# 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’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.

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.

Expert's answer

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

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

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