Physics for Scientists and Engineers with Modern Physics, Technology Update
Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 37, Problem 11P
To determine

The angles measured from the perpendicular bisector of the line joining the speakers where the distant observer would hear maximum and minimum intensity.

Expert Solution & Answer
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Answer to Problem 11P

The angles measured from the perpendicular bisector of the line joining the speakers where the distant observer would hear maximum and minimum intensity are 0°,29.1°and76.3°_ and 14.1°and46.8°_ respectively.

Explanation of Solution

Write the expression to find the wavelength.

    λ=vf                                                                                                                         (I)

Here, λ is the wavelength, v is the velocity if the sound and f is the frequency.

Write the expression for location of maxima.

    dsinθ=mλ                                                                                                             (II)

Here, d is the distance between the speakers, θ is the angle and m is the order.

Write the expression for location of minima.

    dsinθ=(m+12)λ                                                                                                (III)

Conclusion:

Substitute 340m/s for v and 2000Hz for f in equation (I).

    λ=340m/s2000Hz=0.170m

Write the expression to find the angle of maxima from equation (II).

    θ=sin1(mλd)                                                                                                      (IV)

Write the expression to find the angle of minima from equation (III).

    θ=sin1((m+12)λd)                                                                                             (V)

Substitute 0 for m, 0.170m for λ and 0.350m for d in equation (IV).

    θ=sin1((0)(0.170m)0.350m)=0°

Substitute 1 for m, 0.170m for λ and 0.350m for d in equation (IV).

    θ=sin1((1)(0.170m)0.350m)=29.1°

Substitute 2 for m, 0.170m for λ and 0.350m for d in equation (IV).

    θ=sin1((2)(0.170m)0.350m)=76.3°

Higher orders have no solution.

Substitute 0 for m, 0.170m for λ and 0.350m for d in equation (V).

    θ=sin1(12(0.170m)0.350m)=14.1°

Substitute 1 for m, 0.170m for λ and 0.350m for d in equation (V).

    θ=sin1(32(0.170m)0.350m)=46.8°

Higher orders have no solution.

Therefore, the angles measured from the perpendicular bisector of the line joining the speakers where the distant observer would hear maximum and minimum intensity are 0°,29.1°and76.3°_ and 14.1°and46.8°_ respectively.

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Chapter 37 Solutions

Physics for Scientists and Engineers with Modern Physics, Technology Update

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