A bat,flying at 3.00 m/s toward a wall,emits a chirp at 50.0 kHz.If the wall reflects this sound pulse,what is the frequency of the echo received by the bat? (v_sound = 340 m/s) A) 51.5 kHz B) 51.2 kHz C) 40.8 kHz D) 50.9 kHz

Question

Quizplus · Accepted Answer

The frequency of the sound wave will not change upon reflection, only the direction in which it travels. However, the frequency perceived by the bat will be affected by the Doppler effect. 
Using the formula for the frequency observed by a stationary observer as a source moves towards or away from them: 
f' = (v + vo) / (v +/- vs) * f 
where 
f = frequency of source 
v = velocity of sound 
vo = velocity of observer (stationary for this problem) 
vs = velocity of source 
For the original chirp, f = 50.0 kHz and vs = -3.00 m/s (since it is moving towards the wall). Plugging in the values:
f' = (340 + 0) / (340 - (-3.00)) * 50.0 kHz = 50.9 kHz 
Therefore, the frequency of the echo received by the bat is 50.9 kHz. The correct choice is D.

A Bat,flying at 3