Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound wave. Typical the speed of S wave is about `4.0 kms^(-1)`, and that of P wave is `8.0km s^(-1)`. A seismograph records P and S waves from an earthquake. The first P wave arrives 4min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?

Explanation

Following diagram shows the situation as per the statement.

Here, suppose P waves reaches the detector (seismograph) at time t. At per the statement, S wave reaches seismograph 4 min. later. i.e. 240 second later than P wave. Hence S wave will reach seismograph at `(t + 240)` second. Here S wave reaches seismograph later because its veocity is smaller than that of P wave as we are given `v _(P) = 8km//s and v _(S) =4 km //s.`
Now, from the diagram,
(i) For P wave `d = v _(P)t " "...(1)`
(ii) For S wave `d = v _(S) (t + 240) " "...(2)`
From equation (1) and (2),
`v _(P)t = v _(S) (t + 240)`
`therefore 8t =4 (t + 240)`
`therefore 2t = t + 240 implies t = 240 s" "...(3)`
From equation` (1) and (3),`
`d = v _(P) t = 8 xx 240 =1920 km`