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Mechanical Properties Of Fluids

Question
CBSEENPH11020248

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?

Solution
Ultrasonic beep frequency emitted by the bat, ν = 40 kHz 
Velocity of the bat, vb = 0.03 

where,
 = velocity of sound in air 
The apparent frequency of the sound striking the wall is given as: 
straight nu apostrophe space equals open parentheses space fraction numerator straight nu over denominator straight nu space minus space straight nu subscript straight o end fraction close parentheses space straight nu space

space space space equals space open parentheses fraction numerator straight nu over denominator straight nu space minus space 0.03 space straight nu end fraction close parentheses space straight x space 40 space

space space space equals space open parentheses fraction numerator 40 over denominator 0.97 end fraction close parentheses space kHz 
The frequency is reflected by the stationary wall (vs) toward the bat.
straight nu to the power of apostrophe apostrophe end exponent space equals space open parentheses fraction numerator straight nu space plus space straight nu subscript straight o over denominator straight nu end fraction close parentheses straight nu to the power of apostrophe space

space space space space equals space open parentheses fraction numerator straight nu space plus space 0.03 space straight nu over denominator straight nu end fraction close parentheses space straight x space fraction numerator 40 over denominator 0.97 end fraction space

space space space space equals space open parentheses fraction numerator 1.03 space straight x space 40 over denominator 0.97 end fraction close parentheses

space space space space equals space 42.47 space kHz