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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 `kms^(-1)`. A seismograph records P and S waved from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, how far away does the earthquake occur?

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