A person carrying a whistle, emitting continuously a note of frequency 272Hz is running towards a reflecting surface with a speed of 18 km/hr. The speed of sound in air is 345 m/s. The number of beats heard by him per second is
Beats are produced here because of the superposition of the direct sound of actual frequency n (equal to 272 Hz) from the whistle and the reflected sound of apparent frequency n’, given by n’ = [(v + w- vL)/(v + w – vS)]n.
[Note that the frequency of the direct sound is unchanged since both the source and listeners are moving together and there is no relative velocity between them].
In the expression for the apparent frequency of the reflected sound, the wind velocity (w) is zero.
The velocity of source (vS) is positive since the source is the reflected sound image of the whistle and this image moves towards the listener.
The velocity of the listener is negative since he is moving towards the reflected image serving as the source. Therefore, n’ = [(v + vL)/(v – vS)]n = [(345+5)/(345-5)]×272 =280Hz. [Note that 18 km/hr = 5m/s]. Number of beats per second = 280 – 272 = 8.