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 . Where will the source be located at the instant the sound emitted from P reaches the listener?

Step-by-step solution

Given: Speed of the source, v_s = 22 m s ⁻¹ Speed of sound, v = 330 m s ⁻¹ Distance of listener Q from the origin P , d = 330 m The time taken by the sound to travel from the origin P to the listener Q is: t = d v = 330 330 = 1 s During this time, the distance traveled by the source along the positive X-axis is: x = v_s t = 22 1 = 22 m Therefore, the source will be located at x = 22 m when the sound emitted from P reaches the listener.