Question

An earthquake generates both transverse (S) and longitudinal (P) sound waves in the earth. The speed of S waves is about 4 km s–1 and that of P waves is about 8 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. The epic centre of the earthquake is located at a distance of about

• A. 192 km
• B. 384 km
• C. 1920 km
• D. 3840 km

Answer 1

Answer: (C)

1920 km

Answer 2

Let $v_{1},v_{2}$be speed of S waves and P waves and $t_{1},t_{2}$be the time by these waves to travel to reach the seismograph. Let the epicenter of the earthquake is located at a distance d from the seismograph. Then

$d = v_{1}t_{1} = v_{2}t_{2}$ …… (i)

Here, $v_{1} = 4kms^{- 1}andv_{2} = 8kms^{- 1}$

$\therefore 4t_{1} = 8t_{2} \Rightarrow t_{1} = 2t_{2}$ …… (ii)

And $t_{1} - t_{2} = 4\min = 240s$

$\therefore 2t_{2} - t_{2} = 240$ [Using (ii)]

Or $t_{2} = 240s$

Put in Eq. (ii), we get $t_{1} = 2 \times 240s = 480s$

From Eq. (i) We get

D = (4 km$s^{- 1}$) (480 s) = 1920km