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Chapter 16: Q. 43 (page 452)

A bat locates insects by emitting ultrasonic “chirps” and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?

Short Answer

Expert verified

The bat should fly at the speed of86m/s away from you.

Step by step solution

01

Given information

The frequency of bat chirps is f0=25kHz=25000Hz

A bat must fly away from you so that the chirp frequency observed by you is less than 25 kHz, that is, f-=20kHz=20000Hz.

Speed of sound in air isv=343m/s.

02

Speed of bat

Doppler effect for receding source is given byf-=f01+vsv.

Substitute the given values

20000=250001+vs343vs343=1.25-1vs=0.25×343≈86m/s

Therefore, the bat should fly at the speed of 86m/saway from you.

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