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: 48

Answer

They will have to drill 800 meters into the granite.

Work Step by Step

We can find the time $t_w$ for the sound wave to travel through 1000 meters of water (down and back up). $t_w = \frac{d_w}{v_w}$ $t_w = \frac{1000~m}{1500~m/s}$ $t_w = 0.67~s$ We can find the time $t_g$ the sound wave spent traveling in the granite. $t_g = t - t_w$ $t_g = 0.94~s - 0.67~s$ $t_g = 0.27~s$ We can find the total distance the sound wave traveled through granite (down and back up). $d_g = v_g~t_g$ $d_g = (5950~m/s)(0.27~s)$ $d_g = 1600~m$ Since the thickness of the granite is half the total distance, they will have to drill 800 meters into the granite.
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