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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?