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

Options

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

Answer

C

Explanation

Suppose d = distance of epicenter of Earth quake from point of observation
`v_(s)` Speed of S - wave and `v_(p) = S`peed of P - wave then `d = v_(p)t_(p) = v_(S)t_(S) or 8t_(p) = 4.5 t_(s)`
implies `t_(p) = (45)/(8)t_(S)` given that `t_(S) - t_(p) = 240`
implies `t_(S) - (4.5)/(8) t_(S) = 240 implies t_(S) = (240 xx 8)/(3.5) = 548.5 s`
`d = v_(S)t_(S) = 4.5 xx 548.5 = 2468.6 approx 2500 km`.