Question

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?

Answer 1

Source will be at 22 m

Explanation:

(a) The distance of the listener from the origin, d = 330 m.  

The speed of sound in air, V = 330 $ms^-^1$

The time taken by the sound to reach the listener,  t = $\frac {d}{V} = \frac {330}{330}$ s = 1 second.    

(b) Since the direction of the movement of the source is perpendicular to the line joining the source and the person, hence the speed of the source towards the listener will be zero.  

The same frequency of 2.0 kHz will be heard by the person.    

(c) Since the time to reach the listener = 1 s and the speed of the source = 22 $ms^-^1$.  

Hence at this instant, the source will move 22 m.  

Its position will be  at x = 22 m.