Chapter 12, Problem 13P

(a)

To determine

To Calculate: The power output of the sound.

Answer to Problem 13P

The power output of the sound from speaking a person in normal conversation is $9\times {10}^{-6}\text{W}$ .

Explanation of Solution

Given:

The intensity in normal conversation is, $3\times {10}^{-6}\text{}\text{}\text{}\raisebox{1ex}{$\text{W}$}\!\left/ \!\raisebox{-1ex}{${\text{m}}^{\text{2}}$}\right.$ and distance is $\text{5}0\text{cm}$ .

Formula used:

The intensity is expressed as,

  $I=\frac{P}{A}$

Here, $P$ is the power,

  $A$ is the area of cross-section.

Calculation:

By using the above formula, the power is,

  $I=\frac{P}{A}\Rightarrow P=I\times A=I\times \left(4\pi r^2\right)$

Substitute the given values in this formula,

  $\begin{array}{l}P=\left(3\times {10}^{-6}\raisebox{1ex}{$\text{W}$}\!\left/ \!\raisebox{-1ex}{${\text{m}}^{\text{2}}$}\right.\right)\times 4\times 3.14\times {\left(0.50\text{m}\right)}^2\\ =9.4\times {10}^{-6}\text{W}\\ =9\times {10}^{-6}\text{W}\end{array}$

Conclusion:

The power output is $9\times {10}^{-6}\text{W}$ .

(b)

To determine

To Calculate: The number of persons.

Answer to Problem 13P

  $1\times {10}^7$ number of people would produce a total sound output of $\text{1}00\text{W}$ .

Explanation of Solution

Given:

Total sound power output, $100\text{W}$

Calculation:

As per the part A, $9\times {10}^{-6}\text{W}$ power output produces by 1 person. Therefore, the number of peoples is determined if the total sound output is given,

  $100\text{W}\times \left(\frac{1}{9\times {10}^{-6}\text{W}}\right)=1.067\times {10}^7$

  $=1\times {10}^7\text{people}$

Conclusion:

The number of peoples is $1\times {10}^7$ .