Answer to Question #1443 in Mechanics | Relativity for jon allen

Question

Earthquakes produce two kinds of seismic
waves: he longitudinal primary waves (called
P waves) and the transverse secondary waves
(called S waves). Both S waves and P waves
travel through Earth’s crust and mantle, but
at different speeds; the P waves are always
faster than the S waves, but their exact speeds
depend on depth and location. For the pur-
pose of this exercise, we assume the P wave’s
speed to be 9620 m/s while the S waves travel
at a slower speed of 5990 m/s.
If a seismic station detects a P wave and
then 31.6 s later detects an S wave, how far
away is the earthquake center?
Answer in units of km.

Answer 1

V(P) = 9620 m/s, V(S) = 5990 m/s, Time of delay T = 31.6 s
Denote the distance from the earthquake as S, then
T1 = S/V(P),T2 = S/V(S) T2-T1 = T
S(1/5990 - 1/9620) = 31.6
S = 31.6/(1/5990 - 1/9620) = 501628.672 m ≈ 501.629 km