A bat is flitting about in a cave, navigating via ultrasonic bleeps. Assume that the sound emission frequency of the bat is 37.1 kHz. During one fast swoop directly toward aflat wall surface, the bat is moving at 0.027 times the speed of sound in air. What frequency does the bat hear reflected off the wall?NumberUnits

Given that The original frequency of the bat, fs=37.1kHzfs=37100Hz The velocity of the bat…

Answered: A bat is flitting about in a cave,…

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ISBN:9781305952300

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Chapter1: Units, Trigonometry. And Vectors

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A bat is flitting about in a cave, navigating via ultrasonic bleeps. Assume that the sound emission frequency of the bat is 37.1 kHz. During one fast swoop directly toward a
flat wall surface, the bat is moving at 0.027 times the speed of sound in air. What frequency does the bat hear reflected off the wall?
Number
Units

Expert Solution

Step 1

Given that

The original frequency of the bat,

$\begin{array}{l} f_{s} = 37.1 kHz \\ f_{s} = 37100 Hz \end{array}$

The velocity of the bat $v_{b a t} = 0.027 v$ , where v is the velocity of the sound.

The equation for the Doppler shift is,

$\begin{array}{l} f_{o} = \frac{v + v_{o}}{v + v_{s}} f_{s} \\ f_{o} = \frac{1 + \frac{v_{o}}{v}}{1 + \frac{v_{s}}{v}} f_{s} \end{array}$

Here, $f_{o}$ is the observer frequency, $v$ is the velocity of sound, $v_{o}$ is the velocity of the observer, $v_{s}$ is the velocity if the source and $f_{s}$ is the actual frequency of the sound waves.

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