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A stationary source produces a note of f...

A stationary source produces a note of frequency 1000Hz. An observer in a car moving towards the source measures the frequency of sound as 1057 Hz. Find the speed of the car. What will be the frequency of sound as measured by the observer in the car if the car moves away from the source at the same speed ?

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Data : n = 1000 Hz, `n_(a) = 1057 Hz` v= 350 m/s
(i) when the car moves towards the source of sound ` n_(a) = n ((v+v_(0))/(v))`
` 1057 = 1000 ((350 + v_(0))/350)`
` 1.057 = 1 + v_(0)/350`
The speed of the car, ` v_(0) = 350 xx 0.057 = 19.95 m//s `
(ii) When the car moves away from the source of sound `, n_(a) = n ((v-v_(0))/v)`
` n_(a) = 1000 ((350 -19.95)/350) = 1000 (1- (19.95)/350) = 1000 (1-0.057)`
= `1000 xx 0.943`
943 Hz
The frequency of the sound as measured by the observer in the car ` n_(a) = 943` Hz.
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