Misalan Tambayoyin Tattaunawar Microwave
Microwaves wani ɓangare ne na ƙarfin lantarki mai tsawon tsayi daga 1 mm zuwa 1 m. Ana amfani da waɗannan raƙuman ruwa akai-akai a cikin fasahohin zamani daban-daban, kamar sadarwa mara waya, radar, ilmin taurari, da kayan aikin gida kamar tanda na microwave. Ganin mahimmancin aikace-aikacen microwave, yana da mahimmanci ga ɗalibai, musamman waɗanda suka ƙware a fannin kimiyyar lissafi ko injiniyanci, su fahimci muhimman abubuwan da ke cikin microwaves, gami da yadda ake magance matsalolin da suka shafi su. Wannan labarin zai tattauna misalai da yawa na matsaloli kuma ya tattauna microwaves.
Tambaya ta 1: Tsawon Raƙumi da Yawansa
Tambaya:
Ganin cewa microwave yana da mita na 10 GHz, ƙididdige tsawon microwave ɗin. (Yi amfani da saurin haske c = 3 x 10^8 m/s)
Tattaunawa:
Da farko dai, muna tuna da alaƙar da ke tsakanin tsawon tsayi (λ), mita (f), da kuma saurin haske (c):
\[ c = \lambda \cdot f \]
Za mu iya ko maimaita wannan dabarar don nemo tsawon tsayi (λ):
\[ \lambda = \frac{c}{f} \]
Idan aka yi la'akari da mita (f) = 10 GHz = 10 x 10^9 Hz, da kuma saurin haske (c) = 3 x 10^8 m/s, mun haɗa waɗannan dabi'u guda biyu cikin dabarar:
\[ \lambda = \frac{3 \sau 10^8 \, \text{m/s}}{10 \sau 10^9 \, \text{Hz}} \]
\[ \lambda = 0.03 \, \text{m} \]
Don haka, tsawon microwave ɗin shine mita 0,03 ko 3 cm.
Tambaya ta 2: Watsa Wuta da Nisa
Tambaya:
Mai watsa microwave yana fitar da ƙarfin 50 W. A ƙididdige ƙarfin microwave a nisan mita 2 daga tushen watsawa, idan aka yi la'akari da yaduwar isotropic.
Tattaunawa:
Don ƙididdige ƙarfi, muna amfani da lissafin yanki na wutar lantarki a kowace naúrar:
\[ I = \frac{P}{A} \]
P shine ƙarfin (50 W) kuma A shine yankin saman wani yanki mai radius na mita 2:
\[ A = 4 \pi r^2 \]
Shigar da ƙimar r = mita 2 a cikin dabarar yanki:
\[ A = 4 \pi (2 \, \text{m})^2 \]
\[ A = 16 \pi \, \text{m}^2 \]
Sannan a lissafta ƙarfin:
\[ I = \frac{50 \, \text{W}}{16 \pi \, \text{m}^2} \]
Lissafin ƙimomin lambobi:
\[ I \kimanin \frac{50}{50.265} \]
\[ I \kimanin 0.995 \, \text{W/m}^2 \]
Don haka, ƙarfin microwave a nisan mita 2 daga tushen watsawa shine kusan 0.995 W/m².
Tambaya ta 3: Tasirin Doppler a cikin Microwaves
Tambaya:
Mota tana tafiya a gudun kilomita 108/h (mita 30/s) tana kusantar na'urorin radar masu watsa microwaves a mita 5 GHz. Lissafa mitar da radar ke karɓa idan saurin na'urar microwave shine saurin haske.
Tattaunawa:
Yi amfani da tasirin Doppler don mitar da aka karɓa (f'):
\[ f' = f \left(\frac{c + v}{c}\right) \]
Ina:
– f' = mitar da aka karɓa
– f = Mitar tushe = 5 GHz = 5 x 10^9 Hz
– c = gudun haske = 3 x 10^8 m/s
– v = saurin abin hawa = 30 m/s
Sauya dabi'u cikin dabarar:
\[ f' = 5 \sau 10^9 \left(\frac{3 \sau 10^8 + 30}{3 \sau 10^8}\dama) \]
\[ f' \kimanin sau 5 10^9 \left(1 + \frac{30}{3 \sau 10^8}\right) \]
\[ f' \kimanin sau 5 10^9 \left(1 + 1 \sau 10^{-7}\right) \]
\[f' \kimanin sau 5 10^9 \sau 1.0000001 \]
\[ f' \kimanin 5.0000005 \sau 10^9 \]
\[ f' \approx 5.0000005 \, \text{GHz} \]
Don haka, mitar da radar ke karɓa tana kusa da 5.0000005 GHz.
Tambaya ta 4: Shan Ƙarfi ta Kayan Aiki
Tambaya:
Wani abu yana shan ƙarfin microwave 2 W lokacin da ƙarfin raƙuman ruwa ya kai 10 W/m². Lissafa yankin saman kayan.
Tattaunawa:
Yi amfani da alaƙar da ke tsakanin ƙarfin sha da yankin saman da ƙarfi:
\[ P = I \cdot A \]
Maye gurbin dabi'un da aka sani:
\[ 2 \, \text{W} = 10 \, \text{W/m}^2 \cdot A \]
Maganin A:
\[ A = \frac{2 \, \text{W}}{10 \, \text{W/m}^2} \]
\[ A = 0.2 \, \rubutu{m}^2 \]
Saboda haka, yankin saman kayan shine 0,2 m².
Tambaya ta 5: Tsarin Tunani da Tsangwama
Tambaya:
Eriya biyu na microwave suna fitar da raƙuman raƙuman tsayi na santimita 6 a cikin alkibla ɗaya. Idan nisan da ke tsakanin eriya ya kai santimita 12, a wane lokaci ne tsangwama mai gina jiki ta fara faruwa?
Tattaunawa:
Tsangwama mai gina jiki yana faruwa ne lokacin da bambancin hanya tsakanin tushen biyu shine k = ±nλ (n lamba ce mara sifili wacce ta haɗa da 0). A karon farko tsangwama mai gina jiki (n=1):
\[ d = n \lambda/2 \]
Tunda nisan eriya shine 12 cm kuma tsawon tsayin shine 6 cm, bambancin hanya don tsangwama na farko mai ginawa yana faruwa a:
\[ d = n (\lambda/2) \]
Don haka:
\[ 12 = sau 1 (6/2) \]
Don haka nisan da ke wurin shine:
\[ 12 = 1 \sau 3 \]
Domin wannan lissafi yana da alaƙa da samuwar tsarin tsangwama akan abin da yake gabaɗaya, to daga zato mun tsara a kan layin tsakiya na nisan daga tushe ko hanyar bisa ga wanda ba hanya ba, wato matsayin polar na layin bin diddigi wanda ba shi da alaƙa da tsarin matsayi da aka ɗauka.
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Waɗannan su ne wasu misalan matsalolin microwave da kuma yadda za a magance su. Ta hanyar fahimtar da kuma saba da magance irin waɗannan matsaloli, ana fatan zai fi sauƙi a gare ku ku fahimci kuma ku yi amfani da ra'ayoyin microwave a fannoni daban-daban na kimiyya da fasaha.
