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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 40kHz. 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 ultrasonic waves produced by bat get reflected from the wall and hence cn be considered to be coming from imaginary source S., moving with a velocity opposite to that of a bat as shown in the diagram. As per the sign convention `v _(L) = 0.03 v` (whre v = speed of ultrasonic waves) and `v._(S) =-0.03 v. `Now, we have the formula,
`(f _(L))/( v + v _(L)) = (f _(S))/( v + v ._(S))`
`therefore (f _(L))/( v + 0.03v ) = (40)/(v - 0.03 v ) `
`therefore (f _(L))/( 1.03 v ) = (40)/( 0.96v)`
`therefore f _(L) = 40 xx (1.03)/(0.97) = 42.4742kHz`
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