Figure shows a source of sound moving along X-axis at a speed of 22 m s⁻¹ continuously emitting a sound of frequency 2.0 kHz which travels in air at a speed of 330 m s⁻¹. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the sources crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant?

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Solution

Given:
Velocity of sound in air v = 330 ms⁻¹
Distance travelled by the sound s = 330 m
Frequency of the sound n = 2 kHz
(a) Velocity v = $\frac{s}{t}$

∴ Time t = $\frac{330}{330} = 1 s$

(b) The frequency of sound heard by the listener is 2 kHz.
(Since frequency does not depend on distance.)

(c) s = 22 m (= 22 m/s $\times$ 1 s) away from P on x-axis.

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