Waves and Sounds - speed of a bat

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A bat chasing an insect emits a 52 kHz chirp and receives an echo at 52.75 kHz, prompting a calculation of its speed gain. The speed of sound in air is given as 342 m/s. The equation used for the Doppler effect was set up correctly, but the calculation for the observer's velocity (vo) yielded a value that didn't align with expectations. The user seeks assistance in resolving the discrepancy in their calculations to determine the bat's speed gain accurately. Clarification on the Doppler effect application is needed for a correct solution.
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Homework Statement



A bat moving at 4.5 m/s is chasing a flying insect insect. The bat emits a 52 kHz chirp and receives back an echo at 52.75 kHz. At what speed is the bat gaining on its prey? Take the speed of sound in air to be 342 m/s.


Homework Equations




f1 = f ((velocity +/- velocity observer)/(velocity +/- velocity source))

The Attempt at a Solution



To start off, I converted 52 kHz to 52,000 Hz and 52.75 kHz

Then my equation looked like:

52750 = 52000 ((342 - vo)/(342-4.5)

I found vo to be .367788 and subtracted that from 4.5 to find the speed gained, but that doesn't seem to work. Can anyone help?
 
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