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, and that of the P waves is 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

Let vs and vp be the velocities of S and P waves respectively.
Let L be the distance between the epicentre and the seismograph.
Let the time taken by the P waves take time t min. to reach the surface.
Then, the time taken by the S waves take time t+4 min. to reach the surface.
So the distance covered by the P waves and the S waves is equal.
t=4 min
The distance covered by the P waves=8×240 sec=1920 km
Hence, the earthquake occurs at a distance of 1920 km from the seismograph.