Question

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 8.0 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 epicenter of the earthquake is located at a distance about
(a) 25 km
(b) 250 km
(c) 2500 km
(d) 5000 km

Answer 1

Hint: Seismic waves are the waves of energy created by the instant breaking of rock inside the earth. They are nothing but the energy that travels through the earth and it can be recorded on seismographs. P and S waves are a type of them.

Step by step answer: velocity of the S waves, \[{{v}_{1}}\] = 4.5 km/s
velocity of the P waves is \[{{v}_{2}}\] = 8.0 km/s
Let us assume that the time taken by the S and P waves to reach the seismograph be \[{{t}_{1}}\And {{t}_{2}}\].
Given in the question,
\[
  {{t}_{1}}-{{t}_{2}}=(4\times 60)s \\
  \Rightarrow {{t}_{1}}-{{t}_{2}}=240s \\
\]
\[{{t}_{1}}-{{t}_{2}}=240s\]----(1)
Let distance between the epicenters be j km. then, \[j={{v}_{1}}{{t}_{1}}={{v}_{2}}{{t}_{2}}\], since they are equal.
\[
\Rightarrow 4.5\times {{t}_{1}}-8{{t}_{2}}=0 \\
\Rightarrow {{t}_{2}}=\frac{4.5{{t}_{1}}}{8} \\
\]
\[{{t}_{2}}=\frac{4.5{{t}_{1}}}{8}\]---(2)
Now we have two relationships, solving both of them we get,
\[
 \Rightarrow {{t}_{1}}-\frac{4.5{{t}_{1}}}{8}=240 \\
  \Rightarrow3.5{{t}_{1}}=1920 \\
 \Rightarrow {{t}_{1}}=548.57s \\
\]
Thus, the value of \[{{t}_{1}}\]is 548.57 s. putting it to find j,
\[
   j=4.5\times 548.57 \\
  j =2468.57m \\
\]
j= 2500 km (approx.)

So, the correct option is C.

Note: p waves are called primary waves. They are the fastest moving seismic waves. they can move through the rocks and lava. S waves are called secondary waves. They come after the primary waves are the reason of aftershocks