Bats use echolocation to find their prey. Echolocation is based on the emission

Question

Bats use echolocation to find their prey. Echolocation is based on the emission and detection of waves, specifically ultrasound waves in the frequency range (roughly) 20-120 kHz (van Ryckegham scientificamerican.com, accessed January 2018).

The bat is flying at 10 m/s and chasing a moth. The moth is flying directly away from the bat at 2 m/s.

What is the frequency of the ultrasound wave that arrives at the moth?

Retain all the same properties of the ultrasound wave from Part 2 in order to calculate your answer in Hz to 3 s.f. [Be sure to explain your choices of sign.]

[This wave is reflected off the moth and detected by the bat, which uses the changes in frequency to determine how fast the moth is moving. Some species of horseshoe bat can detect differences in frequency of 0.1 Hz: that's one part in a million, if the bat is emitting 100 kHz.]

Explanation / Answer

Vs = velocity of bat = 10 m/s

VL = velocity of moth = 2 m/s

V = speed of sound = 343 m/s

fL = lower frequency of ultrasound = 20 kHz

f'L = lower frequency heard by moth = ?

fu = upper frequency of ultrasound = 120 kHz

f'u = lower frequency heard by moth = ?

using the equation

f'u = (V - VL )fL /(V - Vs ) = (343 - 2) (120)/(343 - 10) = 128.88 kHz

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