Chapter 12, Problem 69GP

To determine

To Calculate:The resultant sound level.

Answer to Problem 69GP

The resultant sound level for the given sound levels is $88.19\text{ dB}$ .

Explanation of Solution

Given:

Sound level $\left(L_1\right)=82\text{ dB}$ .

Sound level $\left(L_2\right)=87\text{ dB}$ .

Formula used:

  $L_1=10\log \left(\frac{I_1}{I_0}\right)$

  $L_2=10\log \left(\frac{I_2}{I_0}\right)$

Here,

  $L_1,L_2$ is loudness of sound,

  $I_1,I_2$ is sound intensity,

  $I_0$ is threshold intensity.

Combined loudness is

  $L=\log (L_1+L_2)$

Here,

  $L$ is combined loudness.

Calculation:

Determine the loudness of sound by taking log base 10

Loudness of the sound $L_1=10\log \left(\frac{I_1}{I_0}\right)$

  $L_1=10\log \left(\frac{82}{10}\right)$

  $L_1=158489319.2$

Loudness of the sound $L_2=10\log \left(\frac{I_2}{I_0}\right)$

  $L_2=10\log \left(\frac{87}{10}\right)$

  $L_2=501187233.6$

Now, combining together applying the log and multiply with 10.

  $L=\log (L_1+L_2)$

  $L=88.19\text{ dB}$

The resultant sound level is $88.19\text{ dB}$ .

Conclusion:

The resultant sound level for the given sound levels is $88.19\text{ dB}$ .