University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 12 - Fluid Mechanics - Problems - Exercises - Page 391: 12.15

Answer

Damage to the eardrum could start to occur at a depth of 2.8 meters.

Work Step by Step

We can find the pressure on the eardrum that could cause damage. $P = \frac{F}{A}$ $P = \frac{F}{\pi~r^2}$ $P = \frac{1.5~N}{(\pi)(4.1\times 10^{-3}~m)^2}$ $P = 2.84\times 10^4~N/m^2$ We can find the depth $h$ under the water surface with this gauge pressure. $\rho~g~h = P$ $h = \frac{P}{\rho~g}$ $h = \frac{2.84\times 10^4~N/m^2}{(1030~kg/m^3)(9.80~m/s^2)}$ $h = 2.8~m$ Damage to the eardrum could start to occur at a depth of 2.8 meters.
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