As shown in the figure, 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 . Determine the time at which the sound emitted from the source at P reaches the listener Q .

Step-by-step solution

The sound is emitted when the source crosses the origin P . According to the given information, the source is at P at time t = 0 . The distance between the origin P and the listener Q is d = 330 m . The speed of sound in air is v = 330 m s ⁻¹ . Note that the speed of sound in a medium is independent of the speed of the source. The time taken for the sound to travel from P to Q is given by: t = Distance Speed of sound t = 330 m 330 m s ⁻¹ = 1 s Since the sound was emitted at t = 0 , it reaches the listener Q at t =