Seismographs measure the arrival times of earthquakes with a precision of 0.125 s. To get the distance to the epicenter of the quake, they compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 3.74 and 7.22 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined

435 m

Explanation:

The precision with which the distance to the source of the earthquake can be estimated is equal to the difference in distance covered by the S- and P-waves in the time of 0.125 s.

The distance covered by each type of wave is given by

where

v is the speed of the waves

t is the time

For S-waves,

v = 3.74 km/s

t = 0.125 s

So the distance covered is

For P-waves,

v = 7.22 km/s

t = 0.125 s

So the distance covered is

So, the precision with which the distance can be determined is:

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