Earthquakes produce two kinds of seismic waves: he longitudinal primary waves (c

Question

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 purpose of this exercise, we assume the P wave’s

speed to be 9630 m/s while the S waves travel

at a slower speed of 5790 m/s.

If a seismic station detects a P wave and

then 75.8 s later detects an S wave, how far

away is the earthquake center?

Answer in units of km

Explanation / Answer

Let tp represent the time it takes the p-wave to travel the
distance D, then tp+75.8 represents the time it takes the
s-wave to travel the same distance, D.

Hence,

D = Vptp =Vs(tp+ts) = 9630tp = 5790(tp + 75.8)

tp = D/9630,

D = 5790(D/9630 +75.8)

solve for D

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