An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9 000 m/s and an S-wave at 4 000 m/s.If P-waves are received at a seismic station 34.0 s before an S-wave arrives,how far is the station from the earthquake center?
A)1.22E+5 m
B)4.90E+5 m
C)2.45E+5 m
D)9.42E+4 m
E)1.70E+5 m

Question

Quizplus · Accepted Answer

Let's assume the distance from the seismic station to the earthquake center as "d."

The time difference between the arrival of P-waves and S-waves, Δt = 34.0 s.

Using the equations:

d = vP × tP   (Equation 1)
d = vS × tS   (Equation 2)

where vP and vS are the velocities of P-waves and S-waves respectively, and tP and tS are the times taken by P-waves and S-waves to travel the distance "d."

Dividing Equation 2 by Equation 1, we get:

vS/vP = tS/tP
tS = tP + Δt
vS/vP = (tP + Δt)/tP

Substituting the given values, we get:

4000/9000 = (tP + 34.0)/tP

Solving for tP, we get:

tP = 18.2 s

Substituting this value in Equation 1, we get:

d = 9000 × 18.2 = 163,800 m = 2.45E+5 m (to two significant figures)

Therefore, the seismic station is approximately 2.45E+5 m or 245 km away from the earthquake center.

The best choice is (C).

An Earthquake Emits Both P-Waves and S-Waves That Travel at Different