Earthquake generate wave within the earth unlike gasous. Earth ca… - Vidyadip

Question

Earthquake generate wave within the earth unlike gasous. Earth can sense both transverse (s) and longitudnal ( $P$ ) waves. The speed of $S$ wave is about 4.0 $km S ^{-1}$ and speed of $P$ wave is about $8 km s ^{-1}$. A seismometer records the $P$ and $S$ wave of an earth quake. The first $P$ wave arrives 4 minute earlier than first $S$ wave. Assuming that the wave travels in straight line. Find out what is the distance to the place where the earthquake occur.

✓

Answer

Given
Speed of transverse (s) waves $v _1=4 km / s$
Time to reach seismometer $=t_1$
Speed of longitudnal wave $( P ) v _2=8 km / s$
Time to reach seismometer $= t _2$
Since both waves originate at the same place and reach the seismometer both will cover same distance $l$ Hence,
$\begin{aligned} & & l & = v _1 t_1= v _2 t_2 \\ \Rightarrow & & 4 t_1 & =8 t_2 \Rightarrow t_1=2 t_2\end{aligned}$
Given : $\quad t_1=t_2+(4 \times 60)$
Put value in equation (1)
$\begin{array}{l}t_2=240 sec . \text { and } \\ t_1=2 t_2=480 sec .\end{array}$
Distance to the place where earthquake occur
$l= v _1 t_1=4 \times 480=1920 km$

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