Find the value of time period of oscillation of the source

Question

A receiver and a source of sonic oscillations of frequency 2000Hz are located along the X-axis. The source swings simple harmonically along that axis with an amplitude of 50 cm. If the frequency band-width registered by the stationary receiver is 200Hz. Find the value of the time period of oscillation of the source. (Velocity of sound = 340 m/s).

Answer 1

Obviously the maximum frequency will be heard when the source is moving with maximum velocity towards the receiver and minimum frequency will be heard when the source recedes with maximum velocity. As the source swing harmonically its maximum velocity equals aω. Hence