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-fifth the car's speed hears a frequency of 420 Hz. What is the speed of the car? Assume the speed of sound in air is 343 m/s 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-fifth the car's speed hears a frequency of 420 Hz. What is the speed of the car? Assume the speed of sound in air is 343 m/s 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-fifth the car's speed hears a frequency of 420 Hz. What is the speed of the car? Assume the speed of sound in air is 343 m/s

Explanation / Answer

this is a question of 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

Frequency of source Fs = 440Hz , Fo = 420 Hz , Vs = x , Vo = x/5

420 = 440 (343 + x/5)/(343 + x )

0.9545 (343+x) = 343+x/5

327.41 + 0.9545 x = 343 + 0.2x

x = 20.66

the speed of the car is 20.66 m/s

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