Mita tana ƙidaya yawan zagayowar da ke faruwa a sakan daya. Kamar igiyoyin ruwa da ke bugun bakin teku ko bugun zuciyarka. Ana auna shi a hertz (Hz). f = 1/T inda T shine lokacin. Hz mafi girma = jijjiga mafi sauri.

• 1 Hz = zagayowar 1 a sakan daya
• Mita = 1 / lokacin (f = 1/T)
• Mita mafi girma = lokacin mafi gajarta
• Mahimmanci ga igiyoyin ruwa, jijjiga, juyawa

Mita da lokacin suna da alaƙa da juna. f = 1/T, T = 1/f. Mita mai girma = lokacin gajere. 1 kHz = lokacin 0.001 s. Wutar AC 60 Hz = lokacin 16.7 ms. Dangantaka ce mai juyawa!

• Lokacin T = lokaci a kowace zagayowar (sakanni)
• Mita f = zagayowar a kowane lokaci (Hz)
• f × T = 1 (koyaushe)
• 60 Hz → T = 16.7 ms

Ga igiyoyin ruwa: λ = c/f (tsawon igiya = gudu/mita). Haske: c = 299,792,458 m/s. 100 MHz = tsawon igiya na 3 m. Mita mafi girma = tsawon igiya mafi gajarta. Dangantaka ce mai juyawa.

• λ = c / f (daidaiton igiya)
• Haske: c = 299,792,458 m/s daidai
• Rediyo: λ a mita zuwa km
• Haske: λ a nanometer

Hz shine awoyin SI (zagayowar/sakan). An sanya masa suna bayan Heinrich Hertz. Gabatarwa daga nano zuwa exa: nHz zuwa EHz. Matakan girma 27! Na duniya ne ga dukkan jijjiga.

• 1 Hz = zagayowar 1/sakan
• kHz (10³), MHz (10⁶), GHz (10⁹)
• THz (10¹²), PHz (10¹⁵), EHz (10¹⁸)
• nHz, µHz, mHz don abubuwan da ke faruwa a hankali

Mita mai kusurwa ω = 2πf (radians/sakan). RPM don juyawa (juyawa/minti). 60 RPM = 1 Hz. Digiri/lokaci don ilimin taurari. Ra'ayoyi daban-daban, manufa daya.

• ω = 2πf (mita mai kusurwa)
• RPM: juyawa a minti daya
• 60 RPM = 1 Hz = 1 RPS
• °/s don juyawa a hankali

Injiniyoyin rediyo suna amfani da tsawon igiya. f = c/λ. 300 MHz = tsawon igiya na 1 m. Infrared: micrometer. Na gani: nanometer. Hasken X-ray: angstrom. Mita ko tsawon igiya—bangare biyu na tsabar kudi daya!

• Rediyo: mita zuwa km
• Microwave: cm zuwa mm
• Infrared: µm (micrometer)
• Na gani/UV: nm (nanometer)

f = 1/T (mita daga lokacin). ω = 2πf (mita mai kusurwa). λ = c/f (tsawon igiya). Dangantaka uku masu muhimmanci. Idan ka san kowane adadi, za ka iya samun sauran.

• f = 1/T (lokacin T a sakanni)
• ω = 2πf (ω a rad/s)
• λ = c/f (c = gudun igiya)
• Makashi: E = hf (dokar Planck)

Duk igiyoyin ruwa suna bin v = fλ (gudu = mita × tsawon igiya). Haske: c = fλ. Sauti: 343 m/s = fλ. f mafi girma → λ mafi gajarta don gudu daya. Mahimmin daidaiton igiya.

• v = f × λ (daidaiton igiya)
• Haske: c = 3×10⁸ m/s
• Sauti: 343 m/s (iska, 20°C)
• Igiyoyin ruwa, igiyoyin girgizar ƙasa—doka daya

Makashin photon: E = hf (tsayayyen Planck h = 6.626×10⁻³⁴ J·s). Mita mafi girma = makashi mafi yawa. Hasken X-ray ya fi karfin makashi fiye da igiyoyin rediyo. Launi = mita a cikin bakan da ake iya gani.

• E = hf (makashin photon)
• h = 6.626×10⁻³⁴ J·s
• X-ray: f mai girma, E mai girma
• Rediyo: f mai ƙanƙanta, E mai ƙanƙanta

Rediyon AM: 530-1700 kHz. FM: 88-108 MHz. TV: 54-700 MHz. WiFi: 2.4/5 GHz. 5G: 24-100 GHz. An inganta kowane tashar don nisa, faɗin tashar, da shiga.

• AM: 530-1700 kHz (nisa mai tsawo)
• FM: 88-108 MHz (inganci mai kyau)
• WiFi: 2.4, 5 GHz
• 5G: 24-100 GHz (gudu mai yawa)

Na gani: 430-750 THz (daga ja zuwa violet). Infrared: <430 THz (na zafi, fiber optics). UV: >750 THz. Hasken X-ray: kewayon EHz. Mitoci daban-daban = siffofi daban-daban, aikace-aikace.

• Ja: ~430 THz (700 nm)
• Kore: ~540 THz (555 nm)
• Violet: ~750 THz (400 nm)
• Infrared: na zafi, fiber (1.55 µm)

Jin ɗan adam: 20-20,000 Hz. Waƙar A4: 440 Hz. Samfurin sauti: 44.1 kHz (CD), 48 kHz (bidiyo). Bidiyo: 24-120 fps. Bugun zuciya: 60-100 BPM = 1-1.67 Hz.

• Sauti: 20 Hz - 20 kHz
• Nootin A4: 440 Hz
• Sautin CD: samfurin 44.1 kHz
• Bidiyo: 24-120 fps

Kowane gabatarwa = ×1000. kHz → MHz ÷1000. MHz → kHz ×1000. Mai sauri: 5 MHz = 5000 kHz.

• kHz × 1000 = Hz
• MHz ÷ 1000 = kHz
• GHz × 1000 = MHz
• Kowane mataki: ×1000 ko ÷1000

f = 1/T, T = 1/f. Masu juyawa. 1 kHz → T = 1 ms. 60 Hz → T = 16.7 ms. Dangantaka ce mai juyawa!

• f = 1/T (Hz = 1/sakanni)
• T = 1/f (sakanni = 1/Hz)
• 1 kHz → lokacin 1 ms
• 60 Hz → 16.7 ms

λ = c/f. Haske: c = 3×10⁸ m/s. 100 MHz → λ = 3 m. 1 GHz → 30 cm. Lissafin hankali mai sauri!

• λ = 300/f(MHz) a mita
• 100 MHz = 3 m
• 1 GHz = 30 cm
• 10 GHz = 3 cm

Tashar FM a 100 MHz. Menene tsawon igiyar?

λ = c/f = (3×10⁸)/(100×10⁶) = mita 3. Yana da kyau ga eriya!

Injin yana juyawa a 1800 RPM. Mita?

f = RPM/60 = 1800/60 = 30 Hz. Lokacin T = 1/30 = 33.3 ms a kowace juyawa.

Haske a tsawon igiya na 600 nm. Wace mita da launi?

f = c/λ = (3×10⁸)/(600×10⁻⁹) = 500 THz = 0.5 PHz. Launi: lemu!

An daidaita sautin kide-kide (A sama da C na tsakiya) zuwa 440 Hz a 1939. Kafin hakan, ya bambanta daga 415-466 Hz! Kiɗan Baroque yayi amfani da 415 Hz. Wasu lokuta kungiyoyin kade-kade na zamani suna amfani da 442-444 Hz don sautin 'mafi haske'.

Idon ɗan adam ya fi jin hasken kore na 555 nm (540 THz). Me yasa? Ƙolin hasken rana kore ne! Juyin halitta ya inganta ganinmu ga hasken rana. Ganin dare yana kaiwa kololuwa a 507 nm (daban-daban kwayoyin halitta).

An zaɓi mita saboda kwayoyin ruwa suna rawar jiki kusa da wannan mita (a zahiri 22 GHz, amma 2.45 yana aiki da kyau kuma yana shiga cikin zurfi). Har ila yau, 2.45 GHz tashar ISM ce wacce ba a ba da lasisi ba. Tashar daya da WiFi—yana iya yin tsangwama!

Bakan lantarki ya kai matakan girma sama da 30. Hasken da ake iya gani (400-700 nm) bai kai octave daya ba! Idan bakan EM ya kasance madannin piano mai maɓalli 90, hasken da ake iya gani zai kasance maɓalli ɗaya ne kawai.

CPU na zamani suna aiki a 3-5 GHz. A 5 GHz, lokacin shine 0.2 nanosecond! Haske yana tafiyar 6 cm ne kawai a cikin zagayowar agogo daya. Wannan shine dalilin da ya sa hanyoyin guntu ke da mahimmanci—jinkirin sigina daga saurin haske ya zama mai mahimmanci.

Hasken gamma mafi karfi daga tushen sararin samaniya ya wuce 10²¹ Hz (zettahertz). Makashin photon >1 MeV. Zai iya ƙirƙirar nau'ikan kwayoyin halitta daga makashi mai tsafta (E=mc²). Kimiyyar lissafi ta zama abin ban mamaki a waɗannan mitoci!

Heinrich Hertz ya tabbatar da wanzuwar igiyoyin lantarki. Ya nuna igiyoyin rediyo. An sanya wa awoyin 'hertz' suna bayansa a 1930.

IEC ta karɓi 'hertz' a matsayin awoyin mita, inda ta maye gurbin 'zagayowar a sakan daya'. Yana girmama aikin Hertz. 1 Hz = zagayowar 1/s.

An karɓi A4 = 440 Hz a matsayin ma'aunin sauti na kide-kide na duniya. Ma'aunin da ya gabata ya bambanta 415-466 Hz.

An karɓi Hertz a hukumance a cikin tsarin SI. Ya zama ma'auni ga duk awoyin mita a duk duniya.

An sake bayyana mita daga saurin haske. c = 299,792,458 m/s daidai. Yana haɗa tsawon igiya da mita daidai.

Mitocin CPU sun kai kewayon GHz. Pentium 4 ya kai 3.8 GHz (2005). Gasar saurin agogo ta fara.

Sake bayyana SI: yanzu an bayyana sakan ta hanyar canjin hyperfine na cesium-133 (9,192,631,770 Hz). Awoyin mafi daidaito!

Hz yana auna zagayowar a sakan daya. RPM yana auna juyawa a minti daya. Suna da alaƙa: 60 RPM = 1 Hz. RPM ya fi Hz girma sau 60. Injin a 1800 RPM = 30 Hz. Yi amfani da RPM don juyawar inji, Hz don abubuwan da suka shafi wutar lantarki/igiyoyin ruwa.

Cikakken zagayowar daya = 2π radians (360°). Idan akwai zagayowar f a sakan daya, to ω = 2πf radians a sakan daya. Misali: 1 Hz = 6.28 rad/s. Dalilin 2π yana canza zagayowar zuwa radians. Ana amfani da shi a kimiyyar lissafi, tsarin sarrafawa, sarrafa sigina.

Yi amfani da λ = c/f inda c shine gudun igiyar. Don haske/rediyo: c = 299,792,458 m/s (daidai). Mai sauri: λ(m) ≈ 300/f(MHz). Misali: 100 MHz → tsawon igiya na 3 m. Mita mafi girma → tsawon igiya mafi gajarta. Dangantaka ce mai juyawa.

An zaɓe shi saboda ruwa yana sha da kyau kusa da wannan mita (ainihin rawar jikin ruwa yana a 22 GHz, amma 2.45 yana shiga cikin kyau). Har ila yau, 2.45 GHz tashar ISM ce wacce ba a ba da lasisi ba—ba a buƙatar lasisi. Tashar daya da WiFi/Bluetooth (yana iya yin tsangwama). Yana aiki da kyau don dumama abinci!

Bakan da ake iya gani: 430-750 THz (terahertz) ko 0.43-0.75 PHz (petahertz). Ja ~430 THz (700 nm), kore ~540 THz (555 nm), violet ~750 THz (400 nm). Yi amfani da THz ko PHz don mitocin haske, nm don tsawon igiyoyin. Ƙaramin yanki na bakan EM!

A fannin lissafi, eh (yana nuna mataki/shugabanci). A fannin kimiyyar lissafi, a'a—mita tana ƙidaya zagayowar, koyaushe tana da kyau. A cikin nazarin Fourier, mitoci marasa kyau suna wakiltar hadaddun haɗe-haɗe. A aikace, yi amfani da adadi masu kyau. Lokacin ma koyaushe yana da kyau: T = 1/f.