Your car horn happens to have the unusual property of emitting a pure tone at a

Question

Your car horn happens to have the unusual property of emitting a pure tone at a frequency of 540 Hz. You drive at 26.0 m/s directly toward a high wall and sound the horn briefly. After a short time, you hear the echo of the sound, after it was reflected by the wall. Assume the speed of sound is 340 m/s.

(a) What is the frequency of the echo, as perceived by a person who is at rest? (Assume the person is between the car and the wall.)

Hz

(b) What is the frequency of the echo, as perceived by you as you drive the car?
Hz

Explanation / Answer

a] For the observer at rest, the wall is stationary and is emitting sound of a certain frequency. The frequency will be:

f = fo [v/v - vs]

f = 540[340/340 - 0] = 540 Hz.

b] Since you are at rest in your frame of reference, for you, the wall is moving towards you at the speed of 26 m/s and is emiting a sound of a certain frequency. Thus, the frequency of the echo as perceived by you will be doppler shifted and will have the value:

f = fo [v/v - vs]

f = 540[340/340 - 26] = 584.71 Hz.

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