stationary source and target approaching?

Question

A sound wave at 1000Hz is sent out from a stationary source toward a target approaching at 20.0m/s. What will be the frequency of the returning signal? Take the speed of sound to be 340m/s.

Answer 1

The frequency received by the target is:

f' = (v + v_t)/(v - v_s) * f
where v is speed of sound, v_o is speed of target (20 m/s), and v_s is speed of source (0 m/s).

Frequency received by source is:

f'' = (v + v_s)/(v - v_t) * f'

Combined, you get:

f'' = (v + v_t)(v + v_s)/[(v - v_s)(v - v_t)]*f

or

f'' = (340 + 20)(340)/[(340)(340 - 20)]*f
= (360)(340)/[(340)(320)]*f
= 360/320 * f
= 1.125 * 1000 Hz
= 1125 Hz