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 km s–1. 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 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 such that
L = vStS ….....(i)
L = vPtP …....(ii)
Where, tS and tP are the time taken by the S and P waves to reach the seismograph from the epicentre respectively.
It is given that vP = 8 km/s
vS = 4 km/s
From equations (i) and (ii),
vS tS = vP tP
⇒ 4tS = 8 tP
⇒ tS = 2 tP …..(iii)
It is also given that tS – tP = 4 min = 240 s
2tP – tP = 240
⇒ tP = 240
And tS = 2 × 240 = 480 s
From equation (ii),
L = 8 km/s × 240 s
⇒ L = 1920 km
Hence, the earthquake occurs at a distance of 1920 km from the seismograph.