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

Question

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 vbat emits sound of frequency fbat; the sound it hears reflected from an insect flying toward it has a higher frequency frefl.

If the bat emits a sound at a frequency of 80.7kHz  and hears it reflected at a frequency of 83.1kHz  while traveling at a speed of 4.3m/s , calculate the speed of the insect. Use 344m/s  for the speed of sound in air. Express your answer using two significant figures. 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 vbat emits sound of frequency fbat; the sound it hears reflected from an insect flying toward it has a higher frequency frefl.

If the bat emits a sound at a frequency of 80.7kHz  and hears it reflected at a frequency of 83.1kHz  while traveling at a speed of 4.3m/s , calculate the speed of the insect. Use 344m/s  for the speed of sound in air. Express your answer using two significant figures.

Explanation / Answer

vi = v [ fL *(v - vb) - fs*(v + vb)] / [fL * (v - vb) + fs*(v +vb)]
= v * (83.1 * (v-4.3) - 80.7 ( v+4.3))/ [83.1 *(v - 4.3) + 80.7*(v + 4.3)]
v = 344 m/s
vi = 344 * ( 83.1* (344-4.3) - 80.7*(344+4.3) ) / (83.1 *(344 - 4.3) + 80.7*(344 + 4.3))
= 0.74 m/s vi = v [ fL *(v - vb) - fs*(v + vb)] / [fL * (v - vb) + fs*(v +vb)]
= v * (83.1 * (v-4.3) - 80.7 ( v+4.3))/ [83.1 *(v - 4.3) + 80.7*(v + 4.3)]
v = 344 m/s
vi = 344 * ( 83.1* (344-4.3) - 80.7*(344+4.3) ) / (83.1 *(344 - 4.3) + 80.7*(344 + 4.3))
= 0.74 m/s

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