Question

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The spced of $S$ waves is about $4.5 \,km / s$ and that of $P$ waves is about $8.0 \,km / s$. A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0\, min$ before the first $S$ wave. The 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 $v_{1}=4.5 \,km / s$.
The velocity of the $P$ waves is $v_{2}=8.0 \,km / s$.
Let the time taken by the $S$ and $P$ waves to reach the
seismograph be $t_{1}$ and $t_{2} .$ It is given that
$t _{1}- t _{2}=4 min =4 \times 60=240\, sec \ldots$ (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}-8 t_{2}=0 $
$\Rightarrow t_{2}=.4 .58 t_{1} \ldots$ (ii)
Using (i) and (ii)
$t_{1}-t_{2}=240$
$ \Rightarrow t_{1}\left(1-\frac{4.5}{8}\right)=240$
$\Rightarrow t_{1}=\frac{240 \times 8}{35}=548.5\, s .$
$\therefore S=v_{1} t_{1}=4.5 \times 548.5$
$=2468.6 \approx 2500\, km .$