An earhquake generates both transverse (S) and logitudinal (P) sound wave in the earth .The speed of (S) wave is about `4.5km//s` and that of (P) wave is about `8.0km//s` A seimsograph records P and S wave fr5om an earthquake The first P wave arrives `4.0 min` before the first S wave The epicenter of the earthpake is located at a distance of about

Options

A. `25 km`
B. `250 km`
C. `2500 km`
D. `5000 km`

Answer

c

Explanation

Distance travelled by both the wave is same Let the time taken by the` S `and `P` waves is each the seismograph be `t_(1)` and `t_(2)` then
`t_(1) - t_(2) = 4 min`
Since `60 s = 1 min`
`:. t_(1) - t_(2) = 60 xx 4 = 240 s`
Let distance of epicentre be s. Then
`s = v_(1)t_(1) = v_(2)t_(2)`
` rArr 4.5 xx t_(1) = 8t_(2)`
`rArr t_(2) = (4.5)/(8)t_(1)`
`:.t_(1) - t_(2) = 240`
`rArr t_(1) (1 - (4.5)/(8)) = 240`
`rArr t_(1) = (240 xx 8)/(3.5) = 548.58 = 2500 km`