Chapter 12, Problem 17P

To determine

To Calculate: The ratio of amplitudes of the two sounds.

Answer to Problem 17P

The ratio of the amplitudes of two sounds is $1.3$ .

Explanation of Solution

Given:

The given sound level is $2.0\text{dB}$ .

Formula used:

The intensity level is given as,

  $\beta \left(\text{in}\text{dB}\right)=10\log \frac{I}{I_0}$

Here, $I$ is intensity of given sound,

  $I_0$ is the hearing intensity.

And, the intensity is directly proportional to the square of the amplitude.

Calculation:

The sound level is given as,

  $\begin{array}{l}\beta =2.0dB=10\log \frac{I_{2.0}}{I_0}\\ =10\log \frac{A_{2.0}^2}{A_0^2}=20\log \frac{A_{2.0}}{A_0}\\ \Rightarrow \frac{A_{2.0}}{A_0}={10}^{0.1}=1.3\end{array}$

Conclusion:

The amplitudes ratio is $1.3$ .