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?

Explanation

Velocity of longitudinal sound wave,
`upsilon_(s) = 4 kms^(-1)`
Velocity of transerse sound wave, `upsilon_(p) = 8 kms^(-1)`
Let earthquake occurs at a distance of x km
If longitudinal wave takes time `t_(s)` and transverse wave takes `t_(p)` time to cover distance x, then :
We can write `t_(s) - t_(p) = 240`
`(x)/(upsilon_(s)) - (x)/(upsilon_(p)) = 240`
`x[(upsilon_(p) - upsilon_(s))/(upsilon_(p) upsilon_(s))] = 240`
`x = 240 [(upsilon_(p) upsilon_(s))/(upsilon_(p) - upsilon_(s))] = 240 [(8 xx 4)/(8-4)]`
`= 240 xx 8`
x = 1920 km