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A bat is flitting about in a cave, navig...

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 ?

Text Solution

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Here,the frequency of sound, emitted by the bat, `v =40 kHz`.
velocity of bat, `v_(s) =0.03v,`where v is velocity of sound.
Apparent frequency of sound striking the wall.
`v' = ( v xxv )/(v -v_(s)) =(v)/(v-0.03v)xx40kHz`
`= (40)/(0.97) kHz`
This frequency is reflected by the wall & is received by the bat moving towards the wall, So `v_(s) =0`
`v_(1)= 0.03 v `
`v'= ((v+v_(1))v')/(v) = ((v+0.03v))/(v)= ((40)/(0.97))`
`= ( 1.03)/( 0.97) xx 40kHz`
`= 42.47kHz`
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