Calculating Doppler Effect: Bat Approaching Wall at 10 m/s & Squeaking at 80 kHz

[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, the wall would reflect the sound at the frequency it heard from the bat. This is because sound is a wave and waves can be reflected off of surfaces. The frequency of the reflected sound is determined by the frequency of the original sound, so the wall will reflect the sound at the same frequency as it heard from the bat.

 

[kerimek]

Yes, your approach of considering both the bat and the wall as either the moving source or the moving observer is correct. This is because the Doppler Effect is dependent on the relative motion between the source and the observer. In this case, the wall is acting as the stationary source and the bat as the moving observer, so the frequency of the echo heard by the bat will be dependent on its velocity compared to the velocity of sound. Similarly, when the bat is considered as the stationary observer and the wall as the moving source, the frequency of the sound emitted by the wall will be dependent on its velocity compared to the velocity of sound. Both of these frequencies will be different due to the Doppler Effect. The wall will reflect the sound at the frequency it "heard" from the bat because the frequency of the reflected sound is dependent on the frequency of the incident sound and the relative motion between the source and the observer.