A source of sound moves along the X-axis at a speed of 22 m s ⁻¹ , continuously emitting a sound of frequency 2.0 kHz that 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 source crosses the origin P . What will be the frequency heard by the listener at the instant the sound emitted from P reaches them?

Step-by-step solution

The sound received by the listener was emitted when the source was at the origin P . At this instant, the velocity of the source is directed along the X-axis, while the line joining the source to the listener lies along the Y-axis. The angle between the velocity vector of the source and the line of sight from the source to the listener is 90^ . The apparent frequency f' heard by the listener is given by the Doppler effect formula: f' = f ( v v - v_s ) where v is the speed of sound and v_s is the speed of the source