A Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, then liste

Question

A 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 flashlight.) 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 If the bat emits a sound at a frequency of 80.0 kHz and hears it reflected at a frequency of 83.6 kHz while traveling at a speed of 4.3 m/s, calculate the speed of the insect. Use 344 m/s for the speed of sound in air. Express your answer using two significant figures. v =

Explanation / Answer

Vs = speed of sound = 344 m/s

fb = frequency given out by the bat = 80000 Hz

fr = frequency reflected back = 83600 Hz

Vb = velocity of the bat = 4.3 m/s

velocity of insect is given as

Vi = [(Vs - Vb) fr - (Vs + Vb) fb ] (Vs) /[(Vs - Vb) fr + (Vs + Vb) fb]

inserting the values

Vi = [(344 - 4.3) (83600) - (344 + 4.3) (80000) ] (344) /[(344 - 4.3) (83600) + (344 + 4.3) (80000)]

Vi = 3.27 m/s

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