During earthquake at one place transverse wave (S) and longitudinal wave (P) are found to be moving towards seismograph with velocities 4.5 km/s and 8.0 km/s respectively. If first P wave is detected by seismograph earlier than S wave by 4 min then epicenter of earthquake must be located approximately at ...... distance from the seismograph.

Options

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

Answer

C

Explanation

Here `v _(S) = 4.5 km//s`
`v_(p) = 8 km//s`

If `t _(S) and t _(p)` are time taken by S and P wave respectively to reach seismograph, then ar per the statement `t _(S) - t _(P) = 4 min = 240 s `
Now, `d = v _(P) t _(P) = 8 t _(P) " "...(1)`
Also `d =v _(S) t _(S) = 4.5 (t _(P) + 240) " "...(2)`
From `(1) and (2) 8t_(P) = 4.5 t _(P) + 1080`
`therefore 3.5 t _(P) = 1080 " "...(3)`
`therefore t _(P) = 308 . 6s `
From (1) and (3),
`d = 8 xx 308.6`
`therefore d = 2468.8 km`
`therefore d ~~2500km`