Question

A receiver and a source of sonic oscillations of frequency v₀ = 2000 Hz are located on the x axis. The source swings harmonically along that axis with a circular frequency ω and an amplitude a = 50 cm. At what value of ω will the frequency bandwidth registered by the stationary receiver be equal to Δv = 200 Hz? The velocity of sound is equal to v = 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 ω to. Hence