Concept explainers
(a)
The intensity of sound when the waves interfere constructively.
(a)
Answer to Problem 57P
The intensity of sound when the waves interfere constructively is
Explanation of Solution
Given that the individual intensities of the waves are
The intensity of the wave is directly proportional to the square of its amplitude.
Let
Write the expression for the ratio of the amplitudes of the two waves.
Solve equation (I) for
Write the expression of the amplitude
Use equation (II) in (III).
Let
Write the expression for the ratio of the amplitudes of the resultant wave and the wave with amplitude
Use equation (IV) in (V) and solve for
Conclusion:
Substitute
Therefore, the intensity of sound when the waves interfere constructively is
(b)
The intensity of sound when the waves interfere destructively.
(b)
Answer to Problem 57P
The intensity of sound when the waves interfere destructively is
Explanation of Solution
Write the expression of the amplitude
Use equation (II) in (VII).
Use equation (VIII) in (V) and solve for
Conclusion:
Substitute
Therefore, the intensity of sound when the waves interfere destructively is
(c)
The intensity of sound after interference if the waves are incoherent.
(c)
Answer to Problem 57P
The intensity of sound after interference if the waves are incoherent is
Explanation of Solution
Write the expression for the resultant intensity when the incoherent waves interfere.
Conclusion:
Substitute
Therefore, the intensity of sound after interference if the waves are incoherent is
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