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 'horseshoe' bat 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 80.9 ({ m kHz}) and hears it reflected at a frequency of 84.0 ({ m kHz}) while traveling at a speed of 4.0 ({ m m/s}) , calculate the speed of the insect.

Use 344 ({ m m/s}) for the speed of sound in air. Express your answer using two significant figures.

.

Explanation / Answer

Source Frequency , f1 = 80.9 Khz

Frequency heard by the insect:
f2 = f1*(c + v_insect)/(c - v_bat)

This frequency is "bounced" back, so essentially re-emitted at the same frequency.
The frequency heard by the bat will be:

f3 = f2*(c + v_bat)/(c - v_insect)

Therefore,
f3 =  f1*(c + v_insect)/(c - v_bat) * (c + v_bat)/(c - v_insect)

Where,
f3 = 84 Khz
f1 = 80.9 khz
c = 344 m/s
v_bat = 4.0 m/s
v_insect = ?

84 = 80.9*(344 + v_insect)/(344 -4) * (344 + 4)/(344 - v_insect)
Solving for v_insect
v_insect = 2.47 m/s

Speed of Insect with which is it moving towards the Bat, v_insect = 2.5 m/s

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.