Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 21 - Superposition - Exercises and Problems - Page 622: 26

Answer

$\rm Perfect \;destructive.$

Work Step by Step

First of all, we need to sketch the problem as seen below. We need to find what kind of interference is at point $\rm P$. We know that the two waves are out of phase, so their wavelength is the same and is given by $$v=\lambda f$$ $$\lambda=\dfrac{v}{f}=\dfrac{3\times 10^8}{3\times 10^6}=\bf 100\;\rm m\tag 1$$ And we know that the path length difference at some point is given by $$\Delta r=r_2-r_1$$ where $\Delta r=r_2-r_1$ while $r_2=\sqrt{4^2+2^2}$ Now since the two waves are out of phase, then If the path length difference was an integer number of $\lambda$, then the interference is perfectly destructive. And if it was some number of wavelengths and a half, then it is perfectly constructive interference. $$\Delta r=1000-800=200\;\rm m$$ Thus, $$\Delta r=\dfrac{200}{100}\lambda=2\lambda$$ So it is perfectly destructive.
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