PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 11, Problem 57P

(a)

To determine

The intensity of sound when the waves interfere constructively.

(a)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound when the waves interfere constructively is 0.25W/m2_.

Explanation of Solution

Given that the individual intensities of the waves are 0.040W/m2, and 0.090W/m2.

The intensity of the wave is directly proportional to the square of its amplitude.

Let A1 and A2 be the amplitudes of the two waves and I1 and I2 be their respective intensities.

Write the expression for the ratio of the amplitudes of the two waves.

A1A2=I1I2 (I)

Solve equation (I) for A1.

A1=A2I1I2 (II)

Write the expression of the amplitude A of the resultant wave after constructive interference.

A=A1+A2 (III)

Use equation (II) in (III).

A=A2I1I2+A2=A2(I1I2+1) (IV)

Let I be the resultant intensity after constructive interference.

Write the expression for the ratio of the amplitudes of the resultant wave and the wave with amplitude A.

AA2=II2 (V)

Use equation (IV) in (V) and solve for I.

A2(I1I2+1)A2=II2I=I2(I1I2+1)2 (VI)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (VI) to find I.

I=(0.090W/m2)(0.040W/m20.090W/m2+1)2=0.25W/m2

Therefore, the intensity of sound when the waves interfere constructively is 0.25W/m2_.

(b)

To determine

The intensity of sound when the waves interfere destructively.

(b)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound when the waves interfere destructively is 0.010W/m2_.

Explanation of Solution

Write the expression of the amplitude A of the resultant wave after destructive interference.

A=|A1A2| (VII)

Use equation (II) in (VII).

A=|A2I1I2A2|=|A2(I1I21)| (VIII)

Use equation (VIII) in (V) and solve for I.

|A2(I1I21)|A2=II2I=I2|I1I21|2 (IX)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (IX) to find I.

I=(0.090W/m2)|0.040W/m20.090W/m21|2=0.01W/m2

Therefore, the intensity of sound when the waves interfere destructively is 0.010W/m2_.

(c)

To determine

The intensity of sound after interference if the waves are incoherent.

(c)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound after interference if the waves are incoherent is 0.130W/m2_.

Explanation of Solution

Write the expression for the resultant intensity when the incoherent waves interfere.

I=I1+I2 (X)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (X) to find I.

I=0.040W/m2+0.090W/m2=0.130W/m2

Therefore, the intensity of sound after interference if the waves are incoherent is 0.130W/m2_.

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Chapter 11 Solutions

PHYSICS

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