need help with following A jet flies directly towards an observer at a speed of 900 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s.a. What frequency is received by the observer?b. What frequency does the observer receive as the plane flies directly away from them?

Whenever there is a relative motion between an observer and a distant sounding source, the frequency…

Answered: A jet flies directly towards an…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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need help with following

A jet flies directly towards an observer at a speed of 900 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s.
a. What frequency is received by the observer?
b. What frequency does the observer receive as the plane flies directly away from them?

Expert Solution

Step 1

Whenever there is a relative motion between an observer and a distant sounding source, the frequency of the sound wave as heard by the observer is different from its true frequency. This is known as Doppler effect in Sound waves.
The apparent frequency as heard by stationary observer when the source is moving towards the observer is given by-
$f = f_{0} (\frac{v}{v - u_{s}})$
where,
$f is apparent frequency f_{0} is true frequency v is speed of sound u_{s} is speed of source$
The apparent frequency as heard by stationary observer when the source is moving away from the observer is given by-
$f = f_{0} (\frac{v}{v + u_{s}})$

Step 2

(a)

Speed of source is, $u_{s} = 900 km / h = 250 m / s$
Actual frequency of sound is, $f_{0} = 3500 Hz$
Speed of sound is, $v = 342 m / s$

Therefore, frequency received by observer is given by-
$\Rightarrow f = f_{0} (\frac{v}{v - u_{s}}) \Rightarrow f = 3500 \times (\frac{342}{342 - 250}) \Rightarrow f = 13010.86 Hz$

(b)

Frequency heard by observer when the jet flies directly away them is given by-
$f = f_{0} (\frac{v}{v + u_{s}}) f = 3500 \times (\frac{342}{342 + 250}) f = 2021.95 Hz$

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