I-sine wave iwukuguquguquka kwamagagasi okuphindaphinda njalo ama-radian angu-2π, noma ama-degree angu-360, futhi ingasetshenziswa ukumodela izenzakalo zemvelo eziningi. I-sine wave yaziwa nangokuthi i-sinusoid.
Igama elithi sine wave lisuselwa kumsebenzi wezibalo we-sine, okuyisisekelo se-waveform. I-sine wave ingelinye lamagagasi alula futhi asetshenziswa kakhulu emikhakheni eminingi.
Kulesi sihloko, ngizochaza ukuthi yini i-sine wave nokuthi kungani inamandla kangaka.
Yini i-sine wave?
I-sine Wave iyi-oscillation ebushelelezi, ephindaphindayo ngendlela yamagagasi aqhubekayo. Kuyijika lezibalo elichazwa ngokomsebenzi we-sine trigonometric, futhi limelelwa ngesithombe njenge-waveform. Iwuhlobo lwegagasi eliqhubekayo elibonakala ngomsebenzi oshelelayo, wezikhathi ezithile, futhi litholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucutshungulwa kwesignali.
The imvamisa of a sine wave inani lokuzungeza noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe. Imvamisa ye-angular, echazwa ngu-ω, izinga loshintsho lwe-agumenti yomsebenzi, futhi ikalwa ngamayunithi ama-radians ngomzuzwana. Inani elingelona uziro lokushintsha kwesigaba, okuboniswa ngu-φ, limelela ukushintshwa kwayo yonke ifomethi yegagasi ngesikhathi, ngevelu engafanele emelela ukubambezeleka, kanye nenani eliphozithivu elimelela kusengaphambili ngemizuzwana. Imvamisa yegagasi elinesine likalwa nge-hertz (Hz).
I-sine wave isetshenziselwa ukuchaza igagasi lomsindo, futhi ichazwa umsebenzi we-sine, f(t) = Isono (ωt + φ). Iphinde isetshenziselwe ukuchaza uhlelo lwe-spring-mass olungavinjelwe ekulinganeni, futhi iwuhlobo lwamagagasi olubalulekile kufiziksi njengoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungalawuleki. Lesi sakhiwo saziwa ngokuthi isimiso se-superposition, futhi siyindawo ye-waveform ngezikhathi ezithile. Lesi sakhiwo siholela ekubalulekeni kokuhlaziywa kwe-Fourier, njengoba kwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo ukuguquguquka kwendawo, x, okumelela indawo endaweni eyodwa lapho igagasi lisakazeka khona.
Ipharamitha yesici yegagasi ibizwa ngokuthi inombolo yegagasi, k, okuyinombolo yegagasi eliyi-angular futhi imele ukulingana phakathi kwemvamisa ye-angular, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza ihlobene ne-angular frequency kanye nobude begagasi, λ, ngesibalo λ = 2π/k. Isibalo segagasi lesine kubukhulu obubodwa sinikezwa ngu-y = A isono (ωt + φ). I-equation evamile kakhudlwana inikezwa ngu-y = Isono (kx – ωt + φ), esinikeza ukususwa kwegagasi endaweni x ngesikhathi t.
Amagagasi e-Sine angaphinde amelwe ngezilinganiso eziningi zendawo. I-equation yegagasi lendiza ehambayo inikezwa ngu-y = A isono (kx – ωt + φ). Lokhu kungahunyushwa njengomkhiqizo wamachashazi wama-vector amabili, futhi kusetshenziselwa ukuchaza amagagasi ayinkimbinkimbi, njengegagasi lamanzi echibini lapho itshe liwa. Izibalo eziyinkimbinkimbi kakhulu ziyadingeka ukuze kuchazwe igama elithi sinusoid, elichaza izici zamagagasi womabili amagagasi e-sine ne-cosine anokushintsha kwesigaba sama-radians angu-π/2, okunikeza igagasi le-cosine isiqalo sekhanda phezu kwegagasi le-sine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine ne-cosine ane-offset yesigaba.
Amagagasi e-sine atholakala emvelweni, kuhlanganise namagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu iyakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amagagasi e-sine asetshenziselwa ukumelela imvamisa eyodwa nama-harmonics. Indlebe yomuntu ibona umsindo njengenhlanganisela yamaza e-sine anama-amplitude ahlukene namaza, futhi ukuba khona kwama-harmonics aphakeme ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elinefrikhwensi efanayo edlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Umsindo wokushaya izandla uqukethe amagagasi e-aperiodic, angaphindi ngokwemvelo, futhi angalandeli iphethini ye-sine wave. Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ukuchaza futhi ukulinganisa noma yikuphi ukuma kwamagagasi ngezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa, futhi kuvame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi. Amagagasi e-Sine asetshenziselwa ukusabalalisa kanye nokuguqula ifomu kumasistimu we-linear asabalalisiwe.
Uyini umlando wamagagasi e-sine?
I-sine wave inomlando omude futhi othokozisayo. Kwaqala ukutholwa isazi sezibalo esingumFulentshi uJoseph Fourier ngo-1822, esabonisa ukuthi noma isiphi isimo samagagasi ngezikhathi ezithile singamelelwa njengesamba samaza anesine. Lokhu kutholakala kwashintsha umkhakha wezibalo ne-physics futhi sekusetshenziswe kusukela ngaleso sikhathi.
• Umsebenzi kaFourier wathuthukiswa futhi isazi sezibalo saseJalimane u-Carl Friedrich Gauss ngo-1833, owabonisa ukuthi amagagasi e-sine angasetshenziswa ukumela noma yiluphi uhlobo lwamagagasi ezikhathi ezithile.
• Ekupheleni kwekhulu le-19, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamasekhethi kagesi.
• Ekuqaleni kwekhulu lama-20, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamagagasi omsindo.
• Ngawo-1950, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamaza okukhanya.
• Ngawo-1960, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamaza omsakazo.
• Ngawo-1970, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamasignali edijithali.
• Ngawo-1980, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwamagagasi kagesi.
• Ngawo-1990, i-sine wave yasetshenziswa ukuchaza ukuziphatha kwezinhlelo ze-quantum mechanical.
• Namuhla, i-sine wave isetshenziswa emikhakheni eyahlukene, okuhlanganisa izibalo, physics, engineering, signal processing, nokunye. Kuyithuluzi elibalulekile lokuqonda ukuziphatha kwamagagasi futhi lisetshenziswa ezinhlelweni ezihlukahlukene, kusukela ekucutshungulweni komsindo nevidiyo kuya ekucabangeni kwezokwelapha kanye namarobhothi.
Sine Wave Mathematics
Ngizobe ngikhuluma ngamagagasi e-sine, ijika lezibalo elichaza i-oscillation ebushelelezi, ephindaphindayo. Sizobheka ukuthi amagagasi e-sine achazwa kanjani, ubudlelwano phakathi kwe-angular frequency nenombolo yegagasi, nokuthi kuyini ukuhlaziywa kwe-Fourier. Sizophinde sihlole ukuthi amagagasi e-sine asetshenziswa kanjani ku-physics, ubunjiniyela, nokucubungula amasignali.
Yini iSine Wave?
I-sine wave iyi-oscillation eshelelayo, ephindaphindayo eyenza igagasi eliqhubekayo. Kuyijika lezibalo, elichazwa umsebenzi we-sine we-trigonometric, futhi livame ukubonakala kumagrafu nama-waveforms. Iwuhlobo lwamagagasi aqhubekayo, okusho ukuthi kuwumsebenzi oshelelayo, wezikhathi ezithile owenzeka ezinkambini zezibalo, zefiziksi, ezobunjiniyela, nezisetshenziswa zesignali.
Igagasi le-sine linefrikhwensi evamile, okuyinombolo yokuzungeza noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe. Lokhu kuvezwa i-angular frequency, ω, elingana no-2πf, lapho u-f eyimvamisa ku-hertz (Hz). I-sine wave nayo ingashintshwa ngokuhamba kwesikhathi, ngevelu elinegethivu elimelela ukubambezeleka kanye nenani eliphozithivu elimelela kusengaphambili ngamasekhondi.
Igagasi elinesine livame ukusetshenziselwa ukuchaza igagasi lomsindo, njengoba lichazwa umsebenzi we-sine. Iphinde isetshenziselwe ukumela isistimu ye-spring mass mass ekulinganeni. I-sine wave iwumqondo obalulekile kufiziksi, njengoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungalawuleki. Le ndawo, eyaziwa ngokuthi isimiso se-superposition, yiyona eholela ekubalulekeni kokuhlaziywa kwe-Fourier, njengoba kwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo phakathi kokuguquguquka kwendawo.
I-equation ye-sine wave endaweni eyodwa inikezwa ngu-y = A isono (ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wushintsho lwesigaba. Ukuze uthole isibonelo somugqa owodwa, uma inani legagasi libhekwa njengocingo, khona-ke isibalo segagasi elinezingqimba ezimbili zobukhulu bendawo sinikezwa y = A isono (kx – ωt + φ), lapho u-k eyigagasi. inombolo. Lokhu kungahunyushwa njengomkhiqizo wama-vector amabili, umkhiqizo wamachashazi.
Amagagasi ayinkimbinkimbi, njengalawo adaleka lapho itshe liwisa echibini, adinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici zakho zombili igagasi le-sine kanye negagasi le-cosine. Ukushintsha kwesigaba sama-radians angu-π/2, noma isiqalo sekhanda, kuthiwa kunikeza igagasi le-cosine, elihola igagasi le-sine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Ukubonisa igagasi le-cosine kungasiza ekuboniseni ubudlelwano obuyisisekelo phakathi kombuthano kanye nemodeli yendiza eyinkimbinkimbi ye-3D, okungasiza ekuboneni ngeso lengqondo ukuba wusizo kwamagagasi e-sine ekuhumusheni phakathi kwezizinda. Le phethini yamagagasi yenzeka emvelweni, okuhlanganisa namagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu iyakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi izethulo zamagagasi e-sine ze-harmonics yefrikhwensi eyodwa nazo ziyabonakala.
Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo yilokho okubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Indlebe yomuntu izwa umsindo njenge-periodic kanye ne-aperiodic. Umsindo wezikhathi ezithile wakhiwe ngamagagasi e-sine, kuyilapho umsindo we-aperiodic uzwakala njengonomsindo. Umsindo ubonakala njenge-aperiodic, njengoba unephethini engaphindi.
Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ukuchaza futhi ukulinganisa noma yikuphi ukuma kwamagagasi ngezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa nokucutshungulwa kwesignali, nokuhlaziywa kwezibalo zochungechunge lwesikhathi. Amagagasi e-Sine angaphinde asakaze ngokushintsha amafomu kumasistimu alayini asabalalisiwe.
Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi anobude nobuningi obufanayo. Lapho la maza edlula phezulu, kwakheka iphethini yegagasi elimile, njengoba kubonakala lapho kuhlwithwa inothi entanjeni. Amagagasi aphazamisayo abonakala ezindaweni ezigxilile zeyunithi yezinhlamvu adala amaza amile, avela kumafrikhwensi athile aziwa ngokuthi amafrikhwensi anomsindo. Lezi zakhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
Ichazwa Kanjani I-Sine Wave?
I-sine wave iwukuzulazula okubushelelezi, okuphindaphindayo kokwakheka kwamagagasi okuqhubekayo. Ichazwa ngokwezibalo njengomsebenzi we-trigonometric, futhi igrafu njenge-sinusoid. I-sine wave iwumqondo obalulekile kufiziksi, njengoba igcina isimo sayo samagagasi lapho ingezwe kwamanye amagagasi e-sine wefrikhwensi efanayo kanye nobukhulu besigaba obungahleliwe. Lesi sakhiwo saziwa ngokuthi isimiso se-superposition, futhi siholela ekubalulekeni kwaso ekuhlaziyeni kukaFourier.
Amagagasi e-sine atholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucubungula amasignali. Zibonakala ngokuvama kwazo, inani lama-oscillation noma imijikelezo eyenzeka ngesikhathi esinikeziwe. Imvamisa ye-angular, ω, izinga loshintsho lwe-agumenti yomsebenzi kuma-radians ngomzuzwana. Inani elingelona uziro lika-φ, ukushintshwa kwesigaba, limelela ukushintshwa kwayo yonke ifomethi yegagasi ngesikhathi, ngevelu engafanele emelela ukubambezeleka, kanye nenani eliphozithivu elimelela kusengaphambili ngemizuzwana.
Ngomsindo, igagasi le-sine lichazwa yi-equation f = ω/2π, lapho u-f eyimvamisa yama-oscillations, futhi ω i-angular frequency. Lesi sibalo sisebenza futhi kusistimu ye-spring mass engavinjelwe ekulinganisweni. Amagagasi e-Sine nawo abalulekile kuma-acoustics, njengoba kuwukuphela kwendlela yamagagasi ebonwa njengemvamisa eyodwa yindlebe yomuntu. Igagasi elilodwa le-sine lakhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu, wonke abonwa njengenothi elifanayo.
Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo yilokho okubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza ukuthi inothi elifanayo lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile. Ukushaya izandla, isibonelo, kuqukethe amagagasi e-aperiodic, angaphindaphindi, ngaphezu kwamagagasi e-sine.
Ekuqaleni kwekhulu le-19, isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal angasetshenziswa njengezakhiwo ezilula ukuchaza noma ukulinganisa noma yikuphi ukuma kwamagagasi ngezikhathi ezithile, kuhlanganise namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elinamandla lokuhlaziya elisetshenziselwa ukutadisha amaza ekugelezeni kokushisa nokucubungula isignali, kanye nokuhlaziywa kwezibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala kunoma iyiphi indlela emkhathini, futhi amelelwa amagagasi ane-amplitude, imvamisa, futhi ehamba ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lesi yisimo esifanayo esenzeka lapho inothi lihlwithwa entanjeni, amagagasi aphazamisayo aboniswa ekugcineni kweyunithi yezinhlamvu. Amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi ama-resonant frequencies, akhiwa imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nempande eyisikwele yesisindo sayo ngobude beyunithi.
Kafushane, igama elithi sinusoid lisetshenziselwa ukuchaza izici zamagagasi womabili amagagasi e-sine ne-cosine, ngokugudluka kwesigaba sama-radians angu-π/2, okusho ukuthi igagasi le-cosine linesiqalo futhi igagasi le-sine lisalela ngemuva. Igama elithi sinusoidal lisetshenziswa ngokuhlanganyela ukubhekisela kuwo womabili amagagasi e-sine ne-cosine ane-offset yesigaba. Lokhu kuboniswa yigagasi le-cosine emfanekisweni ongenhla. Lobu budlelwano obuyisisekelo phakathi kwe-sine ne-cosine bungabonwa kusetshenziswa imodeli yendiza eyinkimbinkimbi ye-3D, ebonisa ngokuqhubekayo ukubaluleka kokuhunyushwa kwale miqondo kuzo zonke izizinda ezihlukene. Iphethini yegagasi yenzeka emvelweni, okuhlanganisa nomoya, umsindo, namaza okukhanya.
Buyini Ubudlelwano Phakathi Kwe-Angular Frequency kanye Nenombolo Yegagasi?
I-sine wave iyijika lezibalo elichaza ukuzungeza okubushelelezi, okuphindaphindayo. Igagasi eliqhubekayo, elaziwa nangokuthi igagasi le-sinusoidal noma i-sinusoid, futhi lichazwa ngokomsebenzi we-sine we-trigonometric. Igrafu ye-sine wave ibonisa i-waveform ezungezayo phakathi kwenani eliphakeme nelincane.
I-angular frequency, ω, izinga loshintsho lwe-agumenti yokusebenza, ikalwa ngama-radians ngomzuzwana. Inani elingelona uziro lika-φ, ukushintshwa kwesigaba, limelela ukushintshwa kwayo yonke ifomethi yegagasi ukuya phambili noma emuva ngesikhathi. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi. I-frequency, f, inombolo yokuzulazula noma imijikelezo eyenzeka ngomzuzwana owodwa, ikalwa nge-hertz (Hz).
I-sine wave ibalulekile kufiziksi ngoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lefrikhwensi efanayo nesigaba nobukhulu obungahleliwe. Lesi sici samagagasi ezikhathi ezithile saziwa ngokuthi umgomo we-superposition futhi yikho okuholela ekubalulekeni kokuhlaziywa kwe-Fourier. Lokhu kuyenza ihluke ngokuzwakalayo futhi yingakho isetshenziswa ku-variable yendawo x, emele indawo kuhlangothi olulodwa. Igagasi lisakazeka ngepharamitha yesici, k, ebizwa ngokuthi inombolo yegagasi noma inombolo ye-angular wave, emele ukulingana phakathi kwe-angular frequency, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza, k, ihlobene ne-angular frequency, ω, kanye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave endaweni eyodwa inikezwa ngu-y = A isono (ωt + φ). Lesi sibalo sinikeza ukususwa kwegagasi kunoma iyiphi indawo x nganoma yisiphi isikhathi t. Kucatshangelwa isibonelo somugqa owodwa, lapho inani legagasi linikezwa y = A isono (ωt + φ).
Ngobukhulu bendawo obubili noma ngaphezulu, isibalo sichaza igagasi lendiza ehambayo. Isikhundla x sinikezwa ngu x = A isono (kx – ωt + φ). Lesi sibalo singahunyushwa ngokuthi ama-vector amabili, umkhiqizo wawo ongumkhiqizo wamachashazi.
Amagagasi ayinkimbinkimbi, njengalawo adaleka lapho itshe lijikijelwa echibini lamanzi, adinga izibalo eziyinkimbinkimbi kakhulu ukuwachaza. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici zakho zombili igagasi le-sine kanye negagasi le-cosine. Ukushintsha kwesigaba sika-π/2 radians (noma 90°) kunikeza igagasi le-cosine isiqalo sekhanda, ngakho kuthiwa lihola igagasi le-sine. Lokhu kuholela ebudlelwaneni obuyisisekelo phakathi kwemisebenzi ye-sine ne-cosine, engabonwa njengendingiliza kumodeli yendiza eyinkimbinkimbi ye-3D.
Ukuba wusizo kokuhunyushwa kwalo mqondo kwezinye izizinda kuboniswa yiqiniso lokuthi iphethini yamagagasi efanayo yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu iyakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile. Amagagasi e-sine ayizethulo zefrikhwensi eyodwa kanye nama-harmonics, futhi indlebe yomuntu iyakwazi ukuzwakalisa amagagasi e-sine ngama-harmonics azwakalayo. Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Umsindo wokushaya izandla uqukethe amagagasi e-aperiodic, angewona wezikhathi ezithile, noma anephethini engaphindi. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ezingasetshenziswa ukuchaza kanye nokulinganisa noma iluphi uhlobo lwamagagasi ezikhathi ezithile, kuhlanganise namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa, futhi kuvame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngendlela eshintshayo ngokusebenzisa amasistimu alayini asabalalisiwe. Lokhu kuyadingeka ukuze kuhlaziywe ukusabalala kwegagasi ngezilinganiso ezimbili noma ngaphezulu. Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi anobude nobuningi obufanayo. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kufana nalokho okwenzekayo lapho kunothi lihlwithwa entanjeni; amaza aphazamisayo avela ezindaweni ezimisiwe zentambo, futhi amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi akhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi anomsindo weyunithi yezinhlamvu alingana nobude bawo futhi ahambisana ngokuphambene nempande eyisikwele yesisindo sayo ngobude beyunithi.
Iyini i-Fourier Analysis?
I-sine wave iwukuzungeza okubushelelezi, okuphindaphindayo okuchazwa ngokwezibalo njengegagasi eliqhubekayo. Yaziwa nangokuthi igagasi le-sinusoidal, futhi ichazwa umsebenzi we-sine we-trigonometric. Igrafu ye-sine wave iyijika elibushelelezi, lezikhathi ezithile elisetshenziswa kwizibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali.
Imvamisa evamile, noma inombolo yokuguquguquka noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe, imelelwa uhlamvu lwesiGreki ω (omega). Lokhu kwaziwa njenge-angular frequency, futhi izinga lapho i-agumenti yomsebenzi eshintsha khona kumayunithi ama-radians.
Igagasi elinesine lingashintshwa ngesikhathi ngokushintsha kwesigaba, esimelelwa uhlamvu lwesiGreki u-φ (phi). Inani elinegethivu limelela ukubambezeleka, futhi inani eliphozithivu limelela kusengaphambili ngamasekhondi. Imvamisa yegagasi elinesine likalwa nge-hertz (Hz).
I-sine wave ivame ukusetshenziselwa ukuchaza amagagasi omsindo, futhi ichazwa umsebenzi we-sine f(t) = Isono (ωt + φ). Ama-oscillations alolu hlobo abonakala kusistimu ye-spring mass mass ngokulingana.
I-sine wave ibalulekile kufiziksi ngoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungahleliwe. Lesi sakhiwo, esibizwa ngokuthi isimiso se-superposition, yisona esiholela ekubalulekeni kwayo ekuhlaziyeni kukaFourier. Lokhu kuyenza ihluke ngokuzwakalayo futhi yingakho isetshenziselwa ukuchaza okuguquguqukayo kwendawo.
Isibonelo, uma u-x emele ubukhulu bendawo yegagasi elisakazekayo, khona-ke ipharamitha yesici k (inombolo yegagasi) imelela ukulingana phakathi kwe-angular frequency ω kanye nesivinini somugqa sokusakazeka ν. Inombolo yegagasi k ihlobene nemvamisa ye-angular ω kanye ne-wavelength λ (lambda) nge-equation k = 2π/λ. I-frequency f kanye nesivinini somugqa v zihlobene ne-equation v = fλ.
Isibalo segagasi lesine endaweni eyodwa ithi y = Isono (ωt + φ). Lesi sibalo singenziwa ngokujwayelekile kubukhulu obuningi, futhi ngesibonelo somugqa owodwa, inani legagasi kunoma iyiphi indawo x nganoma yisiphi isikhathi u-t unikezwa y = A isono (kx – ωt + φ).
Amagagasi ayinkimbinkimbi, njengalawo abonakala lapho itshe lijikijelwa echibini, adinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinalezi zici, futhi lihlanganisa amagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Ukubonisa igagasi le-cosine, ubudlelwano obuyisisekelo phakathi kwegagasi le-sine negagasi le-cosine bufana nobudlelwano phakathi kombuthano kanye nemodeli yendiza eyinkimbinkimbi ye-3D. Lokhu kuyasiza ekuboneni ngeso lengqondo ukubaluleka kokuhunyushwa kwamagagasi e-sine phakathi kwezizinda ezihlukene.
Iphethini yamagagasi yenzeka emvelweni, okuhlanganisa amagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziselwa ukumelela imvamisa eyodwa kanye nama-harmonics.
Indlebe yomuntu izwa umsindo onenhlanganisela yamaza e-sine nomsindo wezikhathi ezithile, futhi ukuba khona kwama-harmonic aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Ukushaya izandla, nokho, kuqukethe amagagasi e-aperiodic, angaphindaphindi. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ezingasetshenziswa ukuchaza kanye nokulinganisa noma iluphi uhlobo lwamagagasi ezikhathi ezithile, kuhlanganise namagagasi ayisikwele.
Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa nokucutshungulwa kwesignali, nokuhlaziywa kwezibalo zochungechunge lwesikhathi. Amagagasi e-Sine angasabalala ngaphandle kokushintsha indlela yawo ezinhlelweni ezisabalalisiwe zomugqa, yingakho edingeka ukuze kuhlaziywe ukusabalala kwamagagasi.
Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi anobude nobuningi obufanayo. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kubonakala lapho inothi lihlwithwa entanjeni, futhi amagagasi aphazamisayo abonakala ekugcineni kwentambo. Amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi akhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
I-Sine ne-Cosine Waves
Kulesi sigaba, ngizobe ngixoxa ngomehluko phakathi kwamagagasi e-sine nawe-cosine, ukuthi kuyini ukushintsha kwesigaba, nokuthi igagasi le-sine lihluke kanjani kumagagasi e-cosine. Ngizophinde ngihlole ukubaluleka kwamagagasi e-sine kuzibalo, i-physics, ubunjiniyela, nokucubungula amasignali.
Uyini Umehluko Phakathi Kwe-Sine kanye ne-Cosine Waves?
Amagagasi e-sine ne-cosine ayimisebenzi yezikhathi ezithile, eshelelayo, futhi eqhubekayo esetshenziselwa ukuchaza izinto eziningi zemvelo, njengamaza omsindo namaza okukhanya. Zibuye zisetshenziswe kwezobunjiniyela, ukucubungula amasignali, kanye nezibalo.
Umehluko omkhulu phakathi kwamagagasi e-sine nawe-cosine ukuthi igagasi le-sine liqala ku-zero, kuyilapho igagasi le-cosine liqala ekushintsheni kwesigaba sama-radians angu-π/2. Lokhu kusho ukuthi igagasi le-cosine linesiqalo sekhanda uma liqhathaniswa negagasi le-sine.
Amagagasi e-Sine abalulekile ku-physics ngoba agcina ukuma kwawo kwamagagasi lapho ehlanganiswa ndawonye. Lesi sakhiwo, esaziwa ngokuthi isimiso se-superposition, yiso esenza ukuhlaziya kukaFourier kube usizo kakhulu. Futhi yenza amagagasi e-sine ahluke ngokwe-acoustically, njengoba angasetshenziswa ukumela imvamisa eyodwa.
Amagagasi e-cosine nawo abalulekile ku-physics, njengoba asetshenziselwa ukuchaza ukunyakaza kwenqwaba emthonjeni ngokulingana. I-equation ye-sine wave ithi f = i-oscillations/isikhathi, lapho u-f eyimvamisa yegagasi futhi u-ω i-angular frequency. Lesi sibalo sinikeza ukususwa kwegagasi kunoma iyiphi indawo x nesikhathi t.
Ngobukhulu obubili noma ngaphezulu, igagasi le-sine lingachazwa ngegagasi lendiza ehambayo. Inombolo yegagasi k iyipharamitha yesici yegagasi, futhi ihlobene nemvamisa ye-angular ω kanye nobude begagasi λ. Isibalo segagasi le-sine ngobukhulu obubili noma ngaphezulu sinikeza ukususwa kwegagasi kunoma iyiphi indawo x nesikhathi t.
Amagagasi ayinkimbinkimbi, njengalawo adalwe yitshe eliwele echibini, adinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici ezifana negagasi le-sine noma igagasi le-cosine, njengokushintshwa kwesigaba. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kumagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Amagagasi e-sine atholakala emvelweni, kuhlanganise namagagasi omoya, amagagasi omsindo, namaza okukhanya. Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi ingabona ubukhona bama-harmonic aphezulu ngaphezu kwemvamisa eyisisekelo. Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo.
Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ezingasetshenziswa ukuchaza kanye nokulinganisa noma yikuphi ukuma kwamagagasi ezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziya i-Fourier iyithuluzi elinamandla elisetshenziselwa ukutadisha amagagasi, njengokugeleza kokushisa nokucubungula isignali. Ibuye isetshenziswe ekuhlaziyweni kwezibalo kanye nochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala kunoma iyiphi indlela emkhathini, futhi amelelwa amagagasi ane-amplitude nemvamisa ahamba ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kwenzeka lapho inothi lihlwithwa entanjeni, njengoba amagagasi ebonakala ezindaweni zokugcina ezingashintshi zentambo. Amagagasi amile avela kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nesisindo sayo ngobude beyunithi.
Iyini i-Phase Shift?
I-sine wave iwukuzungeza okubushelelezi, okuphindaphindayo okuqhubekayo kukho kokubili isikhathi nendawo. Kuyijika lezibalo elichazwa umsebenzi we-sine we-trigonometric futhi livame ukusetshenziselwa ukumela amaza omsindo, amaza okukhanya, nezinye izinhlobo zamagagasi ezinkambini zezibalo, zefiziksi, zobunjiniyela, neziqondiso zesignali. Ifrikhwensi evamile (f) ye-sine wave iyinani lokuzungeza noma imijikelezo eyenzeka ngomzuzwana owodwa, futhi ikalwa nge-hertz (Hz).
Imvamisa ye-angular (ω) izinga loshintsho lwe-agumenti yokusebenza kuma-radians ngomzuzwana, futhi ihlobene nefrikhwensi evamile ngesibalo ω = 2πf. Inani eliyinegethivu elithi φ limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi.
Amagagasi e-Sine avame ukusetshenziselwa ukuchaza amagagasi omsindo, njengoba ekwazi ukugcina ukuma kwawo kwamagagasi lapho ehlanganiswa ndawonye. Lesi sakhiwo siholela ekubalulekeni kokuhlaziywa kwe-Fourier, okwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo ukuguquguquka kwesikhala okuhlukene. Isibonelo, i-variable x imele indawo enobukhulu obubodwa, futhi igagasi lisakazeka ohlangothini lwepharamitha yesici k, ebizwa ngokuthi inombolo yegagasi. Inombolo yegagasi eliyi-angular imele ukulingana phakathi kwe-angular frequency (ω) kanye nesivinini somugqa sokusakazeka (ν). Inombolo yamaza ihlobene ne-angular frequency kanye ne-wavelength (λ) nge-equation λ = 2π/k.
I-equation ye-sine wave endaweni eyodwa inikezwa ngu-y = A isono (ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wushintsho lwesigaba. Lesi sibalo singenziwa jikelele ukuze sinikeze ukugudluzwa kwegagasi kunoma yisiphi isikhundla x nganoma yisiphi isikhathi t emgqeni owodwa, isibonelo, y = Isono (kx – ωt + φ). Uma kucutshungulwa igagasi ngobukhulu bendawo obubili noma ngaphezulu, kudingeka izibalo eziyinkimbinkimbi.
Igama elithi sinusoid livame ukusetshenziselwa ukuchaza igagasi elinezici ezifana negagasi le-sine. Lokhu kufaka phakathi amagagasi e-cosine, anokushintsha kwesigaba sama-radians angu-π/2, okusho ukuthi anesiqalo sekhanda uma kuqhathaniswa namagagasi e-sine. Igama elithi sinusoidal livame ukusetshenziswa ngokuhlanganyela ukuze libhekisele kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Ukubonisa igagasi le-cosine, ubudlelwano obuyisisekelo phakathi kwegagasi le-sine negagasi le-cosine bungabonakala ngendingiliza kumodeli yendiza eyinkimbinkimbi ye-3D. Lokhu kuwusizo ekuhumusheni phakathi kwezizinda, njengoba iphethini yamagagasi efanayo yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namagagasi okukhanya. Indlebe yomuntu iyakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziswa njengezethulo zamathoni efrikhwensi eyodwa.
Ama-harmonics nawo abalulekile emsindweni, njengoba indlebe yomuntu izwa umsindo njengengxube yamaza e-sine nama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwezimbangela eziyisisekelo ukuhlukahluka kwe-timbre yomsindo. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale lihlukile. Kodwa-ke, umsindo okhiqizwa ukushaya izandla uqukethe amagagasi e-aperiodic, okusho ukuthi awakhiwa amaza e-sine.
Amagagasi omsindo ezikhathi ezithile angalinganiswa kusetshenziswa izingqimba ezilula zokwakha zamagagasi e-sinusoidal, njengoba kutholwe isazi sezibalo saseFrance uJoseph Fourier. Lokhu kuhlanganisa amagagasi ayisikwele, akhiwe imvamisa eyisisekelo nama-harmonics aphezulu. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa nokucutshungulwa kwesignali, nokuhlaziywa kwezibalo zochungechunge lwesikhathi.
Amagagasi e-Sine ayakwazi ukusabalala ngaphandle kokushintsha ifomu ezinhlelweni ezisabalalisiwe zomugqa, futhi ngokuvamile ayadingeka ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-sine angahamba ngezindlela ezimbili emkhathini, futhi amelelwa amagagasi ane-amplitude kanye nemvamisa. Lapho amagagasi amabili ahamba ebheke ezinhlangothini ezihlukene edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kufana nalapho kunothi lihlwithwa entanjeni, njengoba amagagasi aphazamisayo ebonakala ekugcineni kwentambo. Amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi akhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu, futhi alinganise ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
I-Sine Wave ihluke kanjani ku-Cosine Wave?
Igagasi elinesine liwukuguquguquka kwegagasi okuzungezayo ngendlela ebushelelezi, ephindaphindayo. Kungumsebenzi we-trigonometric ofakwe igrafu endizeni enezinhlangothi ezimbili, futhi iwuhlelo lwamagagasi oluyisisekelo kuzibalo, i-physics, ubunjiniyela, kanye nokucubungula amasignali. Ibonakala ngokuvama kwayo, noma inombolo yokuzungeza okwenzeka ngesikhathi esinikeziwe, kanye nemvamisa yayo ye-angular, okuyizinga loshintsho lwempikiswano yomsebenzi ngama-radians ngomzuzwana. I-sine wave ingashintshwa ngokuhamba kwesikhathi, ngevelu elinegethivu elimelela ukubambezeleka kanye nenani eliphozithivu elimelela kusengaphambili ngamasekhondi.
Amagagasi e-Sine avame ukusetshenziselwa ukuchaza amagagasi omsindo, futhi avame ukubizwa ngokuthi ama-sinusoids. Abalulekile ku-physics ngoba agcina ukuma kwawo kwegagasi lapho ehlanganiswa ndawonye, futhi ayisisekelo sokuhlaziywa kwe-Fourier, okuwenza ahluke ngokuzwakalayo. Ziphinde zisetshenziselwe ukuchaza okuguquguqukayo kwendawo, nenombolo yegagasi emele ukulingana phakathi kwemvamisa ye-angular kanye nesivinini somugqa sokusakazeka.
I-sine wave nayo isetshenziselwa ukuchaza igagasi elinohlangothi olulodwa, njengocingo. Uma ijayelekile ibe yizinhlangothi ezimbili, isibalo sichaza igagasi lendiza ehambayo. Inombolo yegagasi ihunyushwa ngokuthi i-vector, futhi umkhiqizo wamachashazi wamagagasi amabili uyigagasi eliyinkimbinkimbi.
Amagagasi e-Sine nawo asetshenziselwa ukuchaza ukuphakama kwegagasi lamanzi echibini lapho itshe liwa. Izibalo eziyinkimbinkimbi kakhulu ziyadingeka ukuchaza igama elithi sinusoid, elichaza izici zamagagasi, okuhlanganisa amagagasi e-sine kanye ne-cosine anokushintsha kwesigaba. Igagasi elinesine libambezela igagasi le-cosine ngamaradian angu-π/2, noma isiqalo sekhanda, ngakho umsebenzi we-cosine uhola umsebenzi we-sine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kumagagasi e-sine ne-cosine ane-offset yesigaba.
Ukufanekisa i-cosine wave ubuhlobo obuyisisekelo kumbuthano kumodeli yendiza eyinkimbinkimbi ye-3D, esiza ukubona ngeso lengqondo ukusebenza kwayo ezizindeni zokuhumusha. Le phethini yamagagasi yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ikwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, kanye nokumelwa kwamagagasi e-sine wamafrikhwensi awodwa kanye nokuvumelana kwawo. Indlebe yomuntu izwa umsindo njengegagasi le-sine elinomsindo wezikhathi ezithile, kanye nokuba khona kwama-harmonic aphezulu ngaphezu kwezimbangela eziyinhloko zokuhlukahluka kwe-timbre.
Lesi yisizathu esenza inothi lomculo lemvamisa ethile edlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile. Umsindo wokushaya izandla, isibonelo, uqukethe amagagasi e-aperiodic, angaphindaphindi, kunamagagasi e-sine ngezikhathi ezithile. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ukuchaza kanye nokulinganisa i-waveform yezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziya i-Fourier iyithuluzi elinamandla lokufunda amaza, njengokugeleza kokushisa nokucubungula isignali, kanye nokuhlaziywa kwezibalo zochungechunge lwesikhathi. Amagagasi e-Sine angaphinde asakaze ngokushintsha amafomu ngokusebenzisa amasistimu alayini asabalalisiwe, okudingekayo ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi ane-amplitude efanayo nemvamisa, futhi lapho ebekwe phezulu, kwakhiwa iphethini yegagasi elimile. Lokhu kubonakala lapho inothi lihlwithwa entanjeni, njengoba amagagasi aphazamisayo eboniswa amaphoyinti angashintshi eyunithi yezinhlamvu. Amaza amile ayenzeka kumaza athile, abizwa ngokuthi amaza azwakalayo, futhi akhiwe imvamisa eyisisekelo nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
Izwakala Kanjani I-Sine Wave?
Ngiqinisekile ukuthi uke wezwa ngamagagasi e-sine ngaphambili, kodwa uyazi ukuthi azwakala anjani? Kulesi sigaba, sizohlola ukuthi amagagasi e-sine awuthinta kanjani umsindo womculo, nokuthi asebenzisana kanjani nama-harmonics ukuze akhe izinsimbi ezihlukile. Sizophinde sixoxe ngokuthi amagagasi e-sine asetshenziswa kanjani ekucubunguleni isignali nokusakazwa kwamagagasi. Ekupheleni kwalesi sigaba, uzoba nokuqonda kangcono kwamagagasi e-sine nokuthi awuthinta kanjani umsindo.
Izwakala Kanjani I-Sine Wave?
I-sine wave iyi-oscillation eqhubekayo, ebushelelezi, ephindaphindayo etholakala ezintweni eziningi zemvelo, okuhlanganisa amaza omsindo, amaza okukhanya, ngisho nokunyakaza kwenqwaba esiphethwini. Kuyijika lezibalo elichazwa umsebenzi we-sine we-trigonometric, futhi ngokuvamile igrafu njenge-waveform.
Izwakala kanjani i-sine wave? Igagasi elinesine liyigagasi eliqhubekayo, okusho ukuthi alinawo amaza kufomu lamagagasi. Kungumsebenzi oshelelayo, wezikhathi ezithile onefrikhwensi, noma inombolo yama-oscillation okwenzeka ngesikhathi esinikeziwe. Ukuvama kwayo kwe-angular, noma izinga lokushintsha kwe-agumenti yomsebenzi kumarediya ngomzuzwana, limelelwa uphawu ω. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi.
Imvamisa yegagasi le-sine ikalwa nge-hertz (Hz), futhi iyinani lama-oscillation ngomzuzwana. I-sine wave iyigagasi lomsindo elichazwa umsebenzi we-sine, u-f(t) = Isono (ωt + φ), lapho u-A eyi-amplitude, u-ω imvamisa ye-angular, futhi u-φ wushintsho lwesigaba. Ukushintsha kwesigaba kwama-radians angu-π/2 kunikeza igagasi isiqalo, ngakho ngokuvamile kubizwa ngokuthi umsebenzi we-cosine.
Igama elithi "sinusoid" lisetshenziselwa ukuchaza izici zamagagasi zegagasi le-sine, kanye negagasi le-cosine eline-offset yesigaba. Lokhu kuboniswa igagasi le-cosine, elisala ngemuva kwegagasi le-sine ngokushintsha kwesigaba esingu-π/2 radians. Lobu budlelwano obuyisisekelo phakathi kwamagagasi e-sine ne-cosine bumelwe yindilinga kumodeli yendiza eyinkimbinkimbi ye-3D, esiza ukubona ngeso lengqondo ukuba wusizo kokuhumusha phakathi kwezizinda.
Iphethini yegagasi ye-sine wave yenzeka emvelweni, okuhlanganisa namagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu iyakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi izethulo zamagagasi e-sine ze-harmonics yefrikhwensi eyodwa zisetshenziselwa ukwakha amanothi omculo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre yomsindo. Lesi yisizathu esenza ukuthi inothi elifanayo lomculo elidlalwa ezinsimbini ezahlukene lizwakale lihlukile.
Nokho, umsindo okhiqizwa isandla somuntu awukhiwanga amaza anesine kuphela, njengoba uqukethe namagagasi e-aperiodic. Amagagasi e-aperiodic awaphindaphindi futhi awanayo iphethini, kuyilapho amagagasi e-sine enziwa ngezikhathi ezithile. Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ukuchaza futhi ukulinganisa noma yikuphi ukuma kwamagagasi ngezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elinamandla elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa, futhi kuvame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngokushintsha amafomu ngokusebenzisa amasistimu alayini asabalalisiwe, futhi ayadingeka ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi anobude nobuningi obufanayo, futhi lapho la magagasi edlula phezulu, kwakhiwa iphethini yegagasi elimile. Lokhu kufana nalokho okwenzekayo lapho kunothi lihlwithwa entanjeni; amagagasi aphazamisayo ayadalwa, futhi lapho la maza eboniswa yiziphetho ezingaguquki zentambo, amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi ama-resonant frequencies. Lawa mafrikhwensi azwakalayo akhiwa imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nempande eyisikwele yesisindo sayo ngobude beyunithi.
Iyini indima ye-Harmonics emsindweni?
I-sine wave iyi-oscillation eqhubekayo, ebushelelezi, ephindaphindayo etholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucubungula amasignali. Kuwuhlobo lwegagasi eliqhubekayo elichazwa umsebenzi we-trigonometric, ngokuvamile i-sine noma i-cosine, futhi imelwe igrafu. Kwenzeka kwizibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali.
Imvamisa evamile yegagasi le-sine, noma inombolo yokuzulazula okwenzeka enanini lesikhathi esinikeziwe, imelelwa imvamisa ye-angular ω, elingana no-2πf, lapho u-f eyimvamisa ku-hertz. Inani eliyinegethivu elithi φ limelela ukubambezeleka ngamasekhondi, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi.
Amagagasi e-Sine avame ukusetshenziselwa ukuchaza amagagasi omsindo, njengoba ewuhlobo oluyisisekelo kakhulu lwamagagasi omsindo. Zichazwa ngomsebenzi we-sine, f = Isono (ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wushintsho lwesigaba. Ukushintsha kwesigaba kwama-radians angu-π/2 kunikeza igagasi isiqalo, ngakho kuthiwa umsebenzi we-cosine, ohola umsebenzi we-sine. Igama elithi "sinusoidal" lisetshenziselwa ukubhekisela ngokuhlangene kumagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Okufanekisa lokhu, i-cosine wave iwubudlelwane obuyisisekelo phakathi kombuthano kanye nemodeli yendiza eyinkimbinkimbi ye-3D, esiza ukubona ngeso lengqondo ukusebenza kwayo ekuhumusheni kwezinye izizinda. Le phethini yamagagasi yenzeka emvelweni, okuhlanganisa namagagasi omoya, amaza omsindo, namaza okukhanya.
Indlebe yomuntu ikwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziswa njengezethulo ze-harmonics yefrikhwensi eyodwa. Indlebe yomuntu izwa umsindo njengenhlanganisela yamagagasi e-sine nama-harmonics, kanye nokwengezwa kwamagagasi e-sine ahlukene okuholela ekuguqulweni kwegagasi okuhlukile kanye nezinguquko ku-timbre. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elinefrikhwensi efanayo edlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Kodwa-ke, umsindo awukhiwanga nje kuphela ngamagagasi e-sine nama-harmonics, njengoba umsindo owenziwe ngesandla uqukethe namagagasi e-aperiodic. Amagagasi e-Aperiodic awawona ezikhathini ezithile futhi anephethini engaphindi. Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ezingasetshenziswa ukuchaza noma ukulinganisa noma iluphi uhlobo lwamagagasi ezikhathi ezithile, kuhlanganise namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa, futhi kuvame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngendlela eshintshayo ngokusebenzisa amasistimu alayini asabalalisiwe, futhi ayadingeka ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-sine ahamba ezinhlangothini eziphambene emkhathini angamelwa amagagasi anobude obufanayo kanye nemvamisa, futhi lapho edlula phezulu, kwakhiwa iphethini yegagasi elimile. Yilokhu okwenzekayo lapho inothi lihlwithwa entanjeni: amagagasi aphazamisayo aboniswa ekugcineni kwentambo, futhi amagagasi amile avela kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi azwakalayo akhiwa imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi anomsindo weyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nempande eyisikwele yesisindo ngobude beyunithi yeyunithi ngayinye.
I-Sine Wave Iwuthinta Kanjani I-Timbre Yomsindo?
I-sine wave iyi-oscillation eqhubekayo, ebushelelezi, ephindaphindayo eyingxenye ebalulekile yezibalo, i-physics, ubunjiniyela, nokucutshungulwa kwesignali. Iwuhlobo lwegagasi eliqhubekayo elinomsebenzi oshelelayo, wezikhathi ezithile futhi lenzeka kuzibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali. Imvamisa evamile yegagasi elinesine inombolo yokuzungeza noma imijikelezo eyenzeka ngeyunithi yesikhathi. Lokhu kuchazwa ngokuthi ω = 2πf, lapho u-ω kuyi-angular frequency futhi f kuyi-frequency evamile. I-angular frequency izinga loshintsho lwe-agumenti yokusebenza futhi ikalwa ngama-radians ngomzuzwana. Inani elingelona likaziro elithi ω limelela ukushintshwa kwalo lonke ifomethi yegagasi ngesikhathi, eboniswa ngu-φ. Inani elikunegethivu elithi φ limele ukubambezeleka futhi inani eliphozithivu limelela kusengaphambili ngamasekhondi.
I-sine wave ivame ukusetshenziselwa ukuchaza amaza omsindo, futhi ichazwa umsebenzi we-sine f = sin(ωt). Ama-oscillations aphinde abonakale ohlelweni lwe-spring mass mass ekulinganeni, futhi amagagasi e-sine abalulekile ku-physics ngoba agcina ukuma kwawo kwamagagasi lapho ehlanganiswa ndawonye. Le mpahla yamagagasi e-sine iholela ekubalulekeni kwayo ekuhlaziyeni i-Fourier, okuyenza ihluke ngokuzwakalayo.
Uma igagasi le-sine limelelwe kubukhulu obubodwa bendawo, isibalo sinikeza ukususwa kwegagasi endaweni x ngesikhathi t. Kucatshangelwa isibonelo somugqa owodwa, lapho inani legagasi endaweni ethi x linikezwa isibalo. Ngobukhulu bendawo obuningi, isibalo sichaza igagasi lendiza ehambayo, lapho indawo x imelelwa ivekhtha kanye nenombolo yegagasi k iyivekhtha. Lokhu kungahunyushwa njengomkhiqizo wamachashazi wama-vector amabili.
Amagagasi ayinkimbinkimbi, njengegagasi lamanzi echibini lapho itshe liwisa, adinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici zakho zombili igagasi le-sine kanye negagasi le-cosine. Ukushintsha kwesigaba sama-radians angu-π/2 kuthiwa kunikeza igagasi le-cosine isiqalo, njengoba lihola i-sine wave. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba, njengoba kuboniswa igagasi le-cosine.
Lobu budlelwano obuyisisekelo phakathi kwamagagasi e-sine ne-cosine bungabonwa ngendingiliza kumodeli yendiza eyinkimbinkimbi ye-3D. Le modeli iwusizo ekuhumusheni phakathi kwezizinda ezihlukene, njengoba iphethini yegagasi yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namagagasi okukhanya. Indlebe yomuntu iyakwazi ukubona amagagasi e-sine eyodwa, ezwakala ecacile futhi emsulwa. Amagagasi e-Sine nawo ayizethulo ze-harmonics yemvamisa eyodwa, indlebe yomuntu engayibona.
Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo lemvamisa ethile edlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile. Umsindo wokushaya izandla uqukethe amagagasi e-aperiodic, kunamagagasi e-sine, njengoba kuwumsindo wezikhathi ezithile. Kubonwa njengomsindo, umsindo ubonakala njenge-aperiodic, enephethini engaphindi.
Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ukuchaza futhi ukulinganisa noma yikuphi ukuma kwamagagasi ngezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa nokucutshungulwa kwesignali kanye nokuhlaziywa kwezibalo zochungechunge lwesikhathi. Amagagasi e-Sine angaphinde asakaze ngokushintsha amafomu kumasistimu alayini asabalalisiwe, okudingekayo ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini amelelwa amagagasi anobude nobuningi obufanayo. Lapho la maza edlula phezulu, kwakhiwa iphethini yegagasi elimile, njengoba kubonakala lapho kuhlwithwa inothi entanjeni. Amagagasi aphazamisayo abonakala ezindaweni ezigxilile zeyunithi yezinhlamvu adala amaza amile avela kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi azwakalayo akhiwa imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
I-Sine Waves njengamathuluzi okuhlaziya
Ngizokhuluma ngamagagasi e-sine nokuthi asetshenziswa kanjani njengamathuluzi okuhlaziya ekucubunguleni isignali, ukuhlaziya uchungechunge lwesikhathi kanye nokusakazwa kwamagagasi. Sizohlola ukuthi amagagasi e-sine asetshenziswa kanjani ukuchaza ama-oscillation abushelelezi, aphindaphindayo nokuthi asetshenziswa kanjani kuzibalo, i-physics, ubunjiniyela neminye imikhakha. Sizophinde sibheke ukuthi amagagasi e-sine angasetshenziswa kanjani ukuhlaziya ukusakazeka kwamagagasi nokuthi asetshenziswa kanjani ekuhlaziyeni kukaFourier. Ekugcineni, sizoxoxa ngokuthi amagagasi e-sine asetshenziswa kanjani ukudala umsindo nokuthi asetshenziswa kanjani emculweni.
Kuyini Ukucutshungulwa Kwesiginali?
I-Sine wave iyithuluzi eliyisisekelo elisetshenziswa ekucubunguleni isignali nokuhlaziya uchungechunge lwesikhathi. Ziwuhlobo lwe-waveform eqhubekayo, ebonakala nge-oscillation ebushelelezi, ephindaphindayo enefrikhwensi eyodwa. Amagagasi e-sine asetshenziselwa ukuchaza izinto ezihlukahlukene ezibonakalayo, okuhlanganisa amaza omsindo, amaza okukhanya, nokunyakaza kwenqwaba esiphethwini.
Ukucutshungulwa kwesignali kuyinqubo yokuhlaziya nokushintsha amasignali. Isetshenziswa emikhakheni eyahlukene, okuhlanganisa izibalo, i-physics, ubunjiniyela, kanye nokukhiqizwa komsindo nevidiyo. Amasu okucubungula amasignali asetshenziselwa ukuhlaziya amasignali, ukuthola amaphethini, nokukhipha ulwazi kuwo.
Ukuhlaziywa kochungechunge lwesikhathi kuyinqubo yokuhlaziya amaphuzu edatha aqoqwe phakathi nesikhathi. Isetshenziselwa ukukhomba amathrendi namaphethini kudatha, nokwenza izibikezelo mayelana nemicimbi yesikhathi esizayo. Ukuhlaziywa kochungechunge lwesikhathi kusetshenziswa emikhakheni eyahlukene, okuhlanganisa ezomnotho, ezezimali, nobunjiniyela.
Ukusakazwa kwamagagasi kuyinqubo lapho igagasi lihamba endaweni ethile. Ihlaziywa kusetshenziswa izinhlobonhlobo zezibalo zezibalo, okuhlanganisa i-wave equation ne-sine wave equation. I-Wave propagation isetshenziselwa ukuhlaziya ukuziphatha kwamagagasi omsindo, amaza okukhanya, nezinye izinhlobo zamagagasi.
Kuyini Ukuhlaziywa Kochungechunge Lwesikhathi?
Amagagasi e-Sine ayithuluzi elibalulekile lokuhlaziya izinhlobonhlobo zezinto ezibonakalayo, kusukela kumaza omsindo kuya kumaza okukhanya. Ukuhlaziywa kochungechunge lwesikhathi kuyindlela yokuhlaziya amaphuzu edatha aqoqwe ngesikhathi esithile, ukuze kuhlonzwe amaphethini namathrendi. Isetshenziselwa ukutadisha ukuziphatha kwesistimu ngokuhamba kwesikhathi, nokwenza izibikezelo mayelana nokuziphatha kwesikhathi esizayo.
Ukuhlaziywa kochungechunge lwesikhathi kungasetshenziswa ukuhlaziya amagagasi e-sine. Ingasetshenziselwa ukukhomba imvamisa, ubukhulu, kanye nesigaba segagasi le-sine, kanye nokukhomba noma yiziphi izinguquko kufomethi yegagasi ngokuhamba kwesikhathi. Ingase futhi isetshenziselwe ukukhomba noma yimaphi amaphethini angaphansi kufomethi yegagasi, njengama-periodicity noma amathrendi.
Ukuhlaziywa kochungechunge lwesikhathi kungase futhi kusetshenziselwe ukukhomba noma yiziphi izinguquko ku-amplitude noma isigaba se-sine wave ngokuhamba kwesikhathi. Lokhu kungasetshenziswa ukukhomba noma yiziphi izinguquko ohlelweni ezingase zibangele ukuthi i-waveform ishintshe, njengezinguquko kumvelo noma isistimu ngokwayo.
Ukuhlaziywa kochungechunge lwesikhathi kungase futhi kusetshenziselwe ukukhomba noma yimaphi amaphethini angaphansi kufomu lamagagasi, njengama-periodities noma amathrendi. Lokhu kungasetshenziselwa ukukhomba noma yimaphi amaphethini angaphansi kusistimu okungenzeka abangele ukuthi i-waveform ishintshe, njengezinguquko kumvelo noma isistimu ngokwayo.
Ukuhlaziywa kochungechunge lwesikhathi kungasetshenziswa futhi ukukhomba noma yiziphi izinguquko kumvamisa yegagasi le-sine ngokuhamba kwesikhathi. Lokhu kungasetshenziswa ukukhomba noma yiziphi izinguquko ohlelweni ezingase zibangele ukuthi i-waveform ishintshe, njengezinguquko kumvelo noma isistimu ngokwayo.
Ukuhlaziywa kochungechunge lwesikhathi kungase futhi kusetshenziselwe ukukhomba noma yimaphi amaphethini angaphansi kufomu lamagagasi, njengama-periodities noma amathrendi. Lokhu kungasetshenziselwa ukukhomba noma yimaphi amaphethini angaphansi kusistimu okungenzeka abangele ukuthi i-waveform ishintshe, njengezinguquko kumvelo noma isistimu ngokwayo.
Ukuhlaziywa kochungechunge lwesikhathi kuyithuluzi elinamandla lokuhlaziya amagagasi e-sine futhi kungasetshenziswa ukukhomba amaphethini namathrendi kufomu lamagagasi ngokuhamba kwesikhathi. Ingase futhi isetshenziselwe ukukhomba noma yimaphi amaphethini angaphansi kusistimu okungenzeka abangele ukuthi i-waveform ishintshe, njengezinguquko kumvelo noma isistimu ngokwayo.
I-Wave Propagation ihlaziywa kanjani?
Amagagasi e-Sine awuhlobo lwe-waveform eqhubekayo engasetshenziswa ukuhlaziya ukusakazwa kwamagagasi. Ziyi-oscillation ebushelelezi, ephindaphindayo engatholakala kuzibalo, i-physics, ubunjiniyela, nokucubungula amasignali. Amagagasi e-Sine abonakala ngokuvama kwawo (f), inani lokuzungeza okwenzeka ngesikhathi esinikeziwe, kanye nemvamisa yawo ye-angular (ω), okuyizinga lapho i-agumenti yomsebenzi ishintsha khona kumayunithi ama-radians.
Amagagasi e-Sine asetshenziselwa ukuchaza izinto ezihlukahlukene, okuhlanganisa amaza omsindo, amaza okukhanya, nokunyakaza kwenqwaba esiphethwini. Abalulekile futhi ekuhlaziyeni kukaFourier, okuwenza ahluke ngokuzwakalayo. Igagasi le-sine lingamelwa endaweni eyodwa ngomugqa owodwa, ngenani lamagagasi endaweni ethile ngesikhathi nendawo. Ngobukhulu obuningi, isibalo segagasi le-sine sichaza igagasi lendiza ehambayo, elinesimo (x), inombolo yegagasi (k), kanye nefrikhwensi ye-angular (ω).
Ama-Sinusoid awuhlobo lwe-waveform ehlanganisa womabili amagagasi e-sine ne-cosine, kanye nanoma imaphi amagagasi anoguquko lwesigaba sama-radians angu-π/2 (isiqalo sekhanda). Lokhu kuholela ebudlelwaneni obuyisisekelo phakathi kwamagagasi e-sine ne-cosine, angabonwa ngemodeli yendiza eyinkimbinkimbi ye-3D. Le modeli iwusizo ekuhumusheni ama-waveform phakathi kwezizinda ezihlukene.
Amagagasi e-Sinusoidal angatholakala emvelweni, kuhlanganise namagagasi omoya namagagasi amanzi. Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, kodwa umsindo uvame ukwakhiwa ngamagagasi e-sine amaningi, aziwa ngokuthi ama-harmonics. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre yomsindo. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ezingasetshenziswa ukuchaza kanye nokulinganisa noma yikuphi ukuma kwamagagasi ezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziya i-Fourier iyithuluzi elinamandla lokufunda amaza, futhi lisetshenziswa ekugelezeni kokushisa nasekucubunguleni isignali. Ibuye isetshenziswe ekuhlaziyweni kwezibalo zochungechunge lwesikhathi.
Amagagasi e-sine angasabalala kunoma iyiphi indlela emkhathini, futhi amelelwa amagagasi ane-amplitude nemvamisa ahamba ebheke ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lena iphethini efanayo eyakhiwayo lapho inothi lihlwithwa entanjeni, ngenxa yamagagasi abonakala ezindaweni zokugcina ezingashintshi zeyunithi yezinhlamvu. Amaza amile ayenzeka kumafrikhwensi athile, aziwa ngokuthi amafrikhwensi anomsindo, akhiwa imvamisa eyisisekelo nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude bayo, futhi ahambisana ngokuphambene nesisindo sayo ngobude beyunithi.
I-Sine Wave Spectrum
Ngizobe ngidingida i-sine wave spectrum, okuhlanganisa imvamisa yayo, ubude begagasi, nokuthi ingasetshenziswa kanjani ukudala imiphumela ehlukene yomsindo. Sizohlola ijika lezibalo elichaza i-oscillation eshelelayo, ephindaphindayo, nokuthi lisetshenziswa kanjani kwizibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali. Sizophinde sibheke ukuthi i-sine wave ibaluleke kanjani kufiziksi nokuthi kungani isetshenziswa ekuhlaziyeni kukaFourier. Ekugcineni, sizoxoxa ngokuthi i-sine wave isetshenziswa kanjani emsindweni nokuthi ibonwa kanjani indlebe yomuntu.
Iyini Imvamisa Ye-Sine Wave?
I-sine wave iwukugeleza kwegagasi okuqhubekayo okuzungezayo ngendlela ebushelelezi, ephindaphindayo. Iyingxenye ebalulekile yezenzakalo eziningi ezibonakalayo nezezibalo, ezinjengomsindo, ukukhanya, namasignali kagesi. Imvamisa yegagasi elinesine inombolo yokuzungeza okwenzeka esikhathini esithile. Ikalwa nge-Hertz (Hz) futhi ivamise ukuvezwa ngokwemijikelezo ngomzuzwana. Ubudlelwano phakathi kwe-frequency kanye ne-wavelength ukuthi ukuphakama kwefrikhwensi, bufushane ubude be-waveleng.
Amagagasi e-Sine asetshenziselwa ukudala imisindo ehlukahlukene, kufaka phakathi i-vibrato, i-tremolo, nekhorasi. Ngokuhlanganisa amagagasi amaningi e-sine wamafrikhwensi ahlukene, kungadalwa amagagasi ayinkimbinkimbi. Lokhu kwaziwa ngokuthi i-additive synthesis, futhi isetshenziswa ezinhlotsheni eziningi zokukhiqizwa komsindo. Ukwengeza, amagagasi e-sine angasetshenziswa ukudala imiphumela ehlukahlukene, njengokuguquguquka kwesigaba, ukuvuleka, nokubeka izigaba.
Amagagasi e-Sine nawo asetshenziswa ekucubunguleni isignali, njengasekuhlaziyweni kwe-Fourier, okusetshenziselwa ukutadisha ukusabalala kwamagagasi nokugeleza kokushisa. Zibuye zisetshenziswe ekuhlaziyweni kwezibalo nasekuhlaziyeni uchungechunge lwesikhathi.
Kafushane, amagagasi e-sine awumumo wamagagasi oqhubekayo ozungezayo ngendlela ebushelelezi, ephindaphindayo. Zisetshenziselwa ukudala izinhlobonhlobo zemisindo, futhi zisetshenziselwa ukucubungula isignali nokuhlaziywa kwezibalo. Imvamisa yegagasi le-sine inombolo yokuzungeza okwenzeka enkathini ethile yesikhathi, futhi ubudlelwano phakathi kwefrikhwensi ne-wavelength iwukuthi ukuphakama kwefrikhwensi, bufishane ubude begagasi.
Buyini Ubudlelwano phakathi kweFrequency kanye ne-Wavelength?
I-sine wave iyi-oscillation eqhubekayo, ebushelelezi, ephindaphindayo etholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucubungula amasignali. Ichazwa umsebenzi we-sine we-trigonometric, futhi imelelwa ngesithombe njenge-waveform. I-sine wave ine-frequency, okuyinombolo yokuzungeza noma imijikelezo eyenzeka esikhathini esithile esinikeziwe. Imvamisa ye-angular, echazwa ngu-ω, izinga loshintsho lwe-agumenti yokusebenza, elilinganiswa ngama-radians ngomzuzwana. Lonke i-waveform ayiveli ngesikhathi esisodwa, kodwa ishintshwa ngesikhathi ngokushintshwa kwesigaba, okuchazwa ngu-φ, okukalwa ngemizuzwana. Inani elinegethivu limelela ukubambezeleka, futhi inani eliphozithivu limelela kusengaphambili ngamasekhondi. Imvamisa yegagasi le-sine ikalwa nge-hertz (Hz), futhi iyinani lama-oscillation okwenzeka ngomzuzwana owodwa.
Igagasi elinesine liwukwakheka kwamagagasi okubalulekile kufiziksi, njengoba ligcina ukuma kwalo lapho lingezwa kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungalawuleki. Lesi sakhiwo se-waveform yezikhathi saziwa ngokuthi umgomo we-superposition, futhi yile ndawo eholela ekubalulekeni kokuhlaziywa kwe-Fourier. Lokhu kuyenza ihluke ngokuzwakalayo, njengoba iwukuphela kwendlela yegagasi engasetshenziswa ukudala ukuguquguquka kwendawo. Isibonelo, uma u-x emele indawo eduze kwentambo, khona-ke igagasi eline-sine lefrikhwensi enikeziwe kanye nobude begagasi buzosakazeka ngocingo. Ipharamitha yesici yegagasi yaziwa njengenombolo yegagasi, k, okuyinombolo yegagasi elingu-angular futhi imele ukulingana phakathi kwemvamisa ye-angular, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza ihlobene ne-angular frequency kanye nobude begagasi, λ, ngesibalo λ = 2π/k.
Isibalo segagasi le-sine endaweni eyodwa sinikezwa ngu-y = A isono(ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wukushintshwa kwesigaba. Lesi sibalo singenziwa jikelele ukuze sinikeze ukugudluzwa kwegagasi endaweni ethile, x, ngesikhathi esinikeziwe, t. Ukuze uthole isibonelo somugqa owodwa, inani legagasi endaweni ethile linikezwa ngu-y = A sin(kx – ωt + φ), lapho u-k eyinombolo yegagasi. Uma kucatshangelwa ubukhulu bendawo obungaphezu koyedwa, kudingeka isibalo esiyinkimbinkimbi ukuchaza igagasi.
Igama elithi sinusoid lisetshenziselwa ukuchaza i-waveform enezici zakho kokubili i-sine wave kanye ne-cosine wave. Ukushintsha kwesigaba sama-radians angu-π/2 kuthiwa kunikeza i-sine wave isiqalo, njengoba igagasi le-sine libambezela igagasi le-cosine ngaleli nani. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba. Lokhu kuboniswa kugrafu engezansi, ebonisa igagasi le-cosine elinoguquko lwesigaba esingu-π/2 amarediyani.
Ubudlelwano obuyisisekelo phakathi kwegagasi le-sine nombuthano bungabonwa ngeso lengqondo kusetshenziswa imodeli yendiza eyinkimbinkimbi ye-3D. Lokhu kuwusizo ekuhumusheni i-waveform ibe yizizinda ezihlukene, njengoba iphethini yamagagasi efanayo yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ikwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziswa njengezethulo zamathoni efrikhwensi eyodwa. Ama-harmonics nawo akhona emsindweni, njengoba indlebe yomuntu ingabona ama-harmonics ngaphezu kwemvamisa eyisisekelo. Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo yilokho okubangela ukuhlukahluka kwe-timbre. Lesi yisizathu sokuthi kungani inothi lomculo lemvamisa enikeziwe edlalwa ezinsimbini ezahlukene lizozwakala lihlukile.
Umsindo wokushaya izandla uqukethe namagagasi e-aperiodic, okungamagagasi angekho ngezikhathi ezithile. Amagagasi e-Sine awa ngezikhathi ezithile, futhi umsindo ozwakala njengonomsindo ubonakala ngamagagasi e-aperiodic, anephethini engaphindaphindi. Isazi sezibalo esingumFulentshi uJoseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ezingasetshenziswa ukuchaza kanye nokulinganisa noma iluphi uhlobo lwamagagasi ezikhathi ezithile, kuhlanganise namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elinamandla elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa nokucutshungulwa kwesignali, nokuhlaziywa kwezibalo zochungechunge lwesikhathi. Amagagasi e-Sine angasetshenziswa futhi ukusabalalisa ngokushintsha amafomu kumasistimu emigqa esabalalisiwe. Lokhu kuyadingeka ukuze kuhlaziywe ukusabalala kwamagagasi ezindaweni ezimbili emkhathini, njengoba amagagasi anobude obufanayo kanye nemvamisa ehamba ezinhlangothini eziphambene azophakama ukuze akhe iphethini yegagasi emile. Yilokhu okuzwakalayo lapho kuhlwithwa inothi entanjeni, njengoba amagagasi ebonakala ekugcineni kwentambo. Amagagasi amile avela kumafrikhwensi athile, abizwa ngokuthi ama-resonant frequencies of the string. Lawa mafrikhwensi akhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
I-Sine Wave Ingasetshenziswa Kanjani Ukwenza Imisindo Ehlukene?
I-sine wave iwukugeleza kwegagasi okuqhubekayo okuzungezayo ngendlela ebushelelezi, ephindaphindayo. Ingenye yezindlela zamagagasi ezibaluleke kakhulu futhi isetshenziswa ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucubungula amasignali. Amagagasi e-Sine abonakala ngokuvama kwawo, okuyinani lama-oscillation noma imijikelezo eyenzeka ngenani lesikhathi esinikeziwe. I-angular frequency, okuyizinga lokushintsha kwe-agumenti yomsebenzi kuma-radians ngomzuzwana, ihlobene nefrikhwensi evamile nge-equation ω = 2πf.
Amagagasi e-Sine avame ukusetshenziswa ekukhiqizeni umsindo futhi angasetshenziswa ukudala imisindo ehlukahlukene. Ngokuhlanganisa amaza e-sine ahlukene namaza ahlukene, ama-amplitude, nezigaba, kungadalwa imisindo ehlukahlukene. I-sine wave enefrikhwensi eyodwa yaziwa ngokuthi “isisekelo” futhi iyisisekelo sawo wonke amanothi omculo. Uma amaza e-sine amaningi anamaza ahlukene ehlanganiswa, akha “ama-harmonics” okungamaza aphezulu anezela ku-timbre yomsindo. Ngokungeza ama-harmonics amaningi, umsindo ungenziwa uzwakale uyinkimbinkimbi futhi uthakazelisa. Ukwengeza, ngokushintsha isigaba se-sine wave, umsindo ungenziwa ukuthi uzwakale sengathi uvela ezindaweni ezahlukene.
Amagagasi e-Sine nawo asetshenziswa kuma-acoustics ukukala ukushuba kwamagagasi omsindo. Ngokulinganisa i-amplitude ye-sine wave, ukushuba komsindo kunganqunywa. Lokhu kuwusizo ekulinganiseni ukuphakama komsindo noma ukunquma ukuvama komsindo.
Sengiphetha, amagagasi e-sine ayisakhiwo samaza esibalulekile ezindaweni eziningi zesayensi nobunjiniyela. Asetshenziswa ukwenza imisindo ehlukahlukene futhi asetshenziselwa ukukala ukushuba kwamagagasi omsindo. Ngokuhlanganisa amaza e-sine ahlukene namaza ahlukene, ama-amplitude, nezigaba, kungadalwa imisindo ehlukahlukene.
I-Sine Curve Ingalichaza Kanjani Igagasi?
Kulesi sigaba, ngizobe ngixoxa ngokuthi ijika le-sine lingasetshenziswa kanjani ukuchaza igagasi, ubudlelwano phakathi kwejika le-sine negagasi lendiza, nokuthi ijika le-sine lingasetshenziswa kanjani ukuze ubone ngeso lengqondo amaphethini wamagagasi. Sizohlola ukubaluleka kwamagagasi e-sine kuzibalo, i-physics, ubunjiniyela, nokucutshungulwa kwesignali, nokuthi asetshenziswa kanjani ukumela amaza omsindo nezinye izinhlobo zamagagasi.
I-Sine Curve Ilimelela Kanjani Igagasi?
I-sine wave iwukuzulazula okubushelelezi, okuphindaphindayo okuqhubekayo futhi okune-waveform echazwa umsebenzi we-sine trigonometric. Iwuhlobo lwamagagasi aqhubekayo ashelelayo futhi ahamba ngezikhathi ezithile, futhi atholakala kuzibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali. Ibonakala ngefrikhwensi, okuyinombolo yokuzungeza noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe. I-angular frequency, ω, izinga lapho i-agumenti yomsebenzi ishintsha khona kumayunithi ama-radians ngomzuzwana. I-waveform engeyona yonke i-waveform ibonakala ishintshile ngesikhathi ngokushintsha kwesigaba, φ, esikalwa ngemizuzwana. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi.
I-sine wave ivame ukusetshenziselwa ukuchaza igagasi lomsindo, futhi ichazwa umsebenzi we-sine, f = Isono (ωt + φ). Ama-oscillations nawo atholakala ohlelweni lwe-spring mass mass ekulinganeni, futhi i-sine wave ibalulekile kufiziksi ngoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungalawuleki. Lesi sakhiwo se-waveform sezikhathi ezithile yisona esiholela ekubalulekeni kwaso ekuhlaziyeni i-Fourier, okuyenza ihluke ngokuzwakalayo.
Uma igagasi lisakazeka endaweni eyodwa, ukuguquguquka kwendawo, x, kumelela ubukhulu bendawo lapho igagasi lisakazeka khona, futhi ipharamitha yesici, k, ibizwa ngokuthi inombolo yegagasi. Inombolo yegagasi eliyi-angular imele ukulingana phakathi kwe-angular frequency, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza ihlobene ne-angular frequency, λ (lambda) ubude begagasi, futhi f imvamisa. I-equation v = λf inikeza igagasi lesine endaweni eyodwa. I-equation ejwayelekile inikezwa ukunikeza ukugudluzwa kwegagasi endaweni, x, ngesikhathi, t.
Uma kucatshangelwa isibonelo somugqa owodwa, inani legagasi kunoma iyiphi indawo esikhaleni linikezwa i-equation x = A isono (kx – ωt + φ). Ngobukhulu obubili bendawo, isibalo sichaza igagasi lendiza ehambayo. Uma kuhunyushwa ngokuthi ama-vectors, umkhiqizo wama-vector amabili umkhiqizo wamachashazi.
Kumagagasi ayinkimbinkimbi, njengegagasi lamanzi echibini lapho itshe liwisa, kudingeka izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza izici zegagasi ze-sine wave kanye ne-cosine wave. Ukushintsha kwesigaba sama-radians angu-π/2 kuthiwa kunikeza igagasi le-cosine isiqalo, njengoba lihola i-sine wave. I-sine wave ibambezela igagasi le-cosine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kumagagasi e-sine namagagasi e-cosine ane-offset yesigaba, ebonisa ubuhlobo obuyisisekelo phakathi kwalokhu kokubili. Umbuthano kumodeli yendiza eyinkimbinkimbi ye-3D ungasetshenziswa ukuze ubone ngeso lengqondo ukusizakala kokuhumusha phakathi kwezizinda ezimbili.
Iphethini efanayo yamagagasi yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ikwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine amelela imvamisa eyodwa nama-harmonics. Indlebe yomuntu izwa umsindo njengegagasi lesine elinama-harmonics azwakalayo ngaphezu kwemvamisa eyisisekelo. Ukwengezwa kwamagagasi e-sine ahlukene kubangela uhlobo lwamagagasi oluhlukile, olushintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo lemvamisa ethile edlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Umsindo wokushaya izandla uqukethe amagagasi e-aperiodic, angewona wezikhathi ezithile, futhi amagagasi e-sine awa ngezikhathi ezithile. Umsindo ozwakala njengonomsindo ubonakala njenge-aperiodic, enephethini engaphindi. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ukuchaza kanye nokulinganisa i-waveform yezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier ithuluzi lokuhlaziya elisetshenziselwa ukutadisha amaza, njengokugeleza kokushisa, futhi kuvame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngendlela eshintshayo ngokusebenzisa amasistimu alayini asabalalisiwe, futhi ayadingeka ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-Sine ahamba ezinhlangothini eziphambene emkhathini angamelwa njengamagagasi anobude obufanayo kanye nemvamisa ehamba ezinhlangothini eziphambene. Lapho amagagasi amabili edlula phezulu, kwakhiwa iphethini yegagasi elimile. Lokhu kufana nalapho kunothi lihlwithwa entanjeni, lapho amagagasi aphazamisayo ebonakala ekugcineni kwentambo. Amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Umsindo ohlanganisiwe wenothi elihlwithwe ochungechungeni lwakhiwe imvamisa eyisisekelo nama-harmonic aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
Buyini Ubudlelwano Phakathi Kwejika Eline-Sine kanye Negagasi Lendiza?
I-sine wave iwukuzulazula okubushelelezi, okuphindaphindayo kokwakheka kwamagagasi okuqhubekayo. Ijika lezibalo elichazwe ngokomsebenzi we-sine trigonometric, futhi ngokuvamile lifakwe igrafu njengejika elibushelelezi, le-sinusoidal. Amagagasi e-sine atholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali.
I-sine wave ibonakala ngokuvama kwayo okujwayelekile, inani lama-oscillation noma imijikelezo eyenzeka ngesikhathi esinikeziwe. isikhathi. I-angular frequency, ω, izinga loshintsho lwe-agumenti yomsebenzi, futhi ikalwa ngamayunithi ama-radians ngomzuzwana. Ukwakheka kwegagasi okungelona lonke kubonakala kushintshile ngesikhathi, ngokushintsha kwesigaba, φ, kwamasekhondi angu-ωt. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi.
I-sine wave nayo isetshenziselwa ukuchaza amaza omsindo. Ichazwa ngokusebenza kwe-sine, f(t) = Isono(ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, futhi φ iwukushintsha kwesigaba. Ama-oscillations abuye abonakale ohlelweni lwe-spring mass mass ngokulingana.
Amagagasi e-Sine abalulekile ku-physics ngoba agcina ukuma kwawo kwamagagasi lapho ehlanganiswa ndawonye. Le ndawo, eyaziwa ngokuthi isimiso se-superposition, iholela ekubalulekeni kokuhlaziywa kwe-Fourier, okwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo phakathi kokuguquguquka kwendawo. Isibonelo, uma u-x emele indawo enobukhulu obubodwa, igagasi lisakazeka ngepharamitha yesici, k, ebizwa ngokuthi inombolo yegagasi. Inombolo yegagasi elingu-angular, k, imele ukulingana phakathi kwe-angular frequency, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza, k, ihlobene ne-angular frequency, ω, kanye ne-wavelength, λ, nge-equation λ = 2π/k.
I-equation ye-sine wave endaweni eyodwa inikezwa ngu-y = A isono(ωt + φ). Lesi sibalo sinikeza ukususwa kwegagasi endaweni ethile, x, ngesikhathi esinikeziwe, t. Ngesibonelo somugqa owodwa, uma inani legagasi libhekwa njengentambo, bese kuthi ngezilinganiso ezimbili zendawo, isibalo sichaza igagasi lendiza ehambayo. Indawo, u-x, kanye nenombolo yegagasi, k, ingahunyushwa ngokuthi ama-vector, futhi umkhiqizo wakho kokubili uwumkhiqizo wamachashazi.
Amagagasi ayinkimbinkimbi, njengalawo abonakala echibini lapho itshe liwisa, adinga izibalo eziyinkimbinkimbi ukuze uwachaze. Igama elithi sinusoid lisetshenziselwa ukuchaza izici zamagagasi ezifana ne-sine wave. Igagasi le-cosine lifana negagasi le-sine, kodwa ngokushintsha kwesigaba kwama-radians angu-π/2, noma isiqalo sekhanda. Lokhu kuholela ekutheni i-sine wave ibambezele igagasi le-cosine. Igama elithi sinusoidal lisetshenziswa ngokuhlanganyela ukuze libhekisele kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Ukufanekisa i-cosine wave ubuhlobo obuyisisekelo kumbuthano kumodeli yendiza eyinkimbinkimbi ye-3D, engasetshenziswa ukuze ubone ngeso lengqondo usizo lwamagagasi e-sine ekuhumusheni phakathi kwezizinda. Le phethini yamagagasi yenzeka emvelweni, okuhlanganisa namagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine amelela imvamisa eyodwa nama-harmonics. Indlebe yomuntu izwa umsindo njengegagasi lesine elinama-harmonics ngaphezu kwemvamisa eyisisekelo. Lokhu kubangela ukuhlukahluka kwe-timbre. Isizathu sokuthi inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale lihlukile ingoba umsindo uqukethe amagagasi e-aperiodic ngaphezu kwamagagasi e-sine. Umsindo we-aperiodic ubonwa njengomsindo, futhi umsindo ubonakala ngokuba nephethini engaphindi.
Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ukuchaza kanye nokulinganisa i-waveform yezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elinamandla lokuhlaziya elisetshenziselwa ukutadisha amagagasi, njengokugeleza kokushisa, futhi livame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi. Amagagasi e-Sine angaphinde asakaze ngaphandle kokushintsha isimo kumasistimu alayini asabalalisiwe. Lokhu kuyadingeka ukuze kuhlaziywe ukusabalala kwamagagasi ezindaweni ezimbili emkhathini, futhi kuvezwa amagagasi anobude obufanayo kanye nemvamisa, kodwa ahamba ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kubonakala lapho inothi lihlwithwa entanjeni, futhi amagagasi aphazamisayo abonakala ekugcineni kwentambo. Amaza amile ayenzeka kumaza athile, abizwa ngokuthi amaza azwakalayo, futhi akhiwe imvamisa eyisisekelo nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
I-Sine Curve Ingasetshenziswa Kanjani Ukuze Ubone Ngeso Lengqondo Amaphethini Wave?
Igagasi lesine liyi-oscillation eqhubekayo, ebushelelezi, ephindaphindayo echazwa ijika lezibalo. Kuwuhlobo lwamagagasi aqhubekayo achazwa umsebenzi we-sine we-trigonometric, odwetshwe njenge-waveform. Kwenzeka kwizibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali.
Igagasi le-sine linefrikhwensi evamile, okuyinani lokuzungeza noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe. Lokhu kuvezwa i-angular frequency, ω, elingana no-2πf, lapho u-f eyimvamisa ku-hertz (Hz). I-sine wave ingashintshwa ngokuhamba kwesikhathi, ngevelu elinegethivu elimelela ukubambezeleka kanye nenani eliphozithivu elimelela kusengaphambili ngamasekhondi.
I-sine wave ivame ukusetshenziselwa ukuchaza igagasi lomsindo, njengoba lichazwa umsebenzi we-sine. Imvamisa ye-sine wave, f, iyinani lokuzungeza ngomzuzwana. Lokhu kuyafana nokuzulazula kwesistimu ye-spring mass mass ngokulingana.
I-sine wave ibalulekile kufiziksi ngoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungahleliwe. Lesi sakhiwo se-sine wave saziwa ngokuthi umgomo we-superposition futhi siyindawo ye-waveform yezikhathi ezithile. Lesi sakhiwo siholela ekubalulekeni kokuhlaziywa kwe-Fourier, okwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo phakathi kwezinto eziguquguqukayo zendawo.
Isibonelo, uma u-x emele ubukhulu bendawo lapho igagasi lisakazeka khona, khona-ke ipharamitha yesici k, ebizwa ngokuthi inombolo yegagasi, imele ukulingana phakathi kwe-angular frequency, ω, kanye nesivinini somugqa sokusakazeka, ν. Inombolo yamaza ihlobene ne-angular frequency kanye nobude begagasi, λ, ngesibalo λ = 2π/k.
I-equation ye-sine wave endaweni eyodwa inikezwa ngu-y = A isono (ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wushintsho lwesigaba. Uma kucatshangelwa isibonelo somugqa owodwa, khona-ke inani legagasi kunoma iyiphi indawo x nganoma isiphi isikhathi t linikezwa y = A isono (kx – ωt + φ).
Ezilinganisweni eziningi zendawo, i-equation ye-sine wave inikezwa ngu-y = A isono (kx – ωt + φ), lapho u-A eyi-amplitude, k inombolo yegagasi, x indawo, ω imvamisa ye-angular, t isikhathi, futhi φ wushintsho lwesigaba. Lesi sibalo sichaza igagasi lendiza ehambayo.
Ukuba wusizo kwe-sine wave akukhawulelwe ekuhumusheni ezizindeni ezibonakalayo. Iphethini yegagasi efanayo yenzeka emvelweni, okuhlanganisa namagagasi omoya, amaza omsindo, namaza okukhanya. Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziselwa ukumelela ama-harmonics efrikhwensi eyodwa.
Indlebe yomuntu ingakwazi futhi ukubona umsindo owakhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Lawa mafrikhwensi anomsindo weyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi alinganisa ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
Kafushane, igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici ze-sine wave kanye ne-cosine wave. Igagasi le-sine kuthiwa linokushintsha kwesigaba kwama-radians angu-π/2, okulingana nesiqalo sekhanda, kuyilapho igagasi le-cosine kuthiwa lihola igagasi le-sine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine namagagasi e-cosine, ane-offset yesigaba. Lokhu kuboniswa yi-cosine wave, okuwubudlelwane obuyisisekelo kumbuthano kumodeli yendiza eyinkimbinkimbi ye-3D esetshenziselwa ukubona ngeso lengqondo ukuba wusizo kwegagasi le-sine ekuhumusheni ezizindeni ezibonakalayo.
Sine Waves and Phase
Kulesi sigaba, ngizobe ngihlola ubudlelwano phakathi kwamagagasi e-sine nesigaba. Ngizoxoxa ngokuthi isigaba silithinta kanjani igagasi le-sine nokuthi lingasetshenziswa kanjani ukwakha amagagasi ahlukene. Ngizophinde nginikeze izibonelo ezithile ukukhombisa ukuthi isigaba singasetshenziswa kanjani ezinhlelweni ezahlukahlukene.
Buyini Ubudlelwano phakathi kweSine Wave neSigaba?
I-sine wave iyi-oscillation eshelelayo, ephindaphindayo eqhubekayo futhi enefrikhwensi eyodwa. Kuyijika lezibalo elichazwa umsebenzi we-sine we-trigonometric, futhi ngokuvamile limelelwa igrafu. Amagagasi e-sine atholakala ezindaweni eziningi zezibalo, i-physics, ubunjiniyela, nokucubungula amasignali.
Imvamisa yegagasi le-sine inombolo yokuzulazula noma imijikelezo eyenzeka enkathini ethile yesikhathi, futhi ichazwa ngohlamvu lwesiGreki u-ω (omega). I-angular frequency izinga loshintsho lwe-agumenti yokusebenza, futhi ikalwa ngamayunithi ama-radians ngomzuzwana. Ifomethi yegagasi engeyona yonke ingase ibonakale ishintshile ngesikhathi, ngokushintsha kwesigaba sika-φ (phi) ngemizuzwana. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili ngamasekhondi. Imvamisa yegagasi elinesine likalwa nge-hertz (Hz).
I-sine wave ivame ukusetshenziselwa ukuchaza igagasi lomsindo, njengoba lichazwa umsebenzi we-sine. Isibonelo, f = 1/T, lapho u-T eyinkathi ye-oscillation, futhi f imvamisa ye-oscillation. Lokhu kuyafana nesistimu ye-spring mass mass elingana.
I-sine wave ibalulekile kufiziksi ngoba igcina isimo sayo samagagasi lapho ingezwe kwelinye igagasi le-sine lemvamisa efanayo nesigaba nobukhulu obungahleliwe. Le ndawo yokuba ngezikhathi ezithile iyindawo eholela ekubalulekeni kwayo ekuhlaziyeni iFourier, okuyenza ihluke ngokuzwakalayo.
Lapho igagasi lisakazeka emkhathini, okuguquguquka kwendawo x kumelela indawo enobukhulu obubodwa. Igagasi linepharamitha yesici k, ebizwa ngokuthi inombolo yegagasi, emele ukulingana phakathi kwe-angular frequency ω kanye nesivinini somugqa sokusakazeka ν. Inombolo yegagasi k ihlobene nemvamisa ye-angular ω kanye ne-wavelength λ (lambda) ngesibalo λ = 2π/k. I-frequency f kanye nesivinini somugqa v zihlobene ne-equation v = λf.
Isibalo segagasi le-sine endaweni eyodwa sinikezwa ngu-y = A isono(ωt + φ), lapho u-A eyi-amplitude, ω imvamisa ye-angular, t isikhathi, futhi φ wukushintshwa kwesigaba. Lesi sibalo sinikeza ukususwa kwegagasi endaweni enikeziwe x kanye nesikhathi t. Kucatshangelwa isibonelo somugqa owodwa, onenani elithi y = A sin(ωt + φ) kuwo wonke u-x.
Ngobukhulu bendawo abaningi, isibalo segagasi lendiza ehambayo sinikezwa y = A isono(kx – ωt + φ). Lesi sibalo singahunyushwa njengamavektha amabili endizeni eyinkimbinkimbi, ngomkhiqizo wamavekhtha amabili okuwumkhiqizo wamachashazi.
Amagagasi ayinkimbinkimbi, njengegagasi lamanzi echibini lapho itshe liwisa, adinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza igagasi elinezici zakho zombili igagasi le-sine kanye negagasi le-cosine. Ukushintsha kwesigaba kwama-radians angu-π/2 kunikeza igagasi le-cosine isiqalo sekhanda, futhi kuthiwa lihola i-sine wave. Lokhu kusho ukuthi i-sine wave ibambezela igagasi le-cosine. Igama elithi sinusoidal livame ukusetshenziselwa ukubhekisela ngokuhlangene kokubili amagagasi e-sine namagagasi e-cosine, ane-offset yesigaba noma ngaphandle kwayo.
Ukubonisa igagasi le-cosine, ubudlelwano obuyisisekelo phakathi kwegagasi le-sine negagasi le-cosine bungabonwa ngemodeli yendiza eyinkimbinkimbi ye-3D. Le modeli iwusizo ekuhumusheni iphethini yegagasi eyenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namaza okukhanya.
Indlebe yomuntu iyakwazi ukubona amagagasi e-sine eyodwa, ezwakala ecacile futhi emsulwa. Amagagasi e-Sine avame ukusetshenziswa njengezethulo zamathoni wemvamisa eyodwa, kanye nama-harmonics. Indlebe yomuntu izwa umsindo njengenhlanganisela yamaza e-sine, nokuba khona kwama-harmonic aphezulu ngaphezu kwemvamisa eyisisekelo edala ukuhlukahluka kwe-timbre. Lesi yisizathu sokuthi kungani inothi lomculo elinefrikhwensi efanayo edlalwa ezinsimbini ezahlukene lizozwakala lihlukile.
Ukushaya izandla, nokho, kuqukethe amagagasi e-aperiodic, angewona wezikhathi ezithile futhi anephethini engaphindaphindi. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba zokwakha ezilula ezingasetshenziswa ukuchaza kanye nokulinganisa noma iluphi uhlobo lwamagagasi ezikhathi ezithile, kuhlanganise namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elinamandla lokuhlaziya elisetshenziselwa ukutadisha amagagasi, njengokugeleza kokushisa, futhi livame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngendlela eshintshayo ngokusebenzisa amasistimu alayini asabalalisiwe, futhi ayadingeka ukuze kuhlaziywe ukusabalala kwamagagasi. Amagagasi e-sine angahamba ngezindlela ezimbili emkhathini, futhi amelelwa amagagasi anobude obufanayo kanye nemvamisa kodwa ahamba ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lokhu kufana nenothi elihlwithwa entanjeni, lapho amagagasi eboniswa khona ekugcineni kwentambo. Amaza amile ayenzeka kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi akhiwe imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi e-resonant eyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu, futhi alinganise ngokuphambene nesisindo ngeyunithi ngayinye yobude beyunithi yezinhlamvu.
Isigaba Siyithinta Kanjani Igagasi Le-Sine?
I-sine wave iwuhlobo lwe-waveform eqhubekayo ebonakala ngokuzungeza okubushelelezi, okuphindaphindayo. Kuyijika lezibalo elichazwa umsebenzi we-trigonometric futhi lisetshenziswa ezinkambini zezibalo, zefiziksi, ezobunjiniyela, nezokucubungula amasignali. Imvamisa evamile yegagasi le-sine yinani lokuzungeza noma imijikelezo eyenzeka enanini lesikhathi esinikeziwe, ngokuvamile esikalwa ngamasekhondi. Imvamisa ye-angular, echazwa ngu-ω, izinga loshintsho lwe-agumenti yomsebenzi, ngokuvamile elinganiswa ngama-radians. Ukwakheka kwegagasi okungelona lonke kubonakala kugudluzwe ngesikhathi inani φ, elilinganiswa ngamasekhondi. Iyunithi yefrikhwensi i-hertz (Hz), elingana ne-oscillation eyodwa ngomzuzwana.
I-sine wave ivame ukusetshenziselwa ukuchaza igagasi lomsindo, futhi ichazwa ngomsebenzi we-sine, f(t) = Isono (ωt + φ). Lolu hlobo lwe-waveform luphinde lubonakale ohlelweni lwe-spring mass mass ngokulingana. Amagagasi e-Sine abalulekile ku-physics ngoba agcina ukuma kwawo kwegagasi lapho ehlanganiswa ndawonye, okuyimpahla eyaziwa ngokuthi isimiso se-superposition. Lesi sakhiwo siholela ekubalulekeni kokuhlaziywa kwe-Fourier, okwenza kube nokwenzeka ukuhlukanisa ngokuzwakalayo umsindo owodwa komunye.
Kubukhulu obubodwa, igagasi lesine lingamelwa umugqa owodwa. Isibonelo, inani le-wave ocingweni lingamelwa umugqa owodwa. Ngobukhulu bendawo abaningi, isibalo esijwayelekile siyadingeka. Le zibalo ichaza ukususwa kwegagasi endaweni ethile, x, ngesikhathi esithile, t.
Igagasi eliyinkimbinkimbi, elifana negagasi lamanzi echibini ngemva kokuwa kwetshe, lidinga izibalo eziyinkimbinkimbi. Igama elithi sinusoid lisetshenziselwa ukuchaza i-waveform enezici zakho zombili igagasi le-sine ne-cosine wave. Ukushintsha kwesigaba sika-π/2 radians kuyafana nesiqalo sekhanda, futhi kuyafana nokuthi umsebenzi we-cosine uhola umsebenzi we-sine, noma ukuthi i-sine ibambezela i-cosine. Igama elithi sinusoidal lisetshenziselwa ukubhekisela ngokuhlangene kuwo womabili amagagasi e-sine namagagasi e-cosine ane-offset yesigaba.
Ukubonisa igagasi le-cosine, ubudlelwano obuyisisekelo phakathi kwegagasi le-sine kanye negagasi le-cosine bungabonwa kusetshenziswa indingilizi kumodeli yendiza eyinkimbinkimbi ye-3D. Lokhu kuwusizo ekuhumusheni phakathi kwezizinda ezihlukene, njengoba iphethini yamagagasi efanayo yenzeka emvelweni, okuhlanganisa amaza omoya, amaza omsindo, namagagasi okukhanya.
Indlebe yomuntu ingakwazi ukubona amaza e-sine eyodwa njengokuzwakala kucacile, futhi amaza e-sine avame ukusetshenziselwa ukumelela amaza nama-harmonics awodwa. Lapho amaza e-sine ehlukene ehlanganiswa ndawonye, i-waveform ewumphumela iyashintsha, eshintsha i-timbre yomsindo. Ukuba khona kwama-harmonics aphezulu ngaphezu kwemvamisa eyisisekelo kubangela ukuhlukahluka kwe-timbre. Lesi yisizathu esenza inothi lomculo elidlalwa ezinsimbini ezahlukene lizwakale ngokwehlukile.
Umsindo wokushaya izandla uqukethe amagagasi e-aperiodic, angewona wezikhathi ezithile, ngokungafani namagagasi e-sine, ahamba ngezikhathi ezithile. Isazi sezibalo esingumFulentshi u-Joseph Fourier sathola ukuthi amagagasi e-sinusoidal ayizingqimba ezilula zokwakha ezingasetshenziswa ukuchaza kanye nokulinganisa noma yikuphi ukuma kwamagagasi ezikhathi ezithile, okuhlanganisa namagagasi ayisikwele. Ukuhlaziywa kwe-Fourier iyithuluzi elinamandla lokuhlaziya elisetshenziselwa ukutadisha amagagasi, njengokugeleza kokushisa, futhi livame ukusetshenziswa ekucubunguleni isignali nokuhlaziya izibalo zochungechunge lwesikhathi.
Amagagasi e-Sine angasabalala ngokushintsha amafomu ngokusebenzisa amasistimu alayini asabalalisiwe. Ukuze kuhlaziywe ukusabalala kwamagagasi, amagagasi e-sine ahamba ezinhlangothini ezihlukene emkhathini amelelwa amagagasi anobude obufanayo kanye nemvamisa, kodwa ahamba ezinhlangothini eziphambene. Lapho la magagasi edlula phezulu, kwakheka iphethini yegagasi elimile. Lena iphethini efanayo eyenziwayo lapho inothi lihlwithwa entanjeni. Amagagasi aphazamisayo abonakala ezindaweni ezigxilile zeyunithi yezinhlamvu adala amaza amile avela kumafrikhwensi athile, abizwa ngokuthi amaza anomsindo. Lawa mafrikhwensi azwakalayo akhiwa imvamisa eyisisekelo kanye nama-harmonics aphezulu. Amafrikhwensi anomsindo weyunithi yezinhlamvu alingana nobude beyunithi yezinhlamvu futhi ahambisana ngokuphambene nempande eyisikwele yesisindo ngobude beyunithi yeyunithi ngayinye.
Isigaba Singasetshenziswa Kanjani Ukwakha Ama-Waveform Ahlukene?
Amagagasi e-Sine awuhlobo lwe-waveform eqhubekayo eshelelayo futhi ephindaphindayo, futhi ingasetshenziswa ukuchaza izenzakalo ezihlukahlukene kuzibalo, i-physics, ubunjiniyela, kanye nokucubungula amasignali. Achazwa umsebenzi we-trigonometric, futhi angenziwa igrafu njengejika elibushelelezi, lezikhathi ezithile. Imvamisa yegagasi le-sine yinombolo yokuzungeza noma imijikelezo eyenzeka esikhathini esinikeziwe, ngokuvamile esikalwa nge-Hertz (Hz). I-angular frequency, ω, izinga lapho i-agumenti yomsebenzi ishintsha khona, ikalwa ngama-radians ngomzuzwana. I-sine wave ingase ibonakale ishintshile ngesikhathi, ngokushintsha kwesigaba, φ, kukalwa ngamasekhondi. Inani elinegethivu limelela ukubambezeleka, kuyilapho inani eliphozithivu limelela kusengaphambili.
Isigaba siyisici esibalulekile se-sine wave, futhi singasetshenziswa ukwakha amagagasi ahlukene. Uma amagagasi e-sine amabili anefrikhwensi efanayo nesigaba esinganaki nobukhulu ehlanganiswa, i-waveform ewumphumela iwuhlelo lwamagagasi ezikhathi ezithile olunendawo efanayo. Lesi sakhiwo siholela ekubalulekeni kokuhlaziywa kwe-Fourier, okwenza kube nokwenzeka ukuhlonza nokuhlaziya amasignali ahlukile ngokuzwakalayo.
Isigaba singasetshenziswa ukwakha ama-waveform ahlukene ngezindlela ezilandelayo:
• Ngokugudluza isigaba se-sine wave, kungenziwa ukuthi kuqale endaweni ehlukile ngesikhathi. Lokhu kwaziwa njengokushintsha kwesigaba, futhi kungasetshenziswa ukwakha amagagasi ahlukene.
• Ngokungeza igagasi le-sine elinemvamisa nesigaba esihlukile kumagagasi e-sine ayisisekelo, kungadalwa i-waveform eyinkimbinkimbi. Lokhu kwaziwa ngokuthi i-harmonic, futhi ingasetshenziswa ukudala imisindo ehlukahlukene.
• Ngokuhlanganisa amagagasi e-sine namafrikhwensi ahlukene nezigaba, iphethini yegagasi emile ingadalwa. Lokhu kwaziwa njenge-resonant frequency, futhi ingasetshenziswa ukudala imisindo ehlukene.
• Ngokuhlanganisa amaza e-sine namafrikhwensi ahlukene nezigaba, kungadalwa i-waveform eyinkimbinkimbi. Lokhu kwaziwa njengokuhlaziywa kwe-Fourier, futhi kungasetshenziswa ukuhlaziya ukusakazwa kwamagagasi.
Ngokusebenzisa isigaba ukuze udale amagagasi ahlukene, kungenzeka ukudala imisindo ehlukahlukene futhi uhlaziye ukusakazeka kwamagagasi. Lokhu kuyisici esibalulekile samagagasi e-sine, futhi sisetshenziswa emikhakheni eyahlukene, okuhlanganisa i-acoustics, ukucubungula amasignali, kanye ne-physics.
Ubani Osebenzisa I-Sine Waves Ezimakethe?
Njengomtshali-zimali, ngiyaqiniseka ukuthi uzwile ngamagagasi e-sine nendima yawo ezimakethe zezimali. Kulesi sihloko, ngizobe ngihlola ukuthi ayini amagagasi e-sine, angasetshenziswa kanjani ukwenza izibikezelo, kanye nobudlelwano phakathi kwamagagasi e-sine nokuhlaziywa kobuchwepheshe. Ekupheleni kwalesi sihloko, uzoqonda kangcono ukuthi amagagasi e-sine angasetshenziswa kanjani ukuze uzuze ezimakethe.
Ithini Iqhaza Le-Sine Waves Ezimakethe Zezezimali?
Amagagasi e-Sine awuhlobo lwejika lezibalo elichaza ama-oscillations abushelelezi, aphindaphindayo kumagagasi aqhubekayo. Aziwa nangokuthi amagagasi e-sinusoidal futhi asetshenziswa kwizibalo, i-physics, ubunjiniyela, nezinkambu zokucubungula amasignali. Amagagasi e-Sine abalulekile ezimakethe zezimali, njengoba angasetshenziswa ukwenza izibikezelo nokuhlaziya izitayela.
Ezimakethe zezimali, amagagasi e-sine asetshenziselwa ukukhomba nokuhlaziya amathrendi. Angasetshenziswa ukuhlonza amazinga okusekela nawokumelana, kanye nokuhlonza izindawo ezingase zibe khona zokungena nokuphuma. Amagagasi e-Sine angasetshenziswa futhi ukukhomba nokuhlaziya amaphethini, njengekhanda namahlombe, ama-double top and bottoms, namanye amaphethini eshadi.
Amagagasi e-Sine nawo asetshenziswa ekuhlaziyeni kwezobuchwepheshe. Ukuhlaziywa kobuchwepheshe wucwaningo lokuhamba kwentengo namaphethini ezimakethe zezimali. Abahlaziyi bezobuchwepheshe basebenzisa amagagasi e-sine ukuhlonza amathrendi, amazinga okusekela nawokumelana, kanye nezindawo ezingaba khona zokungena nokuphuma. Aphinde asebenzise amagagasi e-sine ukuze ahlonze amaphethini, njengekhanda namahlombe, phezulu nangaphansi okukabili, namanye amaphethini eshadi.
Amagagasi e-Sine nawo angasetshenziswa ukwenza izibikezelo. Ngokuhlaziya izitayela ezedlule nezamanje, abahlaziyi bezobuchwepheshe bangenza izibikezelo mayelana nokunyakaza kwamanani esikhathi esizayo. Ngokuhlaziya amagagasi e-sine, angakwazi ukuhlonza izindawo zokungena nokuphuma ezingaba khona, kanye nokusekela okungase kube namazinga okumelana.
I-Sine wave iyithuluzi elibalulekile labahlaziyi bezobuchwepheshe ezimakethe zezimali. Angasetshenziselwa ukuhlonza nokuhlaziya izitayela, amazinga okusekela nawokumelana, kanye namaphoyinti angangena nawokuphuma. Angasetshenziswa futhi ukwenza izibikezelo mayelana nokunyakaza kwentengo okuzayo. Ngokuhlaziya amaza e-sine, abahlaziyi bezobuchwepheshe bangathola ukuqonda okungcono kwezimakethe futhi benze izinqumo ezinolwazi.
I-Sine Waves Ingasetshenziswa Kanjani Ukwenza Izibikezelo?
Amagagasi e-Sine asetshenziswa ezimakethe zezimali ukuhlaziya izitayela nokwenza izibikezelo. Ziwuhlobo lwe-waveform ezungezayo phakathi kwamaphoyinti amabili, futhi ingasetshenziswa ukukhomba amaphethini namathrendi ezimakethe. Amagagasi e-Sine asetshenziswa ekuhlaziyeni kwezobuchwepheshe futhi angasetshenziswa ukubikezela ukunyakaza kwamanani okuzayo.
Nazi ezinye zezindlela amaza e-sine angasetshenziswa ngazo ezimakethe:
• Ukuhlonza amazinga okusekela nawokumelana: Amagagasi e-Sine angasetshenziswa ukukhomba amazinga okusekela kanye nokumelana ezimakethe. Ngokubheka iziqongo nemisele ye-sine wave, abathengisi bangakwazi ukukhomba izindawo lapho intengo ingathola khona ukwesekwa noma ukumelana.
• Ukuhlonza ukuhlehla kwethrendi: Ngokubheka i-sine wave, abahwebi bangakwazi ukuhlonza ukuguqulwa kwethrendi okungaba khona. Uma i-sine wave ibonisa ukuthambekela okuya phansi, abahwebi bangabheka izindawo ezingaba khona zosekelo lapho umkhuba ungase uhlehle khona.
• Ukuhlonza amaphethini entengo: Amagagasi e-sine angasetshenziswa ukukhomba amaphethini entengo ezimakethe. Ngokubheka i-sine wave, abahwebi bangakwazi ukukhomba izindawo ezingaba khona zokusekela nokumelana, kanye nokuhlehliswa komkhuba okungaba khona.
• Ukwenza izibikezelo: Ngokubheka i-sine wave, abahwebi bangenza izibikezelo mayelana nomnyakazo wamanani wesikhathi esizayo. Ngokubheka iziqongo nemikhombe ye-sine wave, abahwebi bangakwazi ukuhlonza izindawo ezingaba khona zokusekela nokumelana, kanye nokuhlehla kwethrendi okungaba khona.
Amagagasi e-Sine angaba yithuluzi eliwusizo labathengisi abafuna ukwenza izibikezelo ezimakethe. Ngokubheka i-sine wave, abahwebi bangakwazi ukukhomba izindawo ezingaba khona zokusekela nokumelana, kanye nokuhlehliswa komkhuba okungaba khona. Ngokusebenzisa amagagasi e-sine, abathengisi bangenza izinqumo ezinolwazi mayelana nokuhweba kwabo futhi bakhulise amathuba abo okuphumelela.
Buyini Ubudlelwano Phakathi kwama-Sine Waves kanye Nokuhlaziywa Kwezobuchwepheshe?
I-Sine wave isetshenziswa ezimakethe zezimali ukuhlaziya ukuziphatha kwamanani nokwenza izibikezelo mayelana nokunyakaza kwentengo okuzayo. Asetshenziswa abahlaziyi bezobuchwepheshe ukuhlonza amathrendi, amazinga okusekela kanye nokumelana, nokuhlonza izindawo ezingaba khona zokungena nokuphuma.
Amagagasi e-Sine awuhlobo lwe-waveform yenkathi ethile, okusho ukuthi ayaphinda ngokuhamba kwesikhathi. Zibonakala ngokuzungeza kwazo okubushelelezi, okuphindaphindayo futhi zisetshenziselwa ukuchaza izinhlobonhlobo zezigigaba kuzibalo, i-physics, ubunjiniyela, kanye nokucubungula amasignali. Ezimakethe zezimali, amagagasi e-sine asetshenziselwa ukukhomba amaphethini aphindayo ekunyakazeni kwentengo.
Ubudlelwano phakathi kwamagagasi e-sine nokuhlaziywa kobuchwepheshe ukuthi amagagasi e-sine angasetshenziswa ukukhomba amaphethini aphindayo ekunyakazeni kwentengo. Abahlaziyi bezobuchwepheshe basebenzisa amagagasi e-sine ukuhlonza amathrendi, amazinga okusekela nawokumelana, kanye nokuhlonza izindawo ezingaba khona zokungena nokuphuma.
Amagagasi e-Sine nawo angasetshenziswa ukwenza izibikezelo mayelana nokunyakaza kwentengo okuzayo. Ngokuhlaziya ukuziphatha kwangaphambilini kwezintengo, abahlaziyi bezobuchwepheshe bangakwazi ukuhlonza amaphethini aphindayo futhi basebenzise lawa maphethini ukuze benze izibikezelo mayelana nokunyakaza kwentengo okuzayo.
Amagagasi e-Sine nawo asetshenziselwa ukukhomba imijikelezo ezimakethe. Ngokuhlaziya ukuziphatha kwezintengo ngokuhamba kwesikhathi, abahlaziyi bezobuchwepheshe bangakwazi ukuhlonza imijikelezo ephindayo futhi basebenzise le mijikelezo ukuze benze izibikezelo mayelana nokunyakaza kwamanani okuzayo.
Kafushane, amagagasi e-sine asetshenziswa ezimakethe zezimali ukuhlaziya ukuziphatha kwamanani nokwenza izibikezelo mayelana nokunyakaza kwamanani okuzayo. Asetshenziswa abahlaziyi bezobuchwepheshe ukuhlonza amathrendi, amazinga okusekela nawokumelana, kanye nokuhlonza izindawo ezingaba khona zokungena nokuphuma. I-Sine wave ingase isetshenziselwe ukwenza izibikezelo mayelana nokunyakaza kwentengo okuzayo ngokuhlaziya ukuziphatha okudlule kwezintengo nokukhomba amaphethini aphindayo nemijikelezo.
Umehluko
I-Sine wave vs i-sine wave eyenziwe
I-Sine Wave vs Simulated Sine Wave:
• I-Sine wave iwumumo wamagagasi oqhubekayo olandela iphethini ye-sinusoidal futhi isetshenziswa kuzibalo, i-physics, ubunjiniyela, nokucubungula isignali.
• Igagasi le-sine elilingiswayo liwukwakheka kwamagagasi okwenziwa okudalwe isiguquli samandla ukuze silingise izici zegagasi le-sine.
• Amagagasi e-sine anefrikhwensi eyodwa nesigaba, kuyilapho amaza e-sine afanisiwe enamaza amaningi nezigaba.
• Amaza anesine asetshenziselwa ukumelela amaza omsindo nezinye izinhlobo zamandla, kuyilapho amaza e-sine afanisiwe asetshenziselwa ukunika amandla izinto zikagesi.
• Amagagasi e-sine akhiqizwa imithombo yemvelo, kuyilapho amaza e-sine afanisiwe akhiqizwa iziguquli zamandla.
• Amaza anesine asetshenziswa ekuhlaziyeni i-Fourier ukuze kufundwe ukusakazeka kwamagagasi, kuyilapho amaza e-sine afanisiwe asetshenziselwa ukunika amandla izinto zikagesi.
• Amaza anesine asetshenziselwa ukumelela amagagasi omsindo, kuyilapho amaza e-sine afanisiwe asetshenziselwa ukunika amandla izinto zikagesi.
I-FAQ mayelana ne-sine wave
Ingabe indawo yonke iyigagasi elinesine?
Cha, indawo yonke ayilona igagasi elinesine. I-sine wave iyijika lezibalo elichaza i-oscillation eshelelayo, ephindaphindayo, futhi iwumumo wamagagasi oqhubekayo onefrikhwensi eyodwa. Nokho, indawo yonke iwuhlelo oluyinkimbinkimbi futhi oluguquguqukayo oluhlala lushintsha futhi luthuthuka.
Umkhathi wakhiwe izingxenye eziningi ezihlukahlukene, ezihlanganisa izinto, amandla, nesikhathi somkhathi. Lezi zingxenye zisebenzelana ngezindlela ezihlukahlukene, okuholela ezinhlobonhlobo zezenzakalo, kusukela ekubunjweni kwemithala kuya ekuguqukeni kokuphila. Indawo yonke ibuye ibuswe imithetho ye-physics, esekelwe ezilinganisweni zezibalo.
Umkhathi akulona igagasi elinesine, kodwa linamagagasi amaningi e-sine. Ngokwesibonelo, amaza omsindo angamaza anesine, futhi akhona endaweni yonke. Amaza okukhanya nawo angamaza anesine, futhi akhona endaweni yonke. Ngaphezu kwalokho, indawo yonke iqukethe ezinye izinhlobo eziningi zamagagasi, njengamaza kazibuthe, amaza adonsela phansi, namagagasi e-quantum.
Umkhathi ubuye wakhiwe ngezinhlayiya eziningi ezihlukene, njengama-proton, ama-neutron, nama-electron. Lezi zinhlayiya zisebenzelana ngezindlela ezihlukahlukene, okuholela ezinhlobonhlobo zezenzakalo, kusukela ekwakhekeni kwama-athomu kuya ekuziphendukeleni kwezinkanyezi.
Sengiphetha, indawo yonke ayilona igagasi elinesine, kodwa iqukethe amaza e-sine amaningi. Lawa magagasi e-sine akhona ngendlela yamagagasi omsindo, amaza okukhanya, nezinye izinhlobo zamagagasi. Umkhathi ubuye wakhiwe yizinhlayiya eziningi ezihlukene ezisebenzelana ngezindlela ezihlukahlukene, okuholela ezinhlobonhlobo zezenzakalo.
Ubudlelwano obubalulekile
Isikhulisi:
• I-amplitude iwukugudluzwa okukhulu kwegagasi le-sine lisuke endaweni yalo yokulingana.
• Ikalwa ngamayunithi ebanga, njengamamitha noma izinyawo.
• Futhi ihlobene namandla amagagasi, nama-amplitude aphezulu anamandla engeziwe.
• I-amplitude ye-sine wave ilingana nempande eyisikwele yobuningi bayo.
• I-amplitude ye-sine wave nayo ihlobene nesigaba sayo, ngama-amplitude aphezulu anokushintsha kwesigaba okukhulu.
Impendulo yevameko:
• Impendulo yefrikhwensi isilinganiso sokuthi isistimu isabela kanjani kumafrikhwensi ahlukene wokufaka.
• Ngokuvamile ikalwa ngama-decibel (dB) futhi iyisilinganiso sokuzuza noma ukuncishiswa kwesistimu kumafrikhwensi ahlukene.
• Ukusabela kwemvamisa yegagasi le-sine kunqunywa ubukhulu kanye nesigaba.
• Igagasi le-sine eline-amplitude ephakeme lizoba nokusabela kwefrikhwensi ephezulu kunaleyo ene-amplitude ephansi.
• Ukusabela kwemvamisa yegagasi le-sine nalo lithintwa isigaba salo, ngezigaba eziphakeme eziholela ekuphenduleni kwamafrikhwensi aphezulu.
I-Sawtooth:
• Igagasi le-sawtooth wuhlobo lwe-waveform yenkathi ethile ekhuphuka kakhulu kanye nokwehla kancane kancane.
• Ivamise ukusetshenziswa ekuhlanganiseni umsindo futhi iphinde isetshenziswe kwezinye izinhlobo zokucutshungulwa kwesiginali yedijithali.
• Igagasi le-sawtooth lifana negagasi le-sine ngoba liwukwakheka kwamagagasi ngezikhathi ezithile, kodwa linomumo ohlukile.
• Igagasi le-sawtooth linokwenyuka okubukhali kanye nokwehla kancane kancane, kuyilapho igagasi le-sine likhuphuka kancane kancane kanye nokwehla kancane kancane.
• Igagasi le-sawtooth linemvamisa ephezulu yokusabela kunegagasi le-sine, futhi livame ukusetshenziswa ekuhlanganiseni komsindo ukuze kwakhe umsindo onamandla kakhulu.
• Igagasi le-sawtooth liphinde lisetshenziswe kwezinye izinhlobo zokucutshungulwa kwesignali yedijithali, njengokuguquguquka kwefrikhwensi kanye nokuguqulwa kwesigaba.
Isiphetho
Amagagasi e-Sine ayingxenye ebalulekile ye-physics, izibalo, ubunjiniyela, ukucubungula amasignali, neminye imikhakha eminingi. Ziwuhlobo lwamagagasi aqhubekayo ane-oscillation ebushelelezi, ephindaphindayo, futhi ngokuvamile asetshenziselwa ukuchaza amaza omsindo, amaza okukhanya, nezinye izinhlobo zamagagasi. Amagagasi e-Sine nawo abalulekile ekuhlaziyeni kukaFourier, okuwenza ahluke ngokuzwakalayo futhi kuwavumela ukuthi asetshenziswe eziguquguqukayo zendawo. Ukuqonda amaza e-sine kungasisiza ukuthi siqonde kangcono ukusakazeka kwamagagasi, ukucubungula isignali, nokuhlaziywa kochungechunge lwesikhathi.
NginguJoost Nusselder, umsunguli we-Neaera kanye nomkhangisi wokuqukethwe, ubaba, futhi ngiyathanda ukuzama izinto ezintsha ngesiginci enhliziyweni yesifiso sami, futhi kanye nethimba lami, bengilokhu ngidala izindatshana zebhulogi ezijulile kusukela ngo-2020. ukusiza abafundi abathembekile ngokurekhoda namathiphu esiginci.
