A sound source is moving at 79 m/s toward a stationary listener that is standing

Question

A sound source is moving at 79 m/s toward a stationary listener that is standing in still air. In the reference frame of the source, the listener and the air are moving toward the source at 79 m/s and the source is at rest. Assume that the source emits sound at a frequency of 206 Hz. Assume also that the sound travels through still air at 335 m/s. (a) At what speed, relative to the source, is the sound traveling in the region between the source and the listener? 256 m/s ) Find the wavelength of the sound in the region between the source and the listener. Enter a number (c) Find the frequency heard by the listener. Hz

Explanation / Answer

Part A

Speed of sound with reference frame of source will be = v1 = Vs - Va

Vs = Speed of sound = 335 m/sec

Va = speed of air = 79 m/sec

v1 = 335 - 79 = 256 m/sec

Part B

we know the relation between wavelength and frequency

lambda1 = v/f

v1 = 256 m/sec (from part A)

lambda1 = 256/206 = 1.24 m

Part C

frequency heard by listener will be

f1 = f0*(v1 + v2)/v1

v1 = speed of sound in reference frame of the source = 256 m/sec

v2 = speed of listener = 79 m/sec

f0 = 206 Hz

So,

f1 = 206*(256 + 79)/256

f1 = 269.6 Hz

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