Chapter 11, Problem 44P

(a)

To determine

To Find:The distance at which earthquake occurs.

Answer to Problem 44P

The earthquake occurs at a distance of $1.9\times {10}^3\text{ km}$ at which the particular seismic station detects the arrival of these two types of waves in $2\min$ apart.

Explanation of Solution

Given:

Speed of the S waves, $v_1=5.5\text{ km/s}$

Speed of the P waves, $v_2=8.5\text{ km/s}$

Time between two waves, $t=2\text{ min}=120\text{ s}$

Time for P waves, $t_1=t_2+120$

Formula used:

Both waves travel same distance. This is expressed by the following equation:

  $\Delta x=v_1\times t_1=v_2\times t_2$Here, $v_1$ is the speed of S waves,

  $v_2$ is the speed of P waves,

  $t_1$ is the time for the S waves,

  $t_2$ is the time for the P waves.

Calculation:

Substitute the given values,

  $\begin{array}{l}{v}_1\times t_1=v_2\times t_2\\ v_1\times (t_2+120)=v_2\times t_2\\ v_1\times t_2+v_1\times 120=v_2\times t_2\\ v_1\times 120=(v_2-v_1)\times t_2\end{array}$

On calculating,

  $\begin{array}{l}{t}_2=\frac{v_1\times 120}{v_2-v_1}=\frac{120\times 5.5}{3}=220\text{ s}\\ \Delta x=v_2\times t_2=8.5\times 220=1870\text{ km }=1.9\times {10}^3\text{ km}\end{array}$

Conclusion:

Thus, at $1.9\times {10}^3\text{ km}$ the earthquake will take place. At this point some of the seismic station detects the arrival of these two types of waves in $2\min$ .

(b)

To determine

To Find: The position of the epicenter.

Explanation of Solution

Introduction:

One seismic station is not sufficient enough for the determination of the position of the epicenter as it basically depends on distance and direction.

The distance between the epicenter to seismic station is known but the direction between epicenter and seismic station is not known. So, epicenter lies on a vertical circle of radius $1.9\times {10}^3\text{ km}$ from the seismic station and reading from at least other two seismic station is required to determine the exact position of epicenter.

Conclusion:

For the determination of the position of the epicenter, one seismic station is not sufficient.