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?

Earthquakes generate sound waves inside the earth. Unlike a gas, the e

1.	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?
Answer» Solution :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`