Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, 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 flash-light.) A Rhinolophus flying at speed v bat emits sound of frequency f bat ; the sound it hears reflected from an insect flying toward it has a higher frequency f refl .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Let
be the speed of the bat,
the speed of the insect and
the frequency with which the sound waves both strike and are reflected from the insect. The frequencies at which the bat sends and receives the signals are related by

Solving for
,

Letting
and
gives the result.
If
, and V bat
, V insect
.
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