Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 17, Problem 17.11OQ
To determine

The effect on observed frequency due to wind.

Expert Solution & Answer
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Answer to Problem 17.11OQ

The rank of the observed frequency from highest to lowest is (b)>(d)>(a)>(c)>(e) .

Explanation of Solution

Given info: The speeds of the source and observer are 25m/s respectively.

Formula to calculate the observed frequency by observer is,

f'=(c+vocvs)f (1)

Here,

f' is the observed frequency.

c is the speed of the sound in the vacuum.

f is the emitted frequency.

vo is the speed of observer.

vs is the speed of the source.

For case (a) :

The source and observer are stationary. Hence, the speed of the source and observer are 0 respectively.

Substitute 0 for vo and 0 for vs in equation (1) to find f' .

f'=(c+0c0)ff'=f

Thus, the speed of the observed frequency is equal to the real frequency.

For case (b) :

The source is moving toward the stationary observer. Hence, the speed of the source and observe are 25m/s and 0 .

Substitute 0 for vo and 25m/s for vs in equation (1) to find f' .

f'=(c+0c25m/s)ff'=(cc25m/s)f (2)

Assume the observed frequency is f1 instead of f' .

Substitute f' for f1 in equation (2).

f1=(cc25m/s)f (3)

For case (c) :

The source is moving away from stationary observer. Hence, the speed of the source and observe are -25m/s and 0 .

Substitute 0 for vo and -25m/s for vs in equation (1) to find f' .

f'=(c+0c(25m/s))ff'=(cc+25m/s)f (4)

Assume the observed frequency is f2 instead of f' .

Substitute f' for f2 in equation (4).

f2=(cc+25m/s)f (5)

For case (d) :

The observer is moving toward the stationary source. Hence, the speed of the observer and source are 25m/s and 0 .

Substitute 25m/s for vo and 0 for vs in equation (1) to find f' .

f'=(c+25m/sc0)ff'=(c+25m/sc)f (6)

Assume the observed frequency is f3 instead of f' .

Substitute f' for f3 in equation (6).

f3=(c+25m/sc)f (7)

For case (e) :

The observer is moving away from stationary source. Hence, the speed of the observer and source are -25m/s and 0 .

Substitute -25m/s for vo and 0 for vs in equation (1) to find f' .

f'=(c+(25m/s)c0)ff'=(c25m/sc)f (8)

Assume the observed frequency is f4 instead of f' .

Substitute f' for f4 in equation (8).

f4=(c25m/sc)f (9)

Divide the equation (3) by equation (7).

f1f3=(cc25m/s)f(c+25m/sc)f=v2(v2625m2/s2)

Thus, observed frequency for case (b) is greater than case (d) .

f1>f3

Divide the equation (5) by equation (9).

f2f4=(cc+25m/s)f(c25m/sc)f=v2v2625m2/s2

Thus, observed frequency for case (c)  is greater than case (e) .

f2>f4

The rank of the observed frequency from highest to lowest is,

f1>f3>f'>f2>f4(b)>(d)>(a)>(c)>(e)

Conclusion:

Therefore, the rank of the observed frequency from highest to lowest is (b)>(d)>(a)>(c)>(e)

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Chapter 17 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

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