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 `kms^(-1)`. A seismograph records P and S waved from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, how far away does the earthquake occur?

Options

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

Answer

C

Explanation

Let `v_(1), v_(2)` be speed of S waves and P waves and `t_(1) ,t_(2)` be the time taken by these waves to travel to reach the seismograph. Let the epicentre 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)`
`therefore4t_(1)=8t_(2)rArrt_(1)=2t_(2)`.....(ii)
and `t_(1)-t_(2)=4 min =240 s`
`therefore 2t_(2)-t_(2)=240` [Using (ii)]
or `t_(2)=240 s`
Put in Eq. (ii), we get,
`t_(1)=2xx240 s= 480 s`
From Eq. (i), we get, `d=(4kms^(-1))(480 s)=1920 km`