Question

Earthquakes generate sound waves inside the earth.Unlike a gas, theearth 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 is `8.0 km s^(-1)` .A seismograph records P and S waves from an earthquake.The first P wavearrives 4 min before the first wave.Assuming the waves travel in straight line, at what distance does the earthquake occur ?

Answer 1

Let`v_(1),v_(2)` be the velocity of S waves & P waves & `t_(1),t_(2)` be the time taken by these waves to travel to the position ofseismograph . If l is the distance of occurrence of earthquake from the seismograph , then
`l= v_(1)t_(1) = v_(2)t_(2)`...(i)
now `v_(1) = 4km //s `& ` v_(2)= 8 km//s `
`:. 4t_(1) = 8 t_(2) ` (or) ` t_(1) = 2 t_(2)` ...(ii)
Also `t_(1) - t_(2) = `4 min = 240s
using (ii) `, 2t_(2) - t_(2) =240s, t_(2)= 240s `
`t_(1)=2t_(2)=2 xx 240 = 480 s`
Now from (i) `l= v_(1) t_(1) = 4 xx 480 = 1920 km`
Hence earthquake occurs 1920 km away from the seismograph.