Question

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The spced 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 $4.0min$ before the first $S$ wave. The cpicentre of the earthquake is located at a distance about

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

Answer 1

Answer: (C)

Velocity of the $S$ waves is $v_1=4.5km/s$.
The velocity of the $P$ waves is $v_2=8.0km/s$.
Let the time taken by the $S$ and $P$ waves to reach the
seismograph be $t_1$ and $t_2.$ It is given that
$t_1-t_2=4min=4\times 60=240sec\dots$ (i)
Let the distance of the epicentre $(km)$ be $S$. Then
$S=v_1{t}_1=v_2{t}_2$
$\Rightarrow 4.5\times t_1-8t_2=0$
$\Rightarrow t_2=.4.58t_1\dots$ (ii)
Using (i) and (ii)
$t_1-t_2=240$
$\Rightarrow t_1\left(1-\frac{4.5}{8}\right)=240$
$\Rightarrow t_1=\frac{240\times 8}{35}=548.5s.$
$\therefore S=v_1{t}_1=4.5\times 548.5$
$=2468.6\approx 2500km.$