Chapter 3.3, Problem 85E

To determine

To calculate: The intensity of sound in decibel for the given scenario.

Answer to Problem 85E

  $60\text{ decibel}$ .

Explanation of Solution

Given information:

The number of decibel and intensity of sound is given by −

  $\beta =10\log \left(\frac{I}{{10}^{-12}}\right)$ ;where $\beta$ is number of decibel and $I$ is intensity of sound in watt per square meter.

Intensity of sound is given as ${10}^{-6}$ watt per square meter.

Calculation:

Intensity of sound is given as ${10}^{-6}$ watt per square meter.

So, the number of decibel of sound will be given as-

  $\begin{array}{l}\beta =10\log \left(\frac{I}{{10}^{-12}}\right)\\ \Rightarrow \beta =10\log \left(\frac{{10}^{-6}}{{10}^{-12}}\right)\\ \Rightarrow \beta =10\log {10}^6\\ \Rightarrow \beta =10\times 6\log 10\\ \Rightarrow \beta =60\times 1\left\{\text{Since, }\log 10=1\right\}\\ \Rightarrow \beta =60\text{ decibel}\end{array}$

Hence, intensity of sound in decibel is $60\text{ decibel}$ .