College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 11 - Problems - Page 429: 26


$y(x,t) = (0.120~m)~sin~[~(20.9~rad/m)~x+(134~rad/s)~t~]$

Work Step by Step

In general: $y(x,t) = A~sin(k~x+\omega~t)$ It is given that $A = 0.120~m$ We can find $k$: $k = \frac{2\pi}{\lambda}$ $k = \frac{2\pi}{0.300~m}$ $k = 20.9~rad/m$ We can find $\omega$: $v = \lambda~f$ $v = \lambda~\frac{\omega}{2\pi}$ $\omega = \frac{2\pi~v}{\lambda}$ $\omega = \frac{(2\pi)~(6.40~m/s)}{0.300~m}$ $\omega = 134~rad/s$ We can write the equation for the wave: $y(x,t) = (0.120~m)~sin~[~(20.9~rad/m)~x+(134~rad/s)~t~]$
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