Calculating Doppler Effect: Bat Approaching Wall at 10 m/s with 80 kHz Squeak

[maccha]

A bat is approaching a wall. If it is traveling at 10 m/s and squeaks at 80 kHz, what frequency does it hear in its echo?


f=fo(1 +/- vo/v)
f=fo (1/(1 +/- vs/v))


So I got the right answer by initially making the wall the stationary "observer" and the bat the moving source, and finding the frequency the wall would "hear". Then I made the bat the moving observer and the wall the stationary source- for the frequency emitted by the wall, I used the frequency I found in the first step. I just want to confirm that this makes sense because I feel like I only got the answer by trial and error-so would the wall in fact reflect the sound at the frequency it "heard" from the bat and why?

 

[jbsteele]

Yes, this makes sense. The wall will reflect the sound at the frequency it heard from the bat because the frequency of a reflected sound wave is determined by the properties of the reflecting surface. Since the wall is not a source of sound, it will simply reflect whatever frequency is incident upon it back to the bat.

 

[kerimek]

Your approach to solving this problem is correct. The Doppler effect describes the change in frequency of a wave due to the relative motion of the source and the observer. In this case, the bat is both the source and the observer, and the wall is the stationary object that reflects the sound wave. When the bat is moving towards the wall, the frequency of the sound wave it emits will appear higher to the wall, and when the bat is moving away from the wall, the frequency will appear lower. This is because the sound waves are being compressed or stretched as they travel towards or away from the wall. The wall then reflects the sound wave back to the bat, and the bat perceives this reflected sound wave as an echo. Since the wall is stationary, the frequency of the reflected sound wave will be the same as the frequency that the wall "heard" from the bat. This is why you were able to use the frequency you found in the first step to calculate the frequency of the echo.