Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 16 - Traveling Waves - Exercises and Problems: 12

Answer

(a) $f = 11.5~Hz$ (b) $\lambda = 1.14~m$ (c) $v = 13.1~m/s$

Work Step by Step

We can write the general equation for a wave traveling in the negative x-direction. $D(x,t) = A~sin(kx+\omega t)$ (a) We can find the frequency as: $f = \frac{\omega}{2\pi}$ $f = \frac{72}{2\pi}$ $f = 11.5~Hz$ (b) We can find the wavelength as: $k = \frac{2\pi}{\lambda}$ $\lambda = \frac{2\pi}{k}$ $\lambda = \frac{2\pi~rad}{5.5~rad/m}$ $\lambda = 1.14~m$ (c) We can find the wave speed as: $v = \lambda~f$ $v = (1.14~m)(11.5~Hz)$ $v = 13.1~m/s$
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