wave(doppler effect) question

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[匿名]

2009-03-03 5:34 am

A police speed check operates by reflecting radio waves of frequency 100 MHz from passing cars.
It is found that the frequency after reception has decreased by 18Hz. Should a speeding ticket by issued if the speed limit is70 kmh^-1.

/.\計黎計去都唔識計架車既speed,有無人可以幫幫忙?

更新1:

但個wave先係去個架車到,再俾架車反彈架喎,咁洗唔洗計左去架車既frequency先,再計返俾架車彈返既frequency? thx你既解答先

回答 (2)

天同

2009-03-04 4:33 am

✔ 最佳答案

There occurs two "frquency shifts". The first one is associated with the moving observer (car), and the second one is associated with the source (reflected wave by the car) moving.
Hence, df/f = 2v/c
where df is the shift in frequency (=18 Hz)
f is the original frequency of the radiowave (= 100x10^6 Hz)
v and c are the speeds of the car and radiowave respectively, with c = 3x10^8 m/s
solve for v, and then change the unit from m/s to km/h. Compare it with 70 km/h.

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hlyung

2009-03-03 6:29 am

f=[c/(v+c)]f0
f0 = 100MHz = 100*10^6 Hz
f = (100*10^6 - 18) Hz
c = 3*10^8 m/s
Substituting and find that v = 54 m/s = 194.4 km/h
so a ticket should be issued.

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