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 epicenter of the earthquake is located at a distance about

Options

A. 25km
B. 250km
C. 2500km
D. 5000km

Answer

C

Explanation

Velocity of the S waves is `v_1=4.5km//s`. The velocity of the P waves is `v_2=8.0 km//s`
Let the time taken by the S and P waves to reach the seismograph be `t_1 " and " t_2`. It is given that
`t_1-t_2=4 "min" = 4xx60=240` sec …(i)
Let the distance of the epicentre (km) be S. Then
`S=v_1t_1=v_2t_2`
`rArr 4.5xxt_1-8t_2=0 rArr t_2 = (4.5)/(8) t_1 " " ....(ii)`
Using (i) and (ii)
`t_1-t_2=240 rArr t_1(1-(4.5)/(8))=240`
`rArr t_1(240xx8)/(3.5) = 548.5 s`,
`therefore S=v_1t_1=4.5xx548.5=2468.6~~2500km`