## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

In order to hear the chirp at a lower frequency, the bat would have to fly away from us. We can find the required speed of the bat. $f' = \frac{f}{(1+\frac{v_{source}}{v_{snd}})}$ $1+\frac{v_{source}}{v_{snd}} = \frac{f}{f'}$ $\frac{v_{source}}{v_{snd}} = \frac{f}{f'}-1$ $v_{source} = (\frac{f}{f'}-1)~v_{snd}$ $v_{source} = (\frac{25~kHz}{20~kHz}-1)~(343~m/s)$ $v_{source} = 86~m/s$ The bat would need to fly away from us with a speed of 86 m/s.