Yini ungwaqa?

Encwadini eyedlule, sithole ukuthi umsindo usebenza kanjani. Masiphinde le fomula:

UMSINDO = ITHINI YOMHLABA + WONKE AMA-OVERTON AMANINGI

Ngaphezu kwalokho, njengoba amaJapane encoma izimbali ze-cherry, sizophinde sithande igrafu yokuphendula imvamisa - isici somsindo we-amplitude-frequency (Fig. 1):

Khumbula ukuthi i-eksisi evundlile imele ukuphakama (i-oscillation frequency), futhi i-eksisi eqondile imele ukuphakama (amplitude).

Umugqa ngamunye oqondile uyi-harmonic, owokuqala we-harmonic uvame ukubizwa ngokuthi oyisisekelo. I-Harmonics ihlelwe kanje: i-harmonic yesibili iphakeme izikhathi ezi-2 kunethoni eyisisekelo, eyesithathu ithathu, eyesine ine, njalonjalo.

Ngenxa yobufushane, esikhundleni sokuthi “imvamisa nth harmonic" sizomane sithi "ni-harmonic", futhi esikhundleni sokuthi "imvamisa eyisisekelo" - "imvamisa yomsindo".

Ngakho-ke, uma sibheka impendulo yemvamisa, ngeke kube nzima ngathi ukuphendula umbuzo, yini i-consonance.

Ungabala kanjani ku-infinity?

Ungwaqa ngokwezwi nezwi usho ukuthi “ukukhala okuhlangene”, umsindo ohlangene. Imisindo emibili ehlukene ingazwakala kanjani ndawonye?

Masizidwebe eshadini elifanayo ngaphansi komunye nomunye (Umdwebo 2):

Nansi impendulo: amanye ama-harmonics angaqondana ngokuvama. Kunengqondo ukucabanga ukuthi lapho amafrikhwensi ahambisana kakhulu, imisindo “evamile” iba nemisindo eminingi, futhi ngenxa yalokho, imisindo eyengeziwe iyanda emsindweni walesi sikhawu. Ukunemba ngokuphelele, kubalulekile hhayi nje inani lama-harmonics afanayo, kodwa ingakanani ingxenye yawo wonke ama-harmonics azwakalayo afanayo, okungukuthi, isilinganiso senani lokumatanisa nenani eliphelele lama-harmonics azwakalayo.

Sithola ifomula elula yokubala ungwaqa:

lapho N_isovp inani lama-harmonics afanayo,  N_evamile iyinani eliphelele lama-harmonics omsindo (inani lamaza omsindo ahlukene), kanye nebubi futhi ungwaqa esiwufunayo. Ukuze ulungile ngokwezibalo, kungcono ukubiza inani isilinganiso sokuvama kongwaqa.

Nokho, indaba incane: udinga ukubala N_isovp и N_evamile, hlukanisa omunye nomunye, futhi uthole umphumela oyifunayo.

Inkinga kuphela ukuthi kokubili inani eliphelele lama-harmonics ngisho nenani lama-harmonics afanayo alipheli.

Kwenzekani uma sihlukanisa okungapheli ngokungapheli?

Masiguqule isikali seshadi langaphambilini, “suka” kulo (Umdwebo 3)

Siyabona ukuthi ama-harmonics afanayo ayenzeka kaningi. Isithombe siphindaphindiwe (Fig. 4).

Lokhu kuphindaphinda kuzosisiza.

Kwanele ukubala isilinganiso (1) kwesinye sezinxande ezinamachashazi (isibonelo, kweyokuqala), ngakho-ke, ngenxa yokuphindaphinda kanye nakuwo wonke umugqa, lesi silinganiso sizohlala sinjalo.

Ukuze kube lula, imvamisa yethoni eyisisekelo yomsindo wokuqala (ophansi) izobhekwa njengelingana nobunye, futhi imvamisa yethoni eyisisekelo yomsindo wesibili izobhalwa njengengxenyana engenakuncishiswa.  .

Ake siqaphele kubakaki ukuthi ezinhlelweni zomculo, njengomthetho, kusetshenziswa imisindo eqondile, isilinganiso samafrikhwensi esivezwa ingxenye ethile.  . Isibonelo, isikhawu sesihlanu isilinganiso  , amakwata -  , triton -   njll

Ake sibale isilinganiso (1) ngaphakathi kukanxande wokuqala (Fig. 4).

Kulula kakhulu ukubala inani lama-harmonics afanayo. Ngokusemthethweni, kukhona ezimbili zazo, enye ingowomsindo ophansi, owesibili - kuya phezulu, ku-Fig. 4 amakwe ngokubomvu. Kodwa womabili lawa ma-harmonics azwakala ngemvamisa efanayo, ngokulandelana, uma sibala inani lamafrikhwensi afanayo, kuzoba khona imvamisa eyodwa kuphela.

Ingakanani inani eliphelele lamafrikhwensi omsindo?

Asiphikisane kanje.

Wonke ama-harmonics omsindo ophansi ahlelwe ngezinombolo eziphelele (1, 2, 3, njll.). Ngokushesha nje lapho noma iyiphi i-harmonic yomsindo ophezulu iyinani eliphelele, izohambisana neyodwa ye-harmonics yaphansi. Wonke ama-harmonics omsindo ongenhla ayiziphindaphinda zethoni eyisisekelo , ngakho-ke imvamisa n-th harmonic izolingana ne:

okusho ukuthi, kuzoba inombolo ephelele (kusukela m iyinombolo ephelele). Lokhu kusho ukuthi umsindo ongaphezulu kunxande unama-harmonics ukusuka kwewokuqala (ithoni eyisisekelo) kuye n-o, ngakho-ke, umsindo n amaza.

Njengoba wonke ama-harmonics omsindo ophansi atholakala ngezinombolo eziphelele, futhi ngokusho kuka-(3), ukuqondana kokuqala kwenzeka emvamisa. m, kuvela ukuthi umsindo ophansi ngaphakathi konxande uzonikeza m amaza omsindo.

Kumele kuqashelwe ukuthi imvamisa ehambisanayo m siphinde sibala kabili: lapho sibala amaza omsindo ongenhla nalapho sibala amaza omsindo ongezansi. Kodwa empeleni, i-frequency ingenye, futhi ukuze uthole impendulo efanele, kuzodingeka sisuse imvamisa eyodwa "eyengeziwe".

Ingqikithi yawo wonke amaza omsindo ngaphakathi kukanxande izoba:

Ukufaka u-(2) kanye no-(4) kufomula (1), sithola inkulumo elula yokubala ungwaqa:

Ukuze ugcizelele imisindo esiyibalayo, ungabonisa le misindo kubakaki nebubi:

Usebenzisa ifomula enjalo elula, ungakwazi ukubala ungwaqa wanoma yisiphi isikhawu.

Futhi manje ake sicabangele ezinye izici ze-frequency consonance nezibonelo zokubala kwayo.

Izakhiwo nezibonelo

Okokuqala, ake sibale ongwaqa ukuze uthole izikhawu ezilula futhi siqinisekise ukuthi leyo fomula (6) “iyasebenza”.

Isiphi isikhawu esilula?

Nakanjani prima. Amanothi amabili azwakala ngazwi linye. Eshadini kuzobukeka kanje:

Siyabona ukuthi wonke amaza omsindo ayahambisana. Ngakho-ke, i-consonance kufanele ilingane nalokhu:

Manje ake sishintshe isilinganiso se-unison  kufomula (6), sithola:

Isibalo sihambisana nempendulo "enembile", okufanele ilindelwe.

Ake sithathe esinye isibonelo lapho impendulo enembile isobala ngendlela efanayo - i-octave.

Ku-octave, umsindo ongaphezulu uphakeme izikhathi ezi-2 kunezansi (ngokuvumelana nemvamisa yethoni eyisisekelo), ngokulandelana, kugrafu kuzobukeka kanje:

Kungabonakala kugrafu ukuthi yonke i-harmonic yesibili ihambisana, futhi impendulo enembile ithi: i-consonance ingu-50%.

Masiyibale ngefomula (6):

Futhi futhi, inani elibaliwe lilingana "ne-intuitive".

Uma sithatha inothi njengomsindo ophansi kuya futhi uhlele inani likangwaqa kuzo zonke izikhawu phakathi kwe-octave kugrafu (izikhawu ezilula), sithola isithombe esilandelayo:

Izilinganiso eziphakeme kakhulu zongwaqa ziku-octave, yesihlanu neyesine. Ngokomlando babebhekisela kongwaqa “abaphelele”. Ingxenye yesithathu encane nenkulu, kanye nesithupha encane nenkulu iphansi kancane, lezi zikhathi zibhekwa njengongwaqa “abangaphelele”. Ezinye izikhawu zinezinga eliphansi longwaqa, ngokwesiko ziyingxenye yeqembu lama-dissonance.

Manje sibhala izici ezithile zesilinganiso songwaqa bemvamisa, okuvela kufomula yokubala kwayo:

1. Isilinganiso esiyinkimbinkimbi kakhulu  (inamba eningi m и n), ungwaqa omncane isikhawu.

И m и n kufomula (6) zikunani eliphansi, ngakho-ke, njengoba lezi zinombolo zikhula, isilinganiso songwaqa siyehla.

2. Ungwaqa ophezulu wesikhathi ulingana nongwaqa ophansi wesikhathi.

Ukuze sithole isikhawu esiphansi esikhundleni sokuphumula, sidinga isilinganiso   eguqulayo m и n. Kodwa kufomula (6), akukho lutho oluzoshintsha kusuka esikhundleni esinjalo.

3. Isilinganiso se-consonance yefrikhwensi yesikhawu asincikile ekutheni siyakha ngaliphi inothi.

Uma ususa womabili amanothi ngesikhawu esifanayo phezulu noma phansi (isibonelo, yakha okwesihlanu hhayi kunothi kuya, kodwa kusukela kunothi ре), bese kuba isilinganiso  phakathi kwamanothi ngeke kushintshe, futhi ngenxa yalokho, isilinganiso semvamisa yongwaqa sizohlala sinjalo.

Singanikeza ezinye izici zeconsonance, kodwa okwamanje sizozikhawulela kulokhu.

I-Physics namazwi

Umfanekiso 7 usinika umbono wokuthi ungwaqa osebenza kanjani. Kodwa ingabe yile ndlela esibona ngayo ngempela ukuvumelana kwezikhawu? Ingabe bakhona abantu abangawathandi ongwaqa abaphelele, kodwa ukuvumelana okungavumelani kakhulu kubonakala kumnandi?

Yebo, abantu abanjalo bakhona ngempela. Futhi ukuze uchaze lokhu, imiqondo emibili kufanele ihlukaniswe: ukuvumelana komzimba и ungwaqa ozwakalayo.

Konke esixoxe ngakho kulesi sihloko kuhlobene nokuvumelana komzimba. Ukuze ubale, udinga ukwazi ukuthi umsindo usebenza kanjani, nokuthi ukudlidliza okuhlukene kuhlanganisa kanjani. Ungwaqa womzimba uhlinzeka ngezimfuneko zongwaqa okucatshangwayo, kodwa awukunqumi ngo-100%.

Ungwaqa ozwakalayo unqunywa kalula. Umuntu uyabuzwa ukuthi uyawuthanda yini lo ngwaqa. Uma kunjalo, kuye kuwungwaqa; uma kungenjalo, yi-dissonance. Uma enikezwa izikhawu ezimbili zokuqhathanisa, khona-ke singasho ukuthi enye yazo izobonakala kumuntu okwamanje ihambisana kakhulu, enye incane.

Ingabe ungwaqa ocatshangwayo ungabalwa? Ngisho noma sicabanga ukuthi kungenzeka, khona-ke lesi sibalo sizoba yinkimbinkimbi kakhulu, sizohlanganisa okungapheli okungapheli - okungapheli komuntu: isipiliyoni sakhe, izici zokuzwa kanye namakhono obuchopho. Lokhu okungapheli akulula kakhulu ukubhekana nakho.

Nokho, ucwaningo kule ndawo lusaqhubeka. Ikakhulukazi, umqambi u-Ivan Soshinsky, ohlinzeka ngomusa izinto zomsindo kulawa manothi, usungule uhlelo ongakha ngalo imephu ngayinye yombono wongwaqa kumuntu ngamunye. Isayithi elithi mu-theory.info liyathuthukiswa okwamanje, lapho noma ubani angahlolwa futhi athole izici zokuzwa kwakhe.

Kodwa-ke, uma kukhona ungwaqa obonwayo, futhi uhlukile kowomzimba, liyini iphuzu ekubaleni okwakamuva? Singawuhlela kabusha lo mbuzo ngendlela eyakhayo: le miqondo emibili ihlobana kanjani?

Ucwaningo lukhombisa ukuthi ukuhlobana phakathi kongwaqa okujwayelekile kanye nongwaqa womzimba kukuhleleka okungama-80%. Lokhu kusho ukuthi umuntu ngamunye angaba nezakhe izici, kodwa i-physics yomsindo yenza umnikelo omkhulu encazelweni yongwaqa.

Yiqiniso, ucwaningo lwesayensi kule ndawo lusesekuqaleni. Futhi njengesakhiwo somsindo, sithathe imodeli elula yama-harmonics amaningi, futhi ukubalwa kongwaqa kwasetshenziswa okulula kakhulu - imvamisa, futhi akuzange kucabangele izici ezihlukile zomsebenzi wobuchopho ekucubunguleni isignali yomsindo. Kodwa iqiniso lokuthi ngisho nangaphakathi kohlaka lokwenziwa lula okunjalo izinga eliphezulu kakhulu lokuhlobana phakathi kwethiyori nokuhlola liye latholakala likhuthaza kakhulu futhi lishukumisa ucwaningo olwengeziwe.

Ukusetshenziswa kwendlela yesayensi emkhakheni wokuvumelana komculo akukhawulelwe ekubalweni kongwaqa, kuphinde kuveze imiphumela ethokozisayo.

Ngokwesibonelo, ngosizo lwendlela yesayensi, ukuvumelana komculo kungavezwa ngemidwebo, kuboniswe ngeso lengqondo. Sizokhuluma ngokuthi singakwenza kanjani lokhu ngokuzayo.

Umbhali - Roman Oleinikov