Chapter 11, Problem 47P

(a)

To determine

To Calculate: The intensity of the earthquake wave.

Answer to Problem 47P

The intensity of the earthquake wave when it passed a point of $1\text{km}$ from the source is $4.6\times {10}^9{\text{ W/m}}^{\text{2}}$ .

Explanation of Solution

Given:

Intensity of the earthquake wave passing through the earth, $I_{\text{far from source }}=2\times {10}^6{\text{ W/m}}^{\text{2}}$

Distance nearer to the source, $r_{\text{near}}=1\text{ km}$

Distance far from the source, $r_{\text{far}}=48\text{ km}$

Formula used:

The intensity of the earthquake wave when it passed a point of $1\text{km}$ from the source can be determined by the following formula,

  $I_{\text{near to source}}\times {(r_{\text{near to source}})}^2=I_{\text{far from source}}\times {(r_{\text{far from source}})}^2$

Here,

  $I$ is intensity of source,$r$ is the distance of source of wave.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}$ I_{\text{near to source}}\times {(1\text{ km})}^2=2\times {10}^6\times {(48\text{ km})}^2$I_{\text{near to source}}=\frac{2\times {10}^6\times {(48\text{ km})}^2}{{(1\text{ km})}^2}=4.6\times {10}^9{\text{ W/m}}^{\text{2}}\end{array}$

Conclusion:

Thus, the intensity of the earthquake wave when it passed a point of $1\text{km}$ from the source is $4.6\times {10}^9{\text{ W/m}}^{\text{2}}$ .

(b)

To determine

To Calculate: The power.

Answer to Problem 47P

The rate at which energy pass through an area is $2.3\times {10}^{10}\text{ W}$ .

Explanation of Solution

Given:

Area, $A=5{\text{ m}}^{\text{2}}$

Intensity, $I=4.6\times {10}^9{\text{W/m}}^{\text{2}}$

Formula used:

The rate at which energy pass through an area of $5{\text{m}}^{\text{2}}$ at $1\text{km}$ is determined by the following formula,

  $P=I\times A$

Here,

  $I$ is the intensity of wave.

  $A$ is the area.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}P=4.6\times {10}^9\times 5\\ P=2.3\times {10}^{10}\text{ W}\end{array}$

Conclusion:

Thus, the rate at which energy pass through an area is $2.3\times {10}^{10}\text{ W}$ .