Some bat species eat up to 1,000 mosquitoes in an hour. A bat, flying with a speed of 4.36 m/s, is in pursuit of a mosquito. While in motion, the bat produces a 39.70 kHz sound and hears the sound which is reflected off the mosquito at a frequency of 40.36 kHz. (Assume the speed of sound in air is v = 343 m/s.) How fast is the mosquito flying (in m/s)?
f' = ( v + vo ) / ( v - vo ) x f
where:
f' = observed frequency
f = original frequency at source
v = speed of sound = 343 m/s
vo = speed of observer
vs = speed of source of sound
vm = speed of observer = mosquito speed
f = original frequency at source = 39700 Hz
vs = speed of source of sound = speed of bat = 4.36 m/s;
∴ f' = ( 343 - vm ) / ( 343 - 4.36 ) x39700 = 117.2336( 343 - vm )
Using the doppler equation again for the bat as now being the
receiver of the sound,
vo = speed of observer = 4.36 m/s,
f = original frequency at source = 40591 Hz
v = speed of sound = 343 m/s
vs = speed of source of sound = vm
∴ f' = (343 + 4.36) / (343 + vm) x 117.2336( 343 - vm ) = 40360
Hz
(343 - vm)/(343 + vm) = 0.9911
vm = 1.5324 m/s
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