Waves

Question : 27

Total: 27

A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly towards a flat wall surface, the bat is moving at 0.03 times the speed of the sound in air. What frequency does the bat hear reflected off the wall?

Solution:

Here, υ=40‌kHz,
speed of sound in air, v=340ms–1
∴ v′= speed of bat
=0.03×v =0.03×340=10.20ms–1

The bat moving towards wall acts as a moving source and for the sound waves reflected from the wall, it acts as a moving observer. Thus the source and observer are approaching each other with same speed.
i.e. vs=v0=v′=10.2ms−1
Thus apparent frequency of the reflected sound waves heard by the bat is given by
υ′=

v+v0

v−vs

×υ=

340+10.2

340−10.2

×40‌kHz
=

350.2

329.8

×40=42.47‌kHz

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