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 - Page 588: 45

Answer

See the graph below.

Work Step by Step

We know that the sound wave moves from the sonar until it hits the bottom of the ocean and then bounces up again to the sonar. So the distance traveled by the wave during the time $\Delta t$ is twice the depth of the ocean. Hence the depth is given by $$v=\dfrac{d}{\frac{1}{2}\Delta t}$$ $$d=\frac{1}{2}v\Delta t$$ where $v$ is the sound speed in the water which is about 1.5 km/s. $$d=\frac{1}{2}(1.500)\Delta t=\boxed{0.750\Delta t}$$ Using the given data to find the depth at each given point; \begin{array}{|c|c|c|c|} \hline x\;{\rm (km)}& d\;{\rm(km)}&\Delta t\;{\rm (s)}\\ \hline 0 & \color{red}{\bf 4.5} &6\\ \hline 20& \color{red}{\bf 3} &4\\ \hline 40 & \color{red}{\bf 3} &4 \\ \hline 45 & \color{red}{\bf 6} &8 \\ \hline 50& \color{red}{\bf 3} &4\\ \hline 60& \color{red}{\bf 1.5} &2 \\ \hline \end{array} Now we can easily draw the graph but remember to put the data of the depth in negative since the author needs it under the surface of the ocean which is considered as $y=0$
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