Chapter 12, Problem 73GP

To determine

To Find: The gain in dB.

Answer to Problem 73GP

  $\beta =50\text{ dB}$

Explanation of Solution

Given:

Power out $P_{\text{out}}=\text{1}00\text{ W}$

Power input $P_{\text{in}}=\text{1 mW}=\text{1}\times \text{1}{0}^{-\text{3}}\text{W}$

Formula used:

Write the expression for the sound intensity level.

  $\beta =10\log \left(\frac{P_{\text{out}}}{P_{\text{in}}}\right)$

Here, $P_{\text{out}}$ is the power out,

  $P_{\text{in}}$ is the power input.

Calculation:

Substitute the given data (values) in the formula $\beta$

  $\beta =10\log \left(\frac{P_{\text{out}}}{P_{\text{in}}}\right)$

  $\beta =10\log \left(\frac{100}{1\times {10}^{-3}}\right)\text{ dB}$

  $\beta =50\text{ dB}$

The gain is 50 dB.

Conclusion:

The gain in dB is 50, if a particular stereo puts out 100 W of power for an input 1 mW.