Question

An earthquake generates both transverse $\left(S\right)$ and longitudinal $\left(P\right)$ sound waves in the earth. The speed of $S$ waves is about $4km{s}^{-1}$ and that of $P$ waves is about $8km{s}^{-1}$. A seismograph records $P$ and $S$ waves from an earthquake.The first $P$ wave arrives $4$ min before the first $S$ wave. The epicentre of the earthquake is located at a distance of about

• A. $192km$
• B. $384km$
• C. $1920km$
• D. $3840km$

Answer 1

The correct option is C $1920km$

Let ${\nu }_1,{\nu }_2$ be speed $S$ of $S$ and $P$ waves and $t_1,t_2$ be the time taken by these waves to travel to reach the seismograph. Let the epicenter of the earthquake is located at a distance $d$ from the seismograph. Then,

$d=V_1{t}_1=V_2{t}_2$ ................ .....(i)

Here, $V_1=4km{s}^{-1}$ and $V_2=8km{s}^{-1}$

$\therefore 4t_1=8t_2⟹t_1=2t_2$ ....(ii)

and $t_1-t_2=4min=240s$

$\therefore 2t_2-t_2=240$ .................... [using (ii)]

or $t_2=240s$

put in Eq. (ii), we get,

$t_1=2\times 240s=480s$

From Eq. (i), we get, $d=\left(4km{s}^{-1}\right)\left(480s\right)=1920km$