Chapter 8.5, Problem 59PPS

(a)

To determine

To find: The relative intensity of the Macy’s Thanksgiving Day parade with a loudness of 120 decibels.

Answer to Problem 59PPS

The intensity of the sound is ${10}^{12}$ decibels.

Explanation of Solution

Given:

The equation for the loudness in $L$ in decibels is $L=10{\log }_{10}R$ .

The relative intensity of the sound is $R$ .

The given log equation to measure the intensity is $120=10{\log }_{10}R$ .

The loudness is 120 decibels.

Calculation:

Consider the equation for the loudness is,

  $120=10{\log }_{10}R$

Then, solve the equation as,

  $\begin{array}{l}120=10{\log }_{10}R\\ {10}^{12}=R\end{array}$

Thus, the intensity of the sound is ${10}^{12}$ decibels.

(b)

To determine

To find: The ratio of the intensity.

Answer to Problem 59PPS

The ratio of the intensities is ${10}^4$ .

Explanation of Solution

Given:

The level of the sound is 80 decibels.

Calculation:

Consider the loudness is 80 decibel then the intensity of the sound is,

  $\frac{{10}^{12}}{{10}^8}={10}^4$

The ratio of the intensities is,

  $\frac{{10}^{12}}{{10}^8}={10}^4$