An earthquake generates both transverse (S) and longitudinal (P) sound waves in the earth. The speed of S waves is about 4.5 ~km / s and that of P waves is about 8.0 ~km / s . A seismograph records P and S waves from an earthquake. The first P wave arrives 4.0 ~min before the first S wave. The epicentre of the earthquake is located at a distance about

Step-by-step solution

Velocity of the S waves is v₁=4.5 ~km / s . The velocity of the P waves is v₂=8.0 ~km / s . Let the time taken by the S and P waves to reach the seismograph be t₁ and t₂ . It is given that t₁-t₂=4 ~min =4 60=240 sec ... (i) Let the distance of the epicentre ( km ) be S . Then aligned & S=v₁ t₁=v₂ t₂ & 4.5 t₁-8 t₂=0 t₂= 4.5 8 t₁ aligned Using (i) and (ii) aligned & t₁-t₂=240 t₁ (1- 4.5 8 )=240 & t₁= 240 8 3.5 =548.5 ~s & S=v₁ t₁=4.5 548.5=2468.6 2500 ~km aligned