Chapter 11.5, Problem 62E

(a)

To determine

To Find: The loudness in decibels of such a concert.

Answer to Problem 62E

The absolute magnitude is $1.58$ .

Explanation of Solution

Given:

The loudness of a sound is often given on the decibel (dB) scale. The loudness of a sound $L$ in dB is defined in terms of its intensity $I$ by the equation $L=10\log \frac{I}{I_0}$ where $I_0$ is the minimum intensity audible to the average person (the "threshold of hearing") $1.0\times {10}^{-12}\text{W}/{\text{m}}^2$ .

Calculation:

Consider the loudness formula is,

  $L=10\log \frac{I}{I_0}$

Then, the intensity for the given condition is,

  $\begin{array}{c}L=10\log \frac{I}{1\times {10}^{-12}}\\ =10\left(12\right)\\ =120\text{dB}\end{array}$

(b)

To determine

To Find: The intensity of the whisper when the loudness is of 20 dB

Answer to Problem 62E

The intensity of the whisper is ${10}^{-10}\text{w}/{\text{m}}^2$ .

Explanation of Solution

Consider the loudness formula is,

  $L=10\log \frac{I}{I_0}$

Then, the intensity of the sound formula is,

  $I=I_0{10}^{\frac{L}{10}}$

Then,

  $\begin{array}{c}I=\left(1\times {10}^{-12}\right)\left({10}^{\frac{20}{10}}\right)\\ =\left(1\times {10}^{-12}\right)\left({10}^2\right)\\ ={10}^{-10}\text{w}/{\text{m}}^2\end{array}$