Earthquakes are essentially sound waves traveling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse seismic waves. These travel at different speeds. The speed of longitudinal waves, called P waves, is . Transverse waves, called S waves, travel at a slower . A seismograph records the two waves from a distant earthquake.
If the S wave arrives 2.0 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.
If the S wave arrives 2.0 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.
-
You did not give the velocities, but let's denote the transversal wave velocity by Vt and the longitudinal wave velocity by Vl, then the time T (in seconds) for each to traverse the same distance is
s = Vt * (T + 120)
s = Vl * T
from the latter: T = s/Vl
Substituting this in the first gives
s = Vt * (s/Vl + 120)
Solving for s:
s (1 - Vt/Vl) = 120 * Vt
s = 120 Vt/(1-Vt/Vl)
If you express the velocities in m/s , then the distance will be in meters.
s = Vt * (T + 120)
s = Vl * T
from the latter: T = s/Vl
Substituting this in the first gives
s = Vt * (s/Vl + 120)
Solving for s:
s (1 - Vt/Vl) = 120 * Vt
s = 120 Vt/(1-Vt/Vl)
If you express the velocities in m/s , then the distance will be in meters.