Question

P and S waves from an earthquake travel at different speeds, and this difference helps locate the earthquake "epicenter" (where the disturbance took place). Assuming typical speeds of 8.8 km/s and 5.1 km/s for P and S waves, respectively, how far away did an earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 min apart?

Answer 1

the earthquake's epicenter is L = 1091.2 km away

Step-by-step explanation:

if the P and S waves start from the same place (x=0) :

P would travel the distance L in , L = vP * tP

P would travel the distance L in , L = vS * tS

therefore

vP * tP= vS * tS

if the difference in time d= tS-tP → tS=d+tP , then

vS * tS= vP * tP

vS *(d+tP) = vP * tP

vS*d + vS*tP = vP * tP

vS*d = vP * tP - vS*tP = (vP - vS) * tP

tP = vS*d / (vP - vS)

replacing values

tP = vS*d / (vS - vP) = 5.1 km/s * 1.5 min*60 s/min / ( 8.8 km/s - 5.1 Km/s) = 124 s

therefore

L = vP*tP = 8.8 km/s * 124 s = 1091.2 km