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

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

[tex]d=vt[/tex]

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

[tex]d_s=(3.74)(0.125)=0.4675 km = 467.5 m[/tex]

For P-waves,

v = 7.22 km/s

t = 0.125 s

So the distance covered is

[tex]d_p=(7.22)(0.125)=0.9025 km = 902.5 m[/tex]

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

[tex]\Delta d = 902.5 - 467.5 =435 m[/tex]