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: 25

Answer

$\rm Perfectly\; destructive.$

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 in phase, so their wavelength is the same and is given by $$v=\lambda f$$ $$\lambda=\dfrac{v}{f}\tag 1$$ And we know that the phase difference at some point is given by $$\Delta \phi=\dfrac{2\pi\Delta r}{\lambda}+\phi_0$$ where $\Delta r=r_2-r_1$ while $r_2=\sqrt{4^2+2^2}$ If the phase difference was an intger number of lambda, then the interference is perfectly constructive. And if is was some number of wavelengths and a half, then it is perfectly destructive. Plugging the known; $$\Delta \phi=\dfrac{2\pi(\sqrt{4^2+2^2}-4)}{\lambda}+0$$ Plugging from (1); $$\Delta \phi=\dfrac{2\pi(\sqrt{4^2+2^2}-4)f}{v}=\dfrac{2\pi(\sqrt{4^2+2^2}-4)(1800)}{340}$$ $$\Delta \phi\approx 2.5(2\pi)\;\rm rad$$ So it is perfectly destructive.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.