Animals
Bats and the Doppler Effect
Problem Set Solutions
Question1: Hunting Bat
A bat flies at 15 m/s directly toward a mosquito and emits the ultrasound of 50 kHz. The
mosquito flies at 5 m/s directly away from the bat. The speed of sound in air is 340 m/s. What
is the frequency of the ultrasound reflected from the mosquito, which the bat hears?
First consider: The frequency of the sound reflected from the mosquito (in the mosquito’s frame
of reference) is…
1) the same as the frequency of sound received by the mosquito.
2) larger than the frequency of sound received by the mosquito.
3) smaller than the frequency of sound received by the mosquito.
4) dependant on the direction of the velocity of the mosquito.
Question1 Solutions: Hunting Bat
The frequency of the sound reflected from the mosquito (in the mosquito’s frame of reference) is
the same as the frequency of sound received by the mosquito.
Frequency of the ultrasound reaching the mosquito:
f m  f bs
v  vm
340  5
 50 kHz
 51.5 kHz
v  vb
340  15
In the reference frame of the mosquito the frequency of the reflected wave is the same as the
incoming one: 51.5 kHz.
The frequency received by the bat:
fb  f m
v  vb
340  15
 51.5 kHz
 53.0 kHz
v  vm
340  5
The frequency of the ultrasound reflected from the mosquito, which the bat hears, is 53.0 kHz
Janelle Van Dongen 2009/09/21
University of British Columbia Department of Physics and Astronomy