Question

The P-type wave in an earthquake travels at 7.0 km / s, while the S-type wave travels at 3.0 km / s. The P-type wave is detected 4.5 seconds before the S-type. Determine the distance between the seismograph and the epicenter.
Use meter units in your answer

Answer 1

The P-type wave in an earthquake travels at 7.0 km / s = ( 7000 / 3600 ) m / s = 1.944 m / s.

The S-type wave travels at 3.0 km / s = ( 3000 / 3600 ) m / s = 0.833 m / s.

Let, the distance between the seismograph and the epicenter be d, in m.

Hence, time taken to travel this distance,

by the P - wave = ( d / 1.944 ) s,

and, by the S - wave = ( d / 0.833 ) s.

This difference in time is, according to the question, is 4.5 s.

So, ( d / 0.833 ) - ( d / 1.944 ) = 4.5

or, d ( 1 / 0.833 - 1 / 1.944 ) = 4.5

or, d x 0.686 = 4.5

or, d = 4.5 / 0.686 ~ 6.56.

Hence, the distance between the seismograph and the epicenter is : 6.56 m.