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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 s–1, and that of P wave is 8.0 km s–1. 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?



Answer -

Let vSand vP bethe velocities of S and P waves respectively.

Let L be the distancebetween the epicentre and the seismograph.

We have:

L = vStS (i)

L = vPtP (ii)

Where,

tS and tP arethe respective times taken by the S and P wavesto 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:

vS tS = vP tP

4tS = 8 tP

tS = 2 tP (iii)

It is also given that:

tS – tP =4 min = 240 s

2tP – tP =240

tP = 240

And tS =2 × 240 = 480 s

From equation (ii), we get:

L = 8 ×240

= 1920 km

Hence, the earthquake occurs at a distance of 1920 km fromthe seismograph.

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