Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 24 - The Wave Nature of Light - General Problems - Page 710: 74

Answer

a) Constructive. b) Destructive.

Work Step by Step

a) First of all, we need to find the wavelength of the television signal which is given by $$v=\lambda f$$ Hence, $$\lambda=\dfrac{v}{f}$$ Plugging the known; $$\lambda=\dfrac{3\times 10^8}{75\times 10^6}=\bf 4\;\rm m$$ Now we know that the reflected signal is having180$^\circ$ a phase change. This means that when the signal reached from the station to the receiver with an integer number of wavelengths, then we got a constructive interference if the reflected signal is having an integer number of one-half wavelength, and vice versa. Let's see the number of wavelengths to the receiver from the plane. $$N=\dfrac{y}{\lambda}=\dfrac{122}{4}=\bf 30.5\;\rm wave$$ Therefore, we got $\bf constructive\; interference$ at the receiver. ---- b) By the same approach as we did above, let's see the number of wavelengths to the receiver from the plane while the plane is 22 m (which means that it is above the receiver by 100 m). $$N=\dfrac{y}{\lambda}=\dfrac{100}{4}=\bf 25\;\rm wave$$ Therefore, we got $\bf destructive\; interference$ at the receiver.
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