Answer to Question #266727 in Physics for Mae

Question

Earthquake produce several types of shock waves. The most well-known is the P-waves and the S-waves. In the Earth's crust, the P-waves travel at around 6.5 km/s, while S-waves move at about 3.5 km/s. The actual speeds vary depending of the type of material they are going through. The time delay between the arrival of these two waves at seismic recording station tells geologist how far away the earthquake occured. If the time delay is 33 s, how far from the seismic station did the earthquake occur?

Answer 1

Assume the earthquake happened D km away from the station. Then the P-wave and S-wave would reach the station respectively in:

$$t_P=D/v_P,\space\space\ t_S=D/v_S,$$

the difference in time is

$$\Delta t=t_S-t_P=D\bigg(\frac1{v_S}-\frac1{v_P}\bigg),\\\space\\ D=\Delta t\frac{v_Sv_P}{v_P-v_S}=250\text{ km}.$$