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Physics / College Physics 1 / Chapter 17 / Problem 26

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

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An 8-hour exposure to a sound intensity level of 90.0 dB

Chapter 17, Problem 26

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QUESTION:

Problem 26PE

An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

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QUESTION:

Problem 26PE

An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

ANSWER:

Solution 26PE

Prolong exposure to the high intensity sound may cause temporary or permanent damage to the hearing system.

The expression to find the intensity level of sound is,

$\beta{}$ = (10 dB) ${log}_{10}$ ( $\frac{I}{{I}_{0}}$ )

Rearrange the expression,

$\frac{\beta{}}{10\ dB}$ = ${log}_{10}$ ( $\frac{I}{{I}_{0}}$ )

Here $\beta{}$ is sound in decibel, $I$ is intensity of sound and ${I}_{0}$ is reference intensity of sound.

Substitute, 90 dB for $\beta{}$ and ${10}^{-12}w/$ ${m}^{2}$ for ${I}_{0}$ in the expression of intensity level of sound,

$\frac{(90\ dB)}{10\ dB}$ = ${log}_{10}$ $\left({\frac{I}{{10}^{-12}w/{m}^{2}}}\right)$

9 = ${log}_{10}$ $\left({\frac{I}{{10}^{-12}w/{m}^{2}}}\right)$

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