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# BIO Horseshoe bats (genus Rhinolophus) emit sounds from

ISBN: 9780321675460 31

## Solution for problem 77P Chapter 16

University Physics | 13th Edition

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Problem 77P

BIO Horseshoe bats (genus ?Rhinolophus?) emit sounds from their nostrils and then listen to the frequency of the sound reflected from their prey to determine the prey’s speed. (The “horseshoe” that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight.) A Rhinolophus flying at speed vbat emits sound of frequency fbat; the sound it hears reflected from an insect flying toward it has a higher frequency frefl. (a) Show that the speed of the insect is where v is the speed of sound. (b) If fbat = 80.7 kHz, frefl = 83.5 kHz, and vbat = 3.9 m/s, calculate the speed of the insect.

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Solution 77P When the insect is moving toward the bat, the apparent frequency heard by it is, f = f ( v + vinsec) …..(1) in bat v vbat When the bat is moving toward the insect, the apparent frequency f refl is, v + vbat f refl = f (in vv )…..(2) insect (a) Now, substituting the value of f in from equation (1) in equation (2), v + v v + v f refl = f bat( insec)( bat) v vbat vv insect f 2 refl= v +vv batv insectv insectbat f bat v vv insectv batv bat insect f refl 2 f bat(v vv insect vv bat + v batv insect) = v(v + v bat) + v insect(v + v bat) f refl frefl f batv(v v bat ) fbatv insectv v bat) = v(v + v bat) + v insect(v + v bat) frefl f refl v insect[ f (v v bat)...

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