At rest, a car\'s horn sounds the note A (440 Hz). The horn is sounded while the

Question

At rest, a car's horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car's speed hears a frequency of 413 Hz. (a) Is the cyclist ahead of or behind the car? ahead behind (b) What is the speed of the car? m/s

Explanation / Answer

It is about The Doppler effect : fo=fs(v ± vo/v ± vs) ---> For a source moving toward observer : vs (-) ---> For a source moving taway observer : vs (+) ---> For aobserver moving toward source: vo (+) ---> For aobserver moving away source: vo (-) ----> for stationary vo = vs = 0 fo=fs(v ± vo/v ± vs) fs = 440 Hz fo = 415 Hz vs = + a vo = +1/3 a v = 340 m/s ( the speed of sound wave) 415 = 440 *(340 + 1/3a)/(340 + a) 415/440 (340 + a) = (340 + 1/3a) 0.94(340 + a) = (340 + 1/3a) 319.60 + 0.94a = 340 + 1/3 a (0.94 - 1/3 ) a = 340 - 319.60 a = 33.44 m/s ( it is the speed of the car )

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