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?

LetvsandvpbethevelocitiesofSandPwavesrespectively.
LetLbethedistancebetweentheepicentreandtheseismograph.
LetthetimetakenbythePwavestaketimetmin.toreachthesurface.
Then,thetimetakenbytheSwavestaketimet+4min.toreachthesurface.
SothedistancecoveredbythePwavesandtheSwavesisequal.
8t=4t+4
t=4min
ThedistancecoveredbythePwaves=8×240sec=1920km
Hence,theearthquakeoccursatadistanceof1920kmfromtheseismograph.