itshintshe, njengokutshintsha kokusingqongileyo okanye inkqubo ngokwayo.
Uhlalutyo loluhlu lwexesha sisixhobo esinamandla sokuhlalutya amaza e-sine kwaye sinokusetyenziselwa ukuchonga iipateni kunye nentsingiselo yohlobo lwamaza ngokuhamba kwexesha. Ingasetyenziselwa ukuchonga naziphi na iipatheni ezisisiseko kwinkqubo enokuthi ibangele ukuba i-waveform itshintshe, njengokutshintsha kokusingqongileyo okanye inkqubo ngokwayo.
Kuhlalutywa njani ukusasazwa kwamaza?
Amaza e-Sine luhlobo lwe-waveform eqhubekayo enokusetyenziswa ukuhlalutya ukusasazwa kwamaza. Ziyi-oscillation egudileyo, ephinda-phindayo enokufumaneka kwimathematika, kwifiziksi, kubunjineli, kunye nokusetyenzwa kwemiqondiso. Amaza e-Sine abonakaliswe ngokuphindaphindiweyo kwawo (f), inani le-oscillations eyenzeka ngexesha elinikiweyo, kunye ne-angular frequency (ω), yinqanaba apho ingxabano yomsebenzi itshintsha kwiiyunithi zeeradians.
Amaza e-sine asetyenziselwa ukuchaza iintlobo ezahlukeneyo zeziganeko, kuquka amaza omsindo, amaza okukhanya, kunye nokuhamba kobunzima entwasahlobo. Zikwabalulekile kuhlalutyo lweFourier, nto leyo ezenza zibe zizodwa ngokuvakalayo. I-sine wave inokubonakaliswa kumlinganiselo omnye ngomgca omnye, kunye nexabiso le-wave kwindawo enikiweyo ngexesha kunye nendawo. Kwimilinganiselo emininzi, i-equation ye-sine wave ichaza i-angular frequency wave, enendawo (x), inombolo yamaza (k), kunye ne-angular frequency (ω).
I-Sinusoids luhlobo lwe-waveform ebandakanya zombini amaza e-sine kunye ne-cosine, kunye naluphi na uhlobo lwamaza kunye nokutshintshwa kwesigaba se-π/2 radians (intloko eqalayo). Oku kukhokelela kubudlelwane obusisiseko phakathi kwamaza e-sine kunye ne-cosine, anokuthi abonwe kwimodeli ye-3D yendiza enzima. Lo mzekelo uluncedo ekuguquleleni iifomati zamaza phakathi kwemimandla eyahlukeneyo.
Amaza e-Sinusoidal anokufumaneka kwindalo, kubandakanywa amaza omoya kunye namaza amanzi. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kodwa isandi sihlala siqulunqwe ngamaza e-sine amaninzi, aziwa ngokuba yi-harmonics. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre yesandi. Esi sisizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sokufunda amaza, kwaye sisetyenziselwa ukuhamba kobushushu kunye nokwenziwa komqondiso. Ikwasetyenziswa kuhlalutyo lwamanani oluhlu lwexesha.
Amaza ane-Sine anokusasaza kulo naliphi na icala esithubeni, kwaye amelwe ngamaza ane-amplitude kunye ne-frequency ehamba kumacala achaseneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Le yipatheni efanayo eyenziwa xa inqaku lihluthwa kumtya, ngenxa yamaza abonakaliswe kwiiphelo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezaziwa ngokuba zii-resonant frequencies, ezenziwe ngamaza omoya asisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bawo, kwaye ngokuchanekileyo ngokuhambelana nobunzima bayo ngeyunithi yobude.
I-Sine Wave Spectrum
Ndizakuxoxa nge-sine wave spectrum, kuquka ukuphindaphinda kwayo, ubude bezandi, kunye nendlela enokusetyenziswa ngayo ukwenza izandi ezahlukeneyo. Siza kuphonononga ijika lemathematika elichaza ukuguquguquka okugudileyo, okuphinda-phindayo, kunye nendlela esetyenziswa ngayo kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokusetyenzwa komqondiso. Siza kujonga kwakhona indlela i-sine wave ibaluleke ngayo kwifiziksi kwaye kutheni isetyenziswa kuhlalutyo lweFourier. Okokugqibela, siza kuxoxa ngendlela i-sine wave esetyenziswa ngayo kwisandi kunye nendlela ebonwa ngayo yindlebe yomntu.
Yintoni i-Frequency yeSine Wave?
I-sine wave yindlela eqhubekayo yamaza ejikelezayo ngendlela egudileyo, ephindaphindayo. Yinto esisiseko kwizinto ezininzi ezibonakalayo nezemathematika, njengesandi, ukukhanya, kunye nemiqondiso yombane. Ubuninzi be-sine wave linani lokujikeleza okwenzeka ngexesha elithile. Ilinganiswa ngeHertz (Hz) kwaye ibonakaliswa ngokwemijikelo ngesekhondi. Ubudlelwane phakathi kwamaza obuninzi kunye nobude bokuphakama kukuba okukhona kuphezulu i-frequency, imfutshane ubude be-waveleng.
Amaza e-Sine asetyenziselwa ukwenza iintlobo ezahlukeneyo zesandi, kubandakanya i-vibrato, i-tremolo, kunye ne-chorus. Ngokudibanisa amaza amaninzi e-sine yeefrikhwensi ezahlukeneyo, iifom zamaza ezintsonkothileyo zinokudalwa. Oku kwaziwa njenge-additive synthesis, kwaye isetyenziswa kwiindidi ezininzi zemveliso yomsindo. Ukongeza, amaza e-sine angasetyenziselwa ukwenza iziphumo ezahlukeneyo, ezifana nokutshintsha kwesigaba, ukujika, kunye nesigaba.
Amaza e-Sine nawo asetyenziswa ekusetyenzweni kwemiqondiso, njengakuhlalutyo lweFourier, olusetyenziselwa ukufunda ukwanda kwamaza kunye nokuhamba kobushushu. Zikwasetyenziswa kuhlalutyo lwamanani kunye nohlalutyo lwexesha.
Isishwankathelo, amaza e-sine luhlobo lwamaza oluqhubekayo olujikelezayo ngendlela egudileyo, ephindaphindayo. Zisetyenziselwa ukudala imiphumo eyahlukeneyo yesandi, kwaye zikwasetyenziselwa ukucwangcisa umqondiso kunye nohlalutyo lwamanani. Ubuninzi be-sine wave linani le-oscillations eyenzeka kwixesha elithile, kwaye ubudlelwane phakathi kwe-frequency kunye ne-wavelength kukuba ukuphakama kwe-frequency, mfutshane ubude be-wavelength.
Yintoni ubudlelwane phakathi kweFrequency kunye neWavelength?
I-sine wave yinto eqhubekayo, egudileyo, ephindaphindayo i-oscillation efumaneka kwiindawo ezininzi zemathematika, fiziksi, ubunjineli, kunye nokusetyenzwa komqondiso. Ichazwa ngumsebenzi wesine wetrigonometric, kwaye imelwe ngokomzobo njengomaza. I-sine wave ine-frequency, inani le-oscillations okanye imijikelo eyenzeka kwixesha elithile. I-angular frequency, echazwa ngu-ω, yireyithi yokutshintsha kwengxoxo yokusebenza, elinganiselwa kwiiradians ngesekhondi. Yonke i-waveform ayibonakali kanye, kodwa iguqulwa ngexesha lokutshintshwa kwesigaba, esichazwe ngu-φ, esilinganiswa ngemizuzwana. Ixabiso elilambathayo limele ukulibaziseka, kwaye ixabiso elivumayo limele kwangaphambili kwimizuzwana. Ubuninzi be-sine wave bulinganiswa nge-hertz (Hz), kwaye linani lokujikeleza okwenzeka ngomzuzwana omnye.
I-sine wave yindlela ebalulekileyo yamaza kwifiziksi, njengoko igcina imilo yayo xa idityaniswe kwelinye i-sine wave yesantya esifanayo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati ye-periodic waveform eyaziwa ngokuba ngumgaqo-siseko we-superposition, kwaye yile propati ekhokelela ekubalulekeni kohlalutyo lwe-Fourier. Oku kuyenza ibe yodwa ngokuvakalayo, njengoko ikuphela kwendlela yamaza enokusetyenziselwa ukudala ukuguquguquka kwendawo. Umzekelo, ukuba 'x' imele indawo ecaleni kocingo, ngoko i-sine wave yefrikhwensi enikiweyo kunye ne-wavelength iyakusasaza ecaleni kocingo. Uphawu lweparamitha yomaza yaziwa njengenani lamaza, k, eliyinombolo yamaza e-angular kwaye imele ulungelelwaniso phakathi kwamaza omoya, ω, kunye nesantya somgca sosasazo, ν. Inombolo yamaza inxulumene ne-angular frequency kunye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave kumlinganiselo omnye inikwa ngu-y = A isono(ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, t lixesha, kunye no-φ yi-phase shift. Le nxaki ingenziwa ngokubanzi ukunika ukufuduswa kwamaza kwindawo enikiweyo, x, ngexesha elinikiweyo, t. Ngomzekelo womgca omnye, ixabiso le-wave kwindawo enikiweyo linikezelwa ngu-y = A isono (kx - ωt + φ), apho u-k linani lamaza. Xa kuqwalaselwa ngaphezulu komlinganiselo womhlaba omnye, iequation entsonkothileyo iyafuneka ukuchaza iliza.
Igama elithi sinusoid lisetyenziselwa ukuchaza i-waveform eneempawu ze-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba se-π/2 radians kuthiwa kunika i-sine wave isiqalo, njengoko iliza le-sine libeka iliza le-cosine ngalo mali. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anesigaba sokunciphisa. Oku kubonisiwe kwigrafu engezantsi, ebonisa i-cosine wave enesigaba sokutshintsha kwe-π/2 iiradians.
Ubudlelwane obusisiseko phakathi kwe-sine wave kunye nesangqa sinokubonwa kusetyenziswa imodeli ye-3D yendiza entsonkothileyo. Oku kuluncedo ekuguquleleni i-waveform kwimimandla eyahlukeneyo, njengoko ipateni efanayo yamaza isenzeka kwindalo, kubandakanywa amaza omoya, amaza esandi, kunye namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziswa njengokubonisa iithowuni eziphindaphindiweyo. I-Harmonics ikhona kwisandi, njengoko indlebe yomntu inokubona i-harmonics ukongeza kwi-frequency esisiseko. Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko yinto ebangela ukwahluka kwi-timbre. Esi sizathu sokuba inqaku lomculo lefrikhwensi enikiweyo edlalwa kwizixhobo ezahlukeneyo liya kuvakala ngokwahlukileyo.
Isandi sokuqhwaba ngesandla sikwanalo namaza e-aperiodic, angamaza angaguquguqukiyo. Amaza e-Sine ahamba ngamaxesha, kwaye isandi esibonwa njengengxolo siphawulwa ngamaza e-aperiodic, anepateni engaphindaphindiyo. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu kunye nokulungiswa komqondiso, kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine angasetyenziselwa ukusabalalisa ngokutshintsha iifom kwiinkqubo ezisasazwayo zomgca. Oku kuyafuneka ukuhlalutya ukwanda kwamaza kumacala amabini esithubeni, njengoko amaza ane-amplitude efanayo kunye nokuphindaphinda okuhamba kumacala achaseneyo aya kubeka ngaphezulu ukuze enze ipateni yokuma yamaza. Oku koko kuviwa xa inqaku litsalwa kumtya, njengoko amaza ebonakala kwiindawo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies zomtya. Ezi frikhwensi zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo kubunzima ngeyunithi yobude bomtya.
Ingasetyenziswa njani i-Sine Wave ukwenza izandi ezahlukeneyo?
I-sine wave yindlela eqhubekayo yamaza ejikelezayo ngendlela egudileyo, ephindaphindayo. Yenye yezona ndlela zibalulekileyo zamaza kwaye isetyenziswa kwiindawo ezininzi zemathematika, ifiziksi, ubunjineli, kunye nokusetyenzwa kwemiqondiso. Amaza e-Sine abonakaliswe ngokuphindaphindiweyo kwawo, inani le-oscillations okanye imijikelezo eyenzeka kwixesha elinikiweyo. I-angular frequency, engumyinge wokutshintsha kwengxabano yomsebenzi kwi-radians ngesekhondi, inxulumene nesiqhelo esiqhelekileyo nge-equation ω = 2πf.
Amaza e-Sine asetyenziswa ngokuqhelekileyo kwimveliso yesandi kwaye angasetyenziselwa ukudala imiphumo eyahlukeneyo yesandi. Ngokudibanisa amaza e-sine ahlukeneyo anezandi ezahlukeneyo, i-amplitudes, kunye nezigaba, uluhlu olubanzi lwezandi lunokwenziwa. I-sine wave ene-frequency enye yaziwa ngokuba "yisiseko" kwaye isisiseko sawo onke amanqaku omculo. Xa amaza e-sine amaninzi anezandi ezahlukeneyo edityanisiwe, enza “ii-harmonics” ezizizandi eziphakamileyo ezongeza kwi-timbre yesandi. Ngokongeza i-harmonics ngakumbi, isandi sinokwenziwa ukuba sivakale sinzima kwaye sinomdla. Ukongeza, ngokutshintsha isigaba se-sine wave, isandi sinokwenziwa ukuba sivakale ngathi sivela kumacala ahlukeneyo.
Amaza e-Sine nawo asetyenziswa kwi-acoustics ukulinganisa ubunzulu bamaza esandi. Ngokulinganisa i-amplitude ye-sine wave, ukuqina kwesandi kunokumiselwa. Oku kuluncedo ekulinganiseni ukungxola kwesandi okanye ekumiseleni ukuphindaphindwa kwesandi.
Ukuqukumbela, amaza e-sine ayindlela ebalulekileyo yamaza kwiindawo ezininzi zesayensi kunye nobunjineli. Zisetyenziselwa ukwenza iintlobo ngeentlobo zeziphumo zesandi kwaye zikwasetyenziselwa ukulinganisa ubunzulu bamaza esandi. Ngokudibanisa amaza e-sine ahlukeneyo anezandi ezahlukeneyo, i-amplitudes, kunye nezigaba, uluhlu olubanzi lwezandi lunokwenziwa.
ISine Curve Ingalichaza Njani Iliza?
Kweli candelo, ndiza kube ndixoxa ngendlela igophe lesine elinokusetyenziswa ngayo ukuchaza amaza, unxulumano phakathi kwegophe le-sine kunye namaza endiza, kunye nendlela igophe le-sine enokusetyenziswa ngayo ukujonga iipateni zamaza. Siza kuphonononga ukubaluleka kwamaza e-sine kwimathematika, ifiziksi, ubunjineli, kunye nokusetyenzwa komqondiso, kunye nendlela asetyenziswa ngayo ukumela amaza esandi kunye nolunye uhlobo lwamaza.
ISine Curve Imela Njani Iliza?
I-sine wave yi-oscillation egudileyo, ephinda-phindayo eqhubekayo kwaye inomaza omaza ochazwa ngumsebenzi we-sine trigonometric. Ludidi lwamaza aqhubekayo agudileyo kwaye ngamaxesha athile, kwaye afumaneka kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokucwangcisa imiqondiso. Ibonakaliswa yi-frequency, inani le-oscillations okanye imijikelo eyenzeka kwixesha elinikiweyo. I-angular frequency, ω, lizinga apho impikiswano yokusebenza itshintsha kwiiyunithi zeeradians ngesekhondi. I-waveform engeyiyo yonke into ibonakala iguqulwe ngexesha ngokutshintsha kwesigaba, φ, esilinganiswa ngemizuzwana. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
I-sine wave isoloko isetyenziselwa ukuchaza isandi somsindo, kwaye ichazwa ngumsebenzi wesine, f = Isono (ωt + φ). Ii-oscillations zikwafumaneka kwinkqubo yobunzima bentwasahlobo engaxitywanga kwi-equilibrium, kwaye i-sine wave ibalulekile kwifiziksi kuba igcina imilo yayo yamaza xa idityaniswe kwelinye iliza le-sine lexesha elifanayo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati yamaxesha ngamaxesha yiyo ekhokelela kukubaluleka kwayo kuhlalutyo lwe-Fourier, eyenza ibe yodwa ngokuvakalayo.
Xa amaza asasaza kumlinganiselo omnye, i-spatial variable, x, imele indawo apho amaza asasaza khona, kwaye uphawu lweparameter, k, lubizwa ngokuba yinombolo yamaza. Inombolo ye-angular wave imele ulungelelwaniso phakathi kwe-engular frequency, ω, kunye nesantya somgca sosasazo, ν. I-wavenumber inxulumene ne-angular frequency, λ (lambda) yi-wavelength, kwaye u-f yi-frequency. I-equation v = λf inika i-sine wave kwi-dimensioni enye. Inxaki ngokubanzi inikwa ukunika ukufuduswa kwamaza kwindawo, x, ngexesha, t.
Xa kuqwalaselwa umzekelo womgca omnye, ixabiso le-wave nakweyiphi na indawo kwindawo linikezelwa yi-equation x = A isono (kx - ωt + φ). Kwimilinganiselo emibini yendawo, i-equation ichaza amaza endiza ehambayo. Xa itolikwa njengeevektha, imveliso yeevekhtha ezimbini yimveliso yamachaphaza.
Kumaza antsonkothileyo, anje ngamaza amanzi echibini xa ilitye liwa, kufuneka ii-equations ezintsonkothileyo. Igama elithi sinusoid lisetyenziselwa ukuchaza iimpawu zamaza e-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba se-π/2 radians kuthiwa kunika i-cosine wave isiqalo, njengoko ikhokela i-sine wave. I-sine wave ibeka iliza le-cosine. Igama elithi sinusoidal lisetyenziselwa ukubhekisa ngokudibeneyo kumaza e-sine kunye namaza e-cosine ane-offset yesigaba, ebonisa ubudlelwane obusisiseko phakathi kwezi zimbini. Isangqa kwimodeli yendiza eyinkimbinkimbi ye-3D ingasetyenziselwa ukujonga ukubaluleka koguqulo phakathi kwemimandla emibini.
Ipateni efanayo yamaza yenzeka kwindalo, kuquka amaza omoya, amaza esandi, namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine abonisa amaza omoya kunye neeharmonics. Indlebe yomntu ibona isandi njengezandi zesine ezineeharmonics eziqondakalayo ukongeza kubuninzi obusisiseko. Ukongezwa kwamaza e-sine ahlukeneyo kukhokelela kwindlela eyahlukileyo yamaza, etshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo lefrikhwensi ethile edlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Isandi sokuqhwaba ngesandla siqulathe amaza e-aperiodic, angeyo-periodic, kunye namaza e-sine angamaxesha athile. Isandi esibonwa njengengxolo sibonakaliswe njenge-aperiodic, enepateni engaphindi. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo sohlalutyo esisetyenziselwa ukufunda amaza, afana nokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza ekutshintsheni ifom ngokusebenzisa iinkqubo ezisasazwayo zomgca, kwaye ziyafuneka ukuhlalutya ukusasazwa kwamaza. Amaza amaza ahamba kumacala achaseneyo esithubeni anokubonakaliswa njengamaza anobude obufanayo namaza ahamba kumacala achaseneyo. Xa amaza amabini egqithisile, ipateni yamaza emileyo iyadalwa. Oku kufana naxa inqaku litsalwa kumtya, apho amaza aphazamisayo abonakala kwiincam ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Isandi esiqulunqiweyo senqaku elitsalweyo kumtya siqulunqwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo kubunzima ngeyunithi yobude bomtya.
Buyintoni uBudlelwane phakathi kweSine Curve kunye nePlane Wave?
I-sine wave yi-oscillation egudileyo, ephinda-phindayo yeform yamaza eqhubekayo. Ligophe lemathematika elichazwe ngokomsebenzi wesine trigonometric, kwaye ihlala igrafu njengegophe eligudileyo, le-sinusoidal. Amaza eSine afumaneka kwiindawo ezininzi zemathematika, ifiziksi, ubunjineli, kunye nemimandla yokucwangcisa imiqondiso.
I-sine wave ibonakala ngokuphindaphindiweyo kwayo okuqhelekileyo, inani le-oscillations okanye imijikelo eyenzeka ngexesha elithile. ithuba. I-angular frequency, ω, yireyithi yotshintsho lwengxoxo yomsebenzi, kwaye ithelekiswa neeyunithi zeeradians ngesekhondi. Ifomu engeyonxalenye yamaza ibonakala itshintshiwe ngexesha, kunye nokutshintshwa kwesigaba, φ, semizuzwana ye-ωt. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana.
I-sine wave ikwasetyenziswa ukuchaza amaza esandi. Ichazwa ngumsebenzi wesine, f (t) = Isono (ωt + φ), apho u-A yi-amplitude, ω yi-frequency ye-angular, kwaye φ yi-shift yesigaba. Ii-oscillations zikwabonwa kwi-spring-mass system engenamda kwi-equilibrium.
Amaza eSine abalulekile kwifiziksi kuba agcina imilo yamaza xa edityanisiwe. Le propati, eyaziwa ngokuba ngumgaqo-siseko we-superposition, ikhokelela kukubaluleka kohlalutyo lwe-Fourier, okwenza kube lula ukwahlula ngokuvakalayo phakathi kwezinto eziguquguqukayo zendawo. Umzekelo, ukuba u-x umele indawo kwidimensioni enye, ngoko iliza liyanda ngeempawu zeparamitha, k, ebizwa ngokuba yinombolo yamaza. Inombolo ye-angular wave, k, imele ulungelelwaniso phakathi kwe-engular frequency, ω, kunye nesantya somgca sosasazo, ν. Inombolo yamaza, k, inxulumene ne-engular frequency, ω, kunye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave kumlinganiselo omnye inikwa ngu-y = A isono(ωt + φ). Le nxaki inika ukufuduswa kwamaza kwindawo enikiweyo, x, ngexesha elithile, t. Umzekelo womgca omnye, ukuba ixabiso le-wave libhekwa njengocingo, ngoko kwimilinganiselo emibini yendawo, i-equation ichaza i-wave yendiza ehambayo. Indawo, x, kunye nenani lamaza, k, inokutolikwa njenge vectors, kwaye imveliso yezi zimbini yimveliso yamachaphaza.
Amaza antsonkothileyo, afana nalawo abonwa echibini xa kuwiswa ilitye, afuna iiequations ezintsonkothileyo ukuwachaza. Igama elithi sinusoid lisetyenziselwa ukuchaza iimpawu zamaza ezifana ne-sine wave. I-cosine wave iyafana ne-sine wave, kodwa ngesigaba sokutshintsha kwe-π/2 iiradians, okanye isiqalo sentloko. Oku kukhokelela ekubeni i-sine wave ibambe i-cosine wave. Igama elithi sinusoidal lisetyenziswa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Ukubonisa i-cosine wave lubudlelwane obusisiseko kwisangqa kwimodeli ye-3D yenqwelomoya entsonkothileyo, enokusetyenziswa ukubonisa ukuba luncedo kwamaza e-sine ekuguquleleni phakathi kwemimandla. Le pateni yamaza yenzeka kwindalo, kuqukwa namaza omoya, amaza esandi, kunye namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine abonisa amaza omoya kunye neeharmonics. Indlebe yomntu ibona isandi njenge-sine wave kunye ne-harmonics ukongeza kwi-frequency esisiseko. Oku kubangela ukuhluka kwe-timbre. Isizathu sokuba inqaku lomculo lidlalwe kwizixhobo ezahlukeneyo livakala ngokwahlukileyo kungenxa yokuba isandi sinamaza e-aperiodic ukongeza kumaza e-sine. Isandi se-Aperiodic sibonwa njengengxolo, kwaye ingxolo ibonakala ngokuba nepateni engaphindi.
Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal aziibhloko zokwakha ezilula zokuchaza kunye noqikelelo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha. Amaza e-Sine nawo anokusasaza ngaphandle kokutshintsha uhlobo kwiinkqubo ezisasaziweyo zomgca. Oku kuyafuneka ukuhlalutya ukusasazwa kwamaza kumacala amabini esithubeni, kwaye imelwe ngamaza anobukhulu obufanayo kunye nokuphindaphinda, kodwa ehamba kumacala achaseneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Oku kubonakala xa inqaku litsalwa kumtya, kwaye amaza aphazamisayo abonakala kwiindawo ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies, kwaye aqulunqwe ngamaza omoya asisiseko kunye nee-harmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo kubunzima ngeyunithi yobude bomtya.
Ingasetyenziswa njani iSine Curve ukuJonga iipateni zamaza?
I-sine wave yi-oscillation eqhubekayo, egudileyo, ephindaphindayo echazwa lijiko lemathematika. Ludidi lwamaza aqhubekayo achazwa ngumsebenzi wesine we-trigonometric, owenziwe ngegraphed njenge-waveform. Iyenzeka kwimathematika, kwifiziksi, kubunjineli, nakwiindawo zokusetyenzwa kwemiqondiso.
I-sine wave ine-frequency yesiqhelo, eli nani le-oscillations okanye imijikelo eyenzeka ngexesha elinikiweyo. Oku kumelwa yi-angular frequency, ω, elingana no-2πf, apho i-f yi-frequency kwi-hertz (Hz). I-sine wave inokutshintshwa ngexesha, ngexabiso elingalunganga elimele ulibaziseko kunye nexabiso elilungileyo elimele i-advanced kwimizuzwana.
I-sine wave isoloko isetyenziselwa ukuchaza isandi somsindo, njengoko sichazwa ngumsebenzi wesine. Ubuninzi be-sine wave, f, linani le-oscillations ngesekhondi. Oku kuyafana nokugungxulwa kwenkqubo yentlakohlaza engathintelekiyo kwi-equilibrium.
I-sine wave ibalulekile kwifiziksi kuba igcina imilo yamaza xa idityaniswe kwelinye i-sine wave yamaza aphindaphindiweyo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati ye-sine wave yaziwa ngokuba ngumgaqo-siseko kwaye yipropathi ye-waveform ngamaxesha. Le propati ikhokelela kukubaluleka kohlalutyo lwe-Fourier, okwenza kube lula ukwahlula ngokuvakalayo phakathi kwezinto ezahlukeneyo zesithuba.
Umzekelo, ukuba u-x umele idimension yendawo apho iliza lisasaza khona, ngoko uphawu lweparameter k, ebizwa ngokuba yinombolo yamaza, imele ulungelelwaniso phakathi kwe-angular frequency, ω, kunye nesantya somgca sosasazo, ν. Inombolo yamaza inxulumene ne-angular frequency kunye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave kumlinganiselo omnye inikwe ngu-y = Isono (ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, t lixesha, kwaye φ yi-phase shift. Ukuba umzekelo womgca omnye uqwalaselwa, ngoko ixabiso le-wave nakweyiphi na indawo x nangaliphi na ixesha t linikezelwa y = A isono (kx - ωt + φ).
Kwimilinganiselo emininzi yendawo, iequation yesine wave inikwa ngu y = A isono (kx – ωt + φ), apho u-A bubuxhakaxhaka be-amplitude, k linani lamaza, x yindawo, ω yi-angular frequency, t lixesha, kwaye φ lutshintsho lwesigaba. Le nxaki ichaza iliza lenqwelomoya ehambayo.
Ukuba luncedo kwe-sine wave akuphelelanga ekuguquleleni kwiindawo ezibonakalayo. Ipateni efanayo yamaza yenzeka kwindalo, kubandakanywa amaza omoya, amaza esandi, kunye namaza okukhanya. Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziselwa ukumela i-harmonics yefrikhwensi enye.
Indlebe yomntu inokuqonda isandi esenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Ezi frikhwekhwezi zomtya zilingana nobude bomtya kwaye zithelekiseka ngokuphambeneyo nobunzima ngeyunithi yobude bomtya.
Isishwankathelo, igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu ze-sine wave kunye ne-cosine wave. I-sine wave kuthiwa inesigaba sokutshintsha kwe-π/2 radians, elingana nentloko, ngelixa i-cosine wave kuthiwa ikhokela i-sine wave. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine, kunye nesigaba sokunciphisa. Oku kuboniswa ngamaza e-cosine, olubudlelwane obusisiseko kwisangqa kwimodeli ye-3D yendiza entsonkothileyo esetyenziselwa ukubona ukuba luncedo kwe-sine wave ekuguquleleni kwimimandla ebonakalayo.
Amaza eSine kunye neSigaba
Kweli candelo, ndizakube ndiphonononga ubudlelwane phakathi kwamaza esine kunye nesigaba. Ndizakuxoxa ngendlela isigaba esichaphazela ngayo i-sine wave kunye nokuba ingasetyenziswa njani ukwenza iifom ezahlukeneyo zamaza. Ndiza kubonelela ngeminye imizekelo ukubonisa indlela isigaba esinokusetyenziswa ngayo kwizicelo ezahlukeneyo.
Yintoni ubudlelwane phakathi kweSine Wave kunye neSigaba?
I-sine wave yi-oscillation egudileyo, ephinda-phindayo eqhubekayo kwaye ine-frequency enye. Ligophe lemathematika elichazwa ngumsebenzi wesine wetrigonometric, kwaye isoloko imelwe yigrafu. Amaza e-Sine afumaneka kwiindawo ezininzi zemathematika, i-physics, ubunjineli, kunye nokulungiswa kwemiqondiso.
Ubuninzi be-sine wave linani le-oscillations okanye imijikelo eyenzeka ngexesha elithile, kwaye ichazwa ngonobumba wesiGrike ω (omega). I-angular frequency yireyithi yotshintsho lwengxoxo yokusebenza, kwaye ilinganiswa ngeeyunithi zeeradians ngesekhondi. Ifomu engeyiyo yonke i-waveform inokubonakala itshintshile ngexesha, kunye nokutshintshwa kwesigaba se-φ (phi) ngemizuzwana. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limele ukuqhubela phambili kwimizuzwana. Ubuninzi be-sine wave bulinganiswa nge-hertz (Hz).
I-sine wave isoloko isetyenziselwa ukuchaza isandi somsindo, njengoko sichazwa ngumsebenzi wesine. Umzekelo, f = 1/T, apho i-T iyithuba le-oscillation, kwaye f yi-frequency ye-oscillation. Oku kuyafana nenkqubo ye-spring-mass engathintelekiyo kwi-equilibrium.
I-sine wave ibalulekile kwifiziksi kuba igcina imilo yamaza xa idityaniswe kwelinye i-sine wave yamaza aphindaphindiweyo kunye nesigaba esingenasizathu kunye nobukhulu. Le propati yokuba ngamaxesha yipropati ekhokelela ekubalulekeni kwayo kuhlalutyo lwe-Fourier, eyenza ukuba ibe yodwa ngokuvakalayo.
Xa iliza lisasazeka esithubeni, umahluko wendawo x umele indawo kumlinganiselo omnye. Iliza linophawu lweparameter k, ebizwa ngokuba yinombolo yamaza, emele ulungelelwaniso phakathi kwe-engular frequency ω kunye nesantya somgca sosasazo ν. Inombolo yamaza u-k inxulumene ne-engular frequency ω kunye ne-wavelength λ (lambda) nge-equation λ = 2π/k. I-frequency f kunye nesantya somgca v zihambelana ne-equation v = λf.
I-equation ye-sine wave kumlinganiselo omnye inikwa ngu-y = A isono(ωt + φ), apho u-A yi-amplitude, ω yi-angular frequency, t lixesha, kwaye φ yimo yokutshintsha kwesigaba. Le nxaki inika ukususwa kwamaza kwindawo enikiweyo x kunye nexesha t. Umzekelo womgca omnye uyaqwalaselwa, ngexabiso y = A isono(ωt + φ) kubo bonke x.
Kwimilinganiselo emininzi yendawo, i-equation ye-wave yenqwelomoya ehambayo inikezelwa ngu y = A isono (kx - ωt + φ). Le nxaki inokutolikwa njengeevekhtha ezimbini kwindiza entsonkothileyo, kunye nemveliso yeevekhtha ezimbini ibe yimveliso yamachaphaza.
Amaza antsonkothileyo, anje ngamaza amanzi echibini xa kuwiswa ilitye, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza amaza aneempawu zombini i-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba sika π/2 radians kunika i-cosine wave isiqalo, kwaye kuthiwa ikhokele i-sine wave. Oku kuthetha ukuba i-sine wave ibeka i-cosine wave. Igama elithi sinusoidal lihlala lisetyenziselwa ukubhekisa ngokudibeneyo kumaza e-sine kunye namaza e-cosine, kunye okanye ngaphandle kwesigaba sokunciphisa.
Ukubonisa i-cosine wave, ubudlelwane obusisiseko phakathi kwe-sine wave kunye ne-cosine wave inokubonwa ngemodeli ye-3D yenqwelomoya entsonkothileyo. Lo mzekelo uluncedo ekuguquleleni ipateni yamaza eyenzeka kwindalo, kubandakanywa amaza omoya, amaza omoya, namaza okukhanya.
Indlebe yomntu inokuqonda amaza e-sine enye, isandi esicacileyo kwaye sisulungekile. Amaza e-sine ahlala esetyenziselwa ukubonakaliswa kweetoni eziphindaphindiweyo, kunye nee-harmonics. Indlebe yomntu ibona isandi njengendibaniselwano yamaza e-sine, kunye nobukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko ebangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elinesandi esifanayo esidlalwa kwizixhobo ezahlukeneyo liya kuvakala ngokwahlukileyo.
Ukuqhwaba ngesandla, nangona kunjalo, kuqulethe amaza e-aperiodic, angengawo amaxesha kwaye anepateni engaphindi. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza ekutshintsheni ifom ngokusebenzisa iinkqubo ezisasaziweyo zomgca, kwaye ziyafuneka ukuhlalutya ukusasazwa kwamaza. Amaza ane-Sine anokuhamba kumacala amabini esithubeni, kwaye amelwe ngamaza ane-amplitude efanayo kunye ne-frequency kodwa ehamba kumacala ahlukeneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Oku kufana nenqaku elitsalwa kumtya, apho amaza abonakala kwiincam ezisisigxina zomtya. Amaza amileyo enzeka kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Ezi frikhwensi zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwekhwethe zeresonant zomtya zilingana nobude bomtya, kwaye ngokuphambeneyo zilinganisa ubunzima ngeyunithi yobude bomtya.
ISigaba silichaphazela njani iSine wave?
I-sine wave luhlobo oluqhubekayo lwamaza oluphawulwa ngokugudileyo, okuphindaphindwayo kwe-oscillation. Ligophe lemathematika elichazwa ngumsebenzi wetrigonometric kwaye lisetyenziswa kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokucwangcisa imiqondiso. Isiqhelo esiqhelekileyo se-sine wave linani le-oscillations okanye imijikelo eyenzeka ngexesha elinikiweyo, elidla ngokulinganiswa ngemizuzwana. I-angular frequency, echazwa ngu-ω, ngumyinge wotshintsho lwengxoxo yokusebenza, edla ngokulinganiswa ngeeradians. Ifomu engeyiyo yonke i-waveform ibonakala itshintshile ngexesha ngenani φ, elilinganiswe ngemizuzwana. Iyunithi yokuphindaphinda yi-hertz (Hz), elingana ne-oscillation enye ngesekhondi.
I-sine wave isetyenziswa ngokuqhelekileyo ukuchaza isandi somsindo, kwaye ichazwa ngumsebenzi wesine, f (t) = Isono (ωt + φ). Olu hlobo lwe-waveform lukwabonwa kwi-spring-mass system engathintelekiyo kwi-equilibrium. Amaza eSine abalulekile kwifiziksi kuba agcina imilo yamaza xa edityaniswe kunye, eyipropathi eyaziwa ngokuba ngumgaqo-siseko. Le propati ikhokelela ekubalulekeni kohlalutyo lwe-Fourier, okwenza kube lula ukwahlula ngokuvakalayo isandi esinye kwesinye.
Kwinqanaba elinye, i-sine wave inokumelwa ngumgca omnye. Ngokomzekelo, ixabiso le-wave kwi-wire lingamelwa ngumgca omnye. Kwimilinganiselo emininzi yendawo, iequation ebanzi ngokubanzi iyafuneka. Le nxaki ichaza ukufuduswa kwamaza kwindawo ethile, x, ngexesha elithile, t.
Amaza antsonkothileyo, anje ngamaza amanzi echibini emva kokuwiswa kwelitye, afuna iiequations ezinzima ngakumbi. Igama elithi sinusoid lisetyenziselwa ukuchaza i-waveform eneempawu ze-sine wave kunye ne-cosine wave. Ukutshintsha kwesigaba sika π/2 radians iyafana nentloko, kwaye iyafana nokuthi umsebenzi wecosine ukhokela umsebenzi wesine, okanye isine ibeka icosine. Igama elithi sinusoidal lisetyenziselwa ngokudibeneyo ukubhekisa kuwo omabini amaza e-sine kunye namaza e-cosine anesigaba sokunciphisa.
Ukubonisa i-cosine wave, ubudlelwane obusisiseko phakathi kwe-sine wave kunye ne-cosine wave inokubonwa kusetyenziswa isangqa kwimodeli ye-3D yenqwelomoya entsonkothileyo. Oku kuluncedo kuguqulelo phakathi kwemimandla eyahlukeneyo, njengoko ipateni efanayo yamaza isenzeka kwindalo, kuquka amaza omoya, amaza esandi, namaza okukhanya.
Indlebe yomntu inokuqonda amaza e-sine enye njengesandi esicacileyo, kwaye amaza e-sine ahlala esetyenziselwa ukumela amaza kunye neeharmonics. Xa amaza e-sine ahlukeneyo edityaniswe kunye, utshintsho olubangelwa yi-waveform, olutshintsha i-timbre yesandi. Ubukho be-harmonics ephezulu ukongeza kwi-frequency esisiseko kubangela ukwahluka kwi-timbre. Esi sisizathu sokuba inqaku lomculo elidlalwa kwizixhobo ezahlukeneyo livakala ngokwahlukileyo.
Isandi sokuqhwaba ngesandla siqulathe amaza e-aperiodic, angeyo-periodic, ngokuchaseneyo namaza e-sine, angamaxesha athile. Isazi sezibalo esingumFrentshi uJoseph Fourier ufumanise ukuba amaza e-sinusoidal ziibhloko zokwakha ezilula ezinokuthi zisetyenziswe ukuchaza nokuqikelela naluphi na uhlobo lwamaza okwenziwa ngamaxesha athile, kuquka amaza asisikwere. Uhlalutyo lwe-Fourier sisixhobo esinamandla sohlalutyo esisetyenziselwa ukufunda amaza, njengokuhamba kobushushu, kwaye sisetyenziswa rhoqo ekusetyenzweni komqondiso kunye nohlalutyo lwamanani oluhlu lwexesha.
Amaza e-Sine anokusasaza kwiifom eziguqukayo ngokusasazwa kweenkqubo zomgca. Ukuhlalutya ukusasazwa kwamaza, amaza e-sine ahamba kumacala ahlukeneyo esithubeni amelwe ngamaza anobukhulu obufanayo kunye nokuphindaphinda, kodwa ehamba kumacala achaseneyo. Xa la maza egqithisile, ipateni yamaza emileyo iyadalwa. Le yipatheni efanayo eyenziwayo xa inqaku litsalwa emtya. Amaza aphazamisayo abonakaliswe kwiisiphelo ezisisigxina zomtya adala amaza amileyo avela kwiifrikhwensi ezithile, ezibizwa ngokuba zii-resonant frequencies. Ezi frikhwensi zeresonant zenziwe ngamaza omoya asisiseko kunye neeharmonics eziphezulu. Iifrikhwekhwezi ezivakalayo zomtya zilingana nobude bomtya kwaye ngokuphambeneyo zihambelana nengcambu yobunzima kwiyunithi yobude bomtya.
ISigaba singasetyenziswa njani ukwenza iifomu ezahlukeneyo zamaza?
Amaza e-Sine luhlobo lwe-waveform eqhubekayo egudileyo kwaye iphinda-phinda, kwaye inokusetyenziswa ukuchaza iindidi ngeendidi zeziganeko kwimathematika, i-physics, ubunjineli, kunye nokulungiswa komqondiso. Zichazwa ngumsebenzi wetrigonometric, kwaye zinokugrafu njengegophe eligudileyo, lexesha. Ubuninzi be-sine wave linani le-oscillations okanye imijikelo eyenzeka ngexesha elithile, elidla ngokulinganiswa kwiHertz (Hz). I-angular frequency, ω, yireyithi apho impikiswano yomsebenzi itshintshayo, ilinganiswa ngeeradians ngesekhondi. I-sine wave ingabonakala itshintshiwe ngexesha, kunye nokutshintshwa kwesigaba, φ, kulinganiswe ngemizuzwana. Ixabiso elilambathayo limele ukulibaziseka, ngelixa ixabiso elivumayo limela i-advanced.
Isigaba yipropathi ebalulekileyo ye-sine wave, kwaye ingasetyenziselwa ukudala iifom zamaza ezahlukeneyo. Xa amaza e-sine amabini anezakhelo ezifanayo kunye nesigaba esingenasizathu kunye nobukhulu edityanisiwe, isiphumo se-waveform yi-period waveform enepropathi efanayo. Le propati ikhokelela ekubalulekeni kohlalutyo lwe-Fourier, okwenza kube lula ukuchonga nokuhlalutya iimpawu ezikhethekileyo ze-acoustically.
Inqanaba linokusetyenziswa ukwenza iifomati ezahlukeneyo zamaza ngezi ndlela zilandelayo:
• Ngokutshintsha inqanaba le-sine wave, inokwenziwa ukuba iqale kwindawo eyahlukileyo ngexesha. Oku kwaziwa njengenguqu yesigaba, kwaye ingasetyenziselwa ukwenza iifom zamaza ezahlukeneyo.
• Ngokudibanisa i-sine wave enezandi ezahlukeneyo kunye nesigaba kwi-sine wave esisiseko, i-wave wave entsonkothileyo inokudalwa. Oku kwaziwa njenge-harmonic, kwaye ingasetyenziselwa ukudala izandi ezahlukeneyo.
• Ngokudibanisa amaza e-sine kunye neefrikhwensi ezahlukeneyo kunye nezigaba, ipateni yokuma yamaza inokudalwa. Oku kwaziwa njenge-resonant frequency, kwaye ingasetyenziselwa ukwenza izandi ezahlukeneyo.
• Ngokudibanisa amaza e-sine kunye nee-frequencies ezahlukeneyo kunye nezigaba, i-waveform eyinkimbinkimbi inokudalwa. Oku kwaziwa njengohlalutyo lweFourier, kwaye lunokusetyenziswa ukuhlalutya ukusasazwa kwamaza.
Ngokusebenzisa isigaba ukwenza iifom ezahlukeneyo zamaza, kunokwenzeka ukwenza izandi ezahlukeneyo kunye nokuhlalutya ukusasazwa kwamaza. Le yipropathi ebalulekileyo yamaza e-sine, kwaye isetyenziswa kwiinkalo ezahlukeneyo, kubandakanya i-acoustics, ukusetyenzwa komqondiso, kunye nefiziksi.
Ngubani osebenzisa amaza eSine kwiiMarike?
Njengomtyali-mali, ndiqinisekile ukuba uvile ngamaza e-sine kunye nendima yawo kwiimarike zemali. Kweli nqaku, ndiza kuphonononga ukuba yintoni amaza e-sine, anokusetyenziswa njani ukwenza uqikelelo, kunye nobudlelwane phakathi kwamaza e-sine kunye nohlalutyo lobuchwephesha. Ekupheleni kweli nqaku, uya kuba nokuqonda ngcono ukuba amaza e-sine anokusetyenziswa njani kuncedo lwakho kwiimarike.
Yintoni indima yeSine Waves kwiiMarike zeMali?
Amaza e-Sine luhlobo lwegophe lemathematika elichaza i-oscillation egudileyo, ephindaphindayo kumaza aqhubekayo. Zikwabizwa ngokuba ngamaza e-sinusoidal kwaye asetyenziswa kwimathematika, ifiziksi, ubunjineli, kunye nemimandla yokucwangcisa imiqondiso. Amaza e-Sine abalulekile kwiimarike zezimali, njengoko zingasetyenziselwa ukwenza izibikezelo kunye nokuhlalutya iindlela.
Kwiimarike zemali, amaza e-sine asetyenziselwa ukuchonga kunye nokuhlalutya iintsingiselo. Zingasetyenziselwa ukuchonga amanqanaba enkxaso kunye nokumelana, kunye nokuchonga iindawo ezinokungena kunye nokuphuma. Amaza e-Sine angasetyenziselwa ukuchonga kunye nokuhlalutya iipateni, njengentloko kunye namagxa, ama-double top and bottoms, kunye nezinye iipatheni zetshathi.
Amaza e-sine nawo asetyenziswa kuhlalutyo lobugcisa. Uhlalutyo lobuchwephesha luphononongo lweentshukumo zexabiso kunye neepatheni kwiimarike zemali. Abahlalutyi bobuchwephesha basebenzisa amaza e-sine ukuchonga iintsingiselo, inkxaso kunye namanqanaba okumelana, kunye nokungena kunye namanqaku okuphuma. Bakwasebenzisa amaza e-sine ukuchonga iipateni, ezinjengentloko namagxa, imiphezulu ephindwe kabini kunye namazantsi, kunye nezinye iipateni zetshathi.
Amaza eSine anokusetyenziswa ukwenza uqikelelo. Ngokuhlalutya iindlela ezidlulileyo kunye nezangoku, abahlalutyi bezobugcisa banokwenza izibikezelo malunga nokuhamba kwexabiso elizayo. Ngokuhlalutya amaza e-sine, banokuchonga iindawo ezinokungena kunye nokuphuma, kunye nenkxaso enokubakho kunye namanqanaba okumelana.
Amaza e-Sine sisixhobo esibalulekileyo kubahlalutyi bezobugcisa kwiimarike zemali. Zingasetyenziselwa ukuchonga kunye nokuhlalutya iintsingiselo, amanqanaba enkxaso kunye nokuchasana, kunye namanqaku anokubakho okungena kunye nokuphuma. Zisenokusetyenziswa ukwenza uqikelelo malunga neentshukumo zamaxabiso ezizayo. Ngokuhlalutya amaza e-sine, abahlalutyi bezobugcisa banokufumana ukuqonda okungcono kweemarike kwaye benze izigqibo ezinolwazi ngakumbi.
Ingasetyenziswa Njani Amaza ESine Ukwenza Uqikelelo?
Amaza e-Sine asetyenziswa kwiimarike zezimali ukuhlalutya iindlela kunye nokwenza uqikelelo. Ziluhlobo lwe-waveform ejikelezayo phakathi kwamanqaku amabini, kwaye ingasetyenziselwa ukuchonga iipateni kunye neendlela kwiimarike. Amaza e-Sine asetyenziswa kuhlalutyo lobugcisa kwaye angasetyenziselwa ukuqikelela ukunyakaza kwexabiso elizayo.
Nazi ezinye zeendlela amaza e-sine anokusetyenziswa ngayo kwiimarike:
• Ukuchonga amanqanaba enkxaso kunye nokumelana: Amaza e-Sine angasetyenziselwa ukuchonga amanqanaba enkxaso kunye nokumelana kwiimarike. Ngokujonga iincopho kunye nemikhombe ye-sine wave, abahwebi banokuchonga iindawo apho ixabiso linokufumana inkxaso okanye ukuchasana.
• Ukuchonga uhlengahlengiso: Ngokujonga i-sine wave, abarhwebi banokuchonga uhlengahlengiso olunokubakho. Ukuba i-sine wave ibonisa ukuhla, abarhwebi banokujonga iindawo ezinokubakho zenkxaso apho umkhwa unokubuya umva.
• Ukuchonga iipateni zamaxabiso: Amaza e-Sine angasetyenziselwa ukuchonga iipatheni zamaxabiso kwiimarike. Ngokujonga i-sine wave, abarhwebi banokuchonga iindawo ezinokubakho zenkxaso kunye nokuchasana, kunye neenguqu ezinokubakho.
• Ukwenza uqikelelo: Ngokujonga i-sine wave, abarhwebi banokwenza uqikelelo malunga neentshukumo zexabiso elizayo. Ngokujonga iincopho kunye nemikhombe ye-sine wave, abarhwebi banokuchonga iindawo ezinokubakho zenkxaso kunye nokuchasana, kunye neenguqu ezinokubakho.
Amaza e-Sine anokuba sisixhobo esiluncedo kubahwebi abafuna ukwenza uqikelelo kwiimarike. Ngokujonga i-sine wave, abarhwebi banokuchonga iindawo ezinokubakho zenkxaso kunye nokuchasana, kunye neenguqu ezinokubakho. Ngokusebenzisa amaza e-sine, abarhwebi banokwenza izigqibo ezinolwazi malunga norhwebo lwabo kunye nokwandisa amathuba abo okuphumelela.
Buyintoni ubudlelwane phakathi kwamaza eSine kunye noHlalutyo lobuGcisa?
Amaza e-Sine asetyenziswa kwiimarike zezimali ukuhlalutya ukuziphatha kwamaxabiso kunye nokwenza uqikelelo malunga nokuhamba kwexabiso elizayo. Zisetyenziswa ngabahlalutyi bezobugcisa ukuchonga iindlela, inkxaso kunye namanqanaba okumelana, kunye nokuchonga iindawo ezinokungena kunye nokuphuma.
Amaza e-Sine luhlobo lwe-periodic waveform, oku kuthetha ukuba aphinda emva kwexesha. Ziphawulwa ngokugudiswa kwazo, okuphindaphindwayo kwe-oscillation kwaye zisetyenziselwa ukuchaza uluhlu olubanzi lweziganeko kwimathematika, i-physics, ubunjineli, kunye nokulungiswa komqondiso. Kwiimarike zemali, amaza e-sine asetyenziselwa ukuchonga iipateni eziphindaphindiweyo kwiintshukumo zexabiso.
Ubudlelwane phakathi kwamaza e-sine kunye nohlalutyo lobugcisa kukuba amaza e-sine angasetyenziselwa ukuchonga iipateni eziphindaphindiweyo kwiintshukumo zexabiso. Abahlalutyi bezobugcisa basebenzisa amaza e-sine ukuchonga iintsingiselo, inkxaso kunye namanqanaba okumelana, kunye nokuchonga iindawo ezinokungena kunye nokuphuma.
Amaza e-Sine angasetyenziselwa ukwenza uqikelelo malunga neentshukumo zexabiso elizayo. Ngokuhlalutya ukuziphatha okudlulileyo kwamaxabiso, abahlalutyi bezobugcisa banokuchonga iipatheni eziphindaphindiweyo kwaye basebenzise ezi patheni ukwenza izibikezelo malunga nokuhamba kwexabiso elizayo.
Amaza e-sine nawo asetyenziselwa ukuchonga imijikelo kwiimarike. Ngokuhlalutya ukuziphatha kwamaxabiso ngexesha, abahlalutyi bezobugcisa banokuchonga imijikelo ephindaphindiweyo kwaye basebenzise le mijikelezo ukwenza uqikelelo malunga nokuhamba kwexabiso elizayo.
Ngamafutshane, amaza e-sine asetyenziswa kwiimarike zezimali ukuhlalutya ukuziphatha kwamaxabiso kunye nokwenza uqikelelo malunga neentshukumo zamaxabiso kwixesha elizayo. Zisetyenziswa ngabahlalutyi bezobugcisa ukuchonga iindlela, inkxaso kunye namanqanaba okumelana, kunye nokuchonga iindawo ezinokungena kunye nokuphuma. Amaza e-Sine angasetyenziselwa ukwenza uqikelelo malunga nokuhamba kwexabiso elizayo ngokuhlalutya ukuziphatha okudlulileyo kwamaxabiso kunye nokuchonga iipateni eziphindaphindiweyo kunye nemijikelo.
Ukungafani
I-Sine wave vs i-sine wave wave
I-Sine Wave vs I-Sine Wave efanisiweyo:
• I-Sine wave yifom eqhubekayo yamaza elandela ipateni ye-sinusoidal kwaye isetyenziswa kwimathematika, i-physics, ubunjineli, kunye nokulungiswa komqondiso.
• Iliza le-sine elilinganisiweyo luhlobo lwamaza elenziwe ngokwenziwa sisiguquli samandla ukulinganisa iimpawu zeliza lesine.
• Amaza e-sine anefrikwensi enye kunye nesigaba, ngelixa amaza e-sine afanisiweyo anezandi ezininzi kunye nezigaba.
• Amaza e-sine asetyenziselwa ukumela amaza esandi kunye nezinye iindlela zamandla, ngelixa amaza e-sine afanisiweyo asetyenziselwa ukunika amandla izixhobo zombane.
• Amaza e-sine aveliswa yimithombo yendalo, ngelixa amaza e-sine afanisiweyo enziwa ngabaguquli bamandla.
• Amaza anesine asetyenziswa kuhlalutyo lwe-Fourier ukufunda ukwanda kwamaza, ngelixa amaza e-sine afanisiweyo esetyenziselwa ukunika amandla izixhobo zombane.
• Amaza e-sine asetyenziselwa ukumela amaza esandi, ngelixa amaza e-sine afanisiweyo asetyenziselwa ukunika amandla izixhobo zombane.
FAQ malunga ne-sine wave
Ngaba indalo iliza elinesine?
Akunjalo, indalo ayingomaza. I-sine wave lijiko lemathematika elichaza i-oscillation egudileyo, ephinda-phindayo, kwaye yifomayimaza eqhubekayo enefrikhwensi enye. Indalo yonke, nangona kunjalo, yinkqubo entsonkothileyo neguqukayo ehlala iguquka kwaye iguquka.
Indalo iphela ibunjwe ngamalungu amaninzi awahlukahlukeneyo, kuquka i-matter, amandla kunye nexesha lasesibhakabhakeni. La malungu asebenzisana enye kwenye ngeendlela ezahlukeneyo, nto leyo ekhokelela kwiintlobo ngeentlobo zeziganeko, ukusuka ekuyilweni kweminyele ukuya kwindaleko yobomi. Indalo iphela ilawulwa yimithetho yefiziksi, esekelwe kwizibalo zezibalo.
Indalo iphela ayingomaza anesine, kodwa inamaza amaninzi e-sine. Ngokomzekelo, amaza esandi ngamaza anesine, yaye akhoyo kwindalo iphela. Amaza okukhanya nawo angamaza anesine, kwaye akhona kwindalo iphela. Ukongezelela, indalo iphela inezinye iindidi ezininzi zamaza, njengamaza ombane, amaza omxhuzulane, namaza equantum.
Indalo iphela yenziwe ngamasuntswana amaninzi ahlukeneyo, anjengeeproton, iineutron, neeelectron. La masuntswana anxibelelana ngeendlela ezahlukeneyo, nto leyo ekhokelela kwiintlobo ngeentlobo zezinto ezenzekayo, ukusuka ekubunjweni kweeathomu ukuya ekuguqukeni kweenkwenkwezi.
Ukuqukumbela, indalo iphela ayingomaza anesine, kodwa inamaza amaninzi e-sine. La maza e-sine akhoyo ngendlela yamaza esandi, amaza okukhanya, kunye nezinye iindidi zamaza. Indalo iphela yenziwe ngamasuntswana amaninzi ahlukeneyo asebenzisanayo ngeendlela ezahlukahlukeneyo, nto leyo ebangela ukuba kubekho izinto ezahlukahlukeneyo.
Ubudlelwane obubalulekileyo
Ubungakanani:
• I-amplitude yeyona ndawo iphezulu yokushenxiswa kwe-sine iliza ukusuka kwindawo yayo yolingano.
• Ilinganiswa ngeeyunithi zomgama, njengeemitha okanye iinyawo.
• Ikwanxulumene namandla amaza, kunye ne-amplitudes ephezulu enamandla amakhulu.
• Iamplitude ye-sine wave ilingana nengcambu yesikweri sokuphindaphinda kwayo.
• I-amplitude ye-sine wave nayo inxulumene nesigaba sayo, kunye ne-amplitudes ephezulu ene-shift yesigaba esikhulu.
Impendulo efunyanwa rhoqo:
• Impendulo yefrikhwensi ngumlinganiselo wendlela inkqubo ephendula ngayo kwiifrikhwensi ezahlukeneyo zegalelo.
• Idla ngokulinganiswa ngeedecibels (dB) kwaye ngumlinganiselo wokuzuza okanye ukuthotywa kwenkqubo kumaza ahlukeneyo.
• Ukuphendula rhoqo kwe-sine wave kumiselwa bubungakanani bayo kunye nesigaba.
• I-sine wave ene-amplitude ephezulu iya kuba ne-frequency impendulo ephezulu kune-amplitude esezantsi.
• Ukuphendula rhoqo kwe-sine wave kukwachatshazelwa sisigaba saso, kunye nezigaba eziphezulu ezikhokelela kwiimpendulo eziphezulu zefrikhwensi.
Sawtooth:
• I-sawtooth wave luhlobo lwamaza omaza ngamaxesha athile anokuphakama okubukhali kunye nokuwa ngokuthe ngcembe.
• Ihlala isetyenziswa kwi-audio synthesis kwaye ikwasetyenziswa kwezinye iindidi zokusetyenzwa kophawu lwedijithali.
• Iliza le-sawtooth lifana ne-sine wave kuba luhlobo lwamaza ngamaxesha athile, kodwa linemilo eyahlukileyo.
• Iliza le-sawtooth linokuphakama okubukhali kunye nokuwa ngokuthe ngcembe, ngelixa i-sine wave inokunyuka ngokuthe ngcembe kunye nokuwa ngokuthe ngcembe.
• I-sawtooth wave ine-frequency ephezulu yokuphendula kune-sine wave, kwaye isoloko isetyenziswa kwi-audio synthesis ukwenza isandi esinamandla.
• I-sawtooth wave ikwasetyenziswa kwezinye iindidi zokusetyenzwa komqondiso wedijithali, njengokumodareyitha amaza kunye nohlengahlengiso lwesigaba.
isiphelo
Amaza eSine ayinxalenye ebalulekileyo yefiziksi, imathematika, ubunjineli, ukusetyenzwa komqondiso, kunye nezinye iinkalo ezininzi. Ziluhlobo lwamaza aqhubekayo ane-oscillation egudileyo, ephindaphindayo, kwaye isoloko isetyenziselwa ukuchaza amaza esandi, amaza okukhanya, kunye nezinye iifom zamaza. Amaza eSine nawo abalulekile kuhlalutyo lweFourier, oluwenza abe acoustically awodwa kwaye awavumele ukuba asetyenziswe kwizinto eziguquguqukayo zendawo. Ukuqonda amaza e-sine kunokusinceda ukuba siqonde ngcono ukusasazwa kwamaza, ukusetyenzwa komqondiso, kunye nohlalutyo lothotho lwexesha.
NdinguJoost Nusselder, umseki weNeaera kunye nomthengisi womxholo, utata, kwaye ndiyakuthanda ukuzama izixhobo ezitsha ngesiginkci entliziyweni yothando lwam, kunye neqela lam, ndisenza amanqaku eblogi anzulu ukusukela ngo-2020. ukunceda abafundi abathembekileyo ngokurekhoda kunye neengcebiso zesiginci.
