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 20 - Traveling Waves - Exercises and Problems: 26

Answer

(a) $f = 8.6\times 10^8~Hz$ (b) $\lambda = 23~cm$

Work Step by Step

(a) We can find the frequency of the waves as they travel through the air. $f = \frac{v}{\lambda}$ $f = \frac{3.0\times 10^8~m/s}{0.35~m}$ $f = 8.6\times 10^8~Hz$ We know that the frequency of a wave does not change when moving from one medium to another medium. Therefore, the frequency as the signal travels through the glass is $8.6\times 10^8~Hz$ (b) We can find the speed of the signal as it travels through glass. The index of refraction of glass is $n = 1.5$ $v = \frac{c}{n}$ $v = \frac{3.0\times 10^8~m/s}{1.5}$ $v = 2.0\times 10^8~m/s$ We can find the wavelength. $\lambda = \frac{v}{f}$ $\lambda = \frac{2.0\times 10^8~m/s}{8.6\times 10^8~Hz}$ $\lambda = 0.23~m = 23~cm$
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