Chapter 7.4, Problem 45PPSE

Solution

To find: The physical value to calculate the loudness of the explosion.

Loudness of explosion

102 dB

Given information:

The intensity of a barely audible sound is equal to ${10}^{-12}{\text{W/m}}^2$ . One explosion has an intensity $1.65\times {10}^{-2}{\text{ W/m}}^2$ .

Formula Used:

Loudness in decibels (dB) of a sound is,

  $L=10\log \frac{I}{I_0}$

Calculation:

Here need to calculate the loudness of the explosion. Using this value easily calculate the loudness of the construction work not to exceed 100 dB.

Thus, need loudness of explosion.

Substitute $I=1.65\times {10}^{-2}\text{ and }I={10}^{-12}$ into formula,

  $\begin{array}{c}L=10\log \frac{1.65\times {10}^{-2}}{{10}^{-12}}\\ =10\left(\log 1.65-2\log 10+12\log 10\right)\\ =10\left(0.2175-2+12\right)\\ \approx 102\text{dB}\end{array}$

Thus, the loudness of explosion is 102 dB. It means sound is to high.