Q. An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $S$ waves is about $4.5\ km/s$ 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 epicenter of the earthquake is located at a distance about
A) $25\ km$
B) $250\ km$
C) $2500\ km$
D) $5000\ km$
Explanation
(c) Suppose $d =$ distance of epicenter of Earth quake from point of observation
$v_{S} =$ Speed of $S$-wave and $v_{P} =$ Speed of $P$-wave then
$d = v_{P}t_{P} = v_{S}t_{S}$ or $8t_{P} = 4.5\ t_{S}$
$\Rightarrow t_{P} = \frac{4.5}{8}t_{S},$ given that $t_{S} - t_{P} = 240$
$\Rightarrow t_{S} - \frac{4.5}{8}t_{S} = 240 \Rightarrow t_{S} = \frac{240 \times 8}{3.5} = 548.5\ s$
$\therefore d = v_{S}t_{S} = 4.5 \times 548.5 = 2468.6 \approx 2500km$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.