What is the beat frequency heard by the observer when he listens from the positi

Question

What is the beat frequency heard by the observer when he listens from the position A, in front of the car?

What is the beat frequency heard by the observer when he is between the speakers, at B?

C speaker B speaker A

railroad car is going towards A

Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at 12.0 m/s , as shown in the figure below. The speakers have identical sound frequencies of 335Hz . What is the beat frequency heard by the observer when he listens from the position A, in front of the car? What is the beat frequency heard by the observer when he is between the speakers, at B? C speaker B speaker A railroad car is going towards A

Explanation / Answer

(a) When the stationary observer is at point A, the two sounds emitted from the speakers have the same Doppler effect. Therefore, the beat frequency must be 0.
(b) When the observer is at B, one source from one speaker is moving away from him, the other is moving toward him. According to the Doppler effect, we have:
- Moving toward.
f' = f/(1 - vs/v) = 335/(1 - 12/343) = 347.145Hz
- Moving away
f' = f(1 + vs/v) = 335/(1 + 12/343) = 323.676Hz
Therefore, the beat frequency is: fbeat = 347.145 - 323.676 = 23.4689 Hz
(c) When the stationary observer is at point C, the two sounds emitted from the speakers have the same Doppler effect. Therefore, the beat frequency must be 0.

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