Q32 of 36 Page 110

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-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 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?

Given:


Speed of longitudinal wave in solid = 8 kms-1


Speed of longitudinal wave in liquid = 5 kms-1


When the wave travels across the earth towards the core, it will pass the liquid region and the two solid regions. The first solid region starting from the crust has a radial distance of



For the molten region the radial distance is



And for the solid region of the core the distance is



The time taken to travel to the centre of earth from the crust is therefore,



where vs and vl are the velocities of the longitudinal wave in solid and liquid respectively.



To travel to a diametrical opposite point the time will be equal to 2t = 1975 s. Therefore, the seismometer will record the earthquake after 1975 seconds after the earthquake initiates.


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(a) speed of sound in air at room temperature


(b) speed of sound in air at 0° C


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(a) y = 5 cos (4x) sin (20t)


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