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  • 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 toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air.

Q.15.27 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 toward a flat wall surface, the bat is moving at 0.03  times the speed of sound in air. What frequency does the bat hear reflected off the wall ?

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best_answer

Apparent frequency striking the wall and getting reflected is

The frequency emitted by the bats is \nu =40kHz

Speed of sound is v

Speed of bat is 0.03v

\\\nu'=(\frac{v}{v-v_{s}})\nu \\ =\frac{v}{v-0.03v}\times 40kHz\\ =41.237kHz

Frequency of sound as heard by the bat

\\\nu''=(\frac{v+v_{o}}{v})\nu'\\ =\frac{v+0.03v}{v}\times \nu' \\=1.03\times 41.237kHz \\ =42.474kHz

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