Question

A source emitting a sinusoidal sound wave of frequency 480 Hz travels towards a wall at a speed 15 m –1. Find the ** frequency perceived by an observer moving at a speed 10 ms–1 under the following situations, if the speed of sound in air is 330 m –1: (i) the observer is going away from the source and the wall (Fig. 9.3). (ii) the observer is travelling towards the source and the wall. (iii) the observer is in between the wall and the source, and moving away from the wall. (iv) the observer is in between the wall and the source, and moving towards the wall.

Answer 1

(i) First we consider the sound travelling directly from the source ( *) to the observer (O).

The frequency received by O is

The observer will also receive the sound reflected from the wall. Suppose at any instant, S′ is the image of behind the wall (Fig. 9.3). The image S′ is moving at a speed 15 m –1 towards the observer. We may consider S′ as the source of the reflected sound wave. Thus, the frequency perceived by O due to the reflected wave is

(ii) The frequencies perceived by O due to the waves from the source and the reflected waves are

(iii) The apparent frequencies are

The **** frequency = 518.1 – 487.6 = 30.5 Hz.

(iv) The apparent frequencies are

The **** frequency = 518.1 – 487.6 = 30.5 Hz.