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

Question #1443
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&rsquo;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&rsquo;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.
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 &asymp; 501.629 km

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