Question

12. The earth has a radius of 6400 km. The inner core of
1000 km radius is solid. Outside it, there is a region
from 1000 km to a radius of 3500 km which is in
molten state. Then again from 3500 km to 6400 km,
the earth is solid. Only longitudinal (P) waves can
travel inside a liquid. Assume that the P wave has
a speed of 8 km s' in solid parts and of 5 kms!
in liquid parts of the earth. An earthquake occurs at
some place close to the surface of the earth. Find the
time after which it will be recorded in a seismometer
at a diametrically opposite point on the earth if wave
travels along diameter.
​

Answer 1

As the wave travels along the diameter of earth starting from X, is has to travel the following distances to get recorded in a seismometer at X′figure

• s1 = distance through solid portion=  XB+AA′+B′X′

           = (2900+2×1000+2900) km

           = 7800km

• s2 = distance through molten portion  = BA+A′B′

             = (2500+2500)km

             = 5000km

Now  

υ1 = 8km/s and υ2 = 5km/s

Therefore, total time taken will be -

T = t1+t2 = s1/υ1 + s2/υ2

= 7800/8 + 5000/5

t = 975 + 1000

= 1975 sec