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Question

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about 4.0 km s1 and that of P wave is 8.0 km s1. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur ?

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Solution

Let vSand vP be the velocities of S and P waves respectively.
Let L be the distance between the epicentre and the seismograph.
We have:
L=vStS ...(i)
L=vPtP ...(ii)
Where,
tS and tP are the respective times taken by the S and P waves to reach the seismograph from the epicentre
It is given that:
vP= 8 km/s
vS= 4 km/s
From equations (i) and )ii), we have:
vStS=vPtP
4tS=8tP
tS=2tP ...(iii)
It is also given that:
tStP=4min=240s
2tPtP=240
tP=240
And tS=2×240=480s
From equation (ii), we get:
L=8×240
=1920km
Hence, the earthquake occurs at a distance of 1920 km from the seismograph.

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