Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 16 - Waves-I - Questions - Page 471: 7a

Answer

We can rank those choices of $\phi$ according to the average rate at which the waves will transport energy: $0 ~wavelength \gt 0.2 ~wavelength \gt 0.5 ~wavelength$

Work Step by Step

The average rate of power is proportional to $A^2$ where $A$ is the amplitude. If $\phi = 0$, the waves are in phase, so the interference is fully constructive. The amplitude of the resultant wave is the sum of the two amplitudes. If $\phi = 0.2$ a wavelength, the interference is intermediate but closer to fully constructive. The amplitude of the resultant wave is greater than the amplitude of one wave but less than the sum of the amplitudes of both waves. If $\phi = 0.5$ a wavelength, the waves are out of phase by half a wavelength, so the interference is fully destructive. The amplitude of the resultant wave is the difference of the two amplitudes. In this case, the amplitude of the resultant wave is zero. We can rank those choices of $\phi$ according to the average rate at which the waves will transport energy: $0 ~wavelength \gt 0.2 ~wavelength \gt 0.5 ~wavelength$
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