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 the air. What frequency does the bat hear reflected off the wall?

Asked by Pragya Singh | 1 year ago |  180

##### Solution :-

The sound emission frequency of the bat = 40 kHz

The velocity of the bat, vb = 0.03 v

here v is the velocity of the sound in air

The apparent frequency of the sound hitting the wall

f’ =$$(\dfrac{v}{v-v_{b}})f$$

f’ =$$(\dfrac{v}{v-0.03v})\times 40$$

= $$\dfrac{40}{0.97}$$ kHz

The frequency gets reflected by the wall and is received by the bat moving towards the wall.

f” = $$(\dfrac{v+v_{b}}{v})\times f'$$

f” =$$(\dfrac{v+0.03v}{v})\times \dfrac{40}{0.97}$$

=( $$\dfrac{ 1.03 \times 40}{0.97}$$) = 42.47 kHz

Answered by Abhisek | 1 year ago

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