question_answer 59)

                  The earth has a radius of 6400 km. The inner core of 1000 kin radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 kin which is in molten state. Then again from 3500 kin to 6400 km die earth is solid. Only longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a speed of \[8\,km\,{{s}^{-1}}\]in solid parts and of \[5\,km\,{{s}^{-1}}\] in liquid parts of the earth. An earthquake occurs at some place close to the surface of die 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:

                  Earth quake generates sound waves inside the earth. During earth-quake earth experiences both transverse (S) and longitudinal (P) sound waves. The speed of P waves is double the speed of S waves.                 The time after which seismometer records the P waves is given by                 \[t=2\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}})\]                           ?.. (i)                 \[{{t}_{1}}=\]time taken by the wave to travel distance  from 100 km to \[3500\,km=\,\frac{2500\,km}{5\,km\,{{s}^{-1}}}\,=500\,s\]                 \[{{t}_{2}}=\] time taken by the wave to travel distance from 3500 km to \[6400\text{ }km=\,\frac{2900\,km}{8\,km\,{{s}^{-1}}}=\text{ }362.5\text{ }s\]                 \[{{t}_{3}}=\]  time taken by the wave to travel inner \[(1000\,km)=\,\frac{1000\,km}{8\,km\,{{s}^{-1}}}\,=125\,s\]                 \[\therefore \] \[t=\,2(500\,+\,362.5\,+125)\,=\,1975.5\,g\,\]                 \[=32\] minutes \[55.5\,s\]