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

Question

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Answer 1

Question

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

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Answer 2

Question

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

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Answer 3

Question

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

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Answer 4

Question

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

Answer 6

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

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° and 76.3°_ and 14.1° and 46.8°_ 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 340 m/s for v and 2000 Hz for f in equation (I).

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.

Answer 7

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.

Answer 8

Expert Solution & Answer

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° and 76.3°_ and 14.1° and 46.8°_ respectively.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

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

λ=340 m/s2000 Hz=0.170 m

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

θ=sin−1(mλd) (IV)

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

θ=sin−1((m+12)λd) (V)

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

θ=sin−1((0)(0.170 m)0.350 m)=0°

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

θ=sin−1((1)(0.170 m)0.350 m)=29.1°

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

θ=sin−1((2)(0.170 m)0.350 m)=76.3°

Higher orders have no solution.

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

θ=sin−1(12(0.170 m)0.350 m)=14.1°

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

θ=sin−1(32(0.170 m)0.350 m)=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° and 76.3°_ and 14.1° and 46.8°_ respectively.