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earthquakes generate sound waves inside the earth...

Question:
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?

Answer:

Let v_Sand v_P be the velocities of S and P waves respectively.

Let L be the distance between the epicentre and the seismograph.

We have:

L = v_St_S (i)

L = v_Pt_P (ii)

Where,

t_S and t_P are the respective times taken by the S and P waves to reach the seismograph from the epicentre

It is given that:

v_P = 8 km/s

v_S= 4 km/s

From equations (i) and (ii), we have:

v_S t_S = v_P t_P

4t_S = 8 t_P

t_S = 2 t_P (iii)

It is also given that:

t_S - t_P = 4 min = 240 s

2t_P - t_P = 240

t_P= 240

And t_S = 2 x 240 = 480 s

From equation (ii), we get:

L = 8 x 240

= 1920 km

Hence, the earthquake occurs at a distance of 1920 km from the seismograph.

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