The earth has a radius of 6400 km. The inner core of the 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in a 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 km/s in liquid parts of the earth. An earthquake occurs at someplace close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter?
The earth has a radius of 6400 km. The inner core of the 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in a 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 km/s in liquid parts of the earth. An earthquake occurs at someplace close to the surface of the earth. Calculate 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:

Exemplar Solutions Physics Class 11 Chapter 15 - 10

According to the question, r1 = 1000 km, r2 = 3500 km, r3 = 6400 km and d1 = 1000 km

And we can calculate,

d2 = 3500 – 1000

d2 = 2500 km

d3 = 6400 – 3500

d3 = 2900 km

Expression for the solid distance is given as follows:

2(d1 + d3) = 2(1000 + 2900)

2(d1 + d3) = 2(3900)

The wave takes the following amount of time to produce an earthquake:

= (3900)(2)/8 sec

Now the liquid distance is given by

2d2 = (2)(2500)

Similarly, the time taken by the seismic wave in the liquid part is

= (2)(2500)/5

As a result, total time taken equals the time spent by the wave during the earthquake’s creation plus the time spent by the seismic wave in the liquid part.

Time=2\left[ \frac{3900}{8}+\frac{2500}{5} \right]=1975\sec

Time=32\min 55\sec