Question

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $(S)$ waves is about $4.5km/s$ and that of $(P)$ waves is about $8.0km/s$. A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0\min$ before the first $S$ wave. The epicentre of the earthquake is located at a distance of about

• A. $25km$
• B. $250km$
• C. $2500km$
• D. $5000km$

Answer 1

Answer: (C)

Distance travelled by both the waves is same.
Let the time taken by the $S$ and $P$ waves to reach the seismograph be $t_1$ and $t_2$ then
$t_1-t_2=4\min$
Since, $60s=1\min$
$\therefore t_1-t_2=60\times 4=240s$
Let distance of epicentre be $s$. Then
$s=v_1{t}_1=v_2{t}_2$
$\Rightarrow 4.5\times t_1=8t_2$
$\Rightarrow t_2=\frac{4.5}{8}{t}_1$
$\therefore t_1-t_2=240$
$\Rightarrow t_1\left(1-\frac{4.5}{8}\right)=240$
$\Rightarrow t_1=\frac{240\times 8}{3.5}=548.58s$
$\therefore s=v_1{t}_1=4.5\times 548.5=2500km$