Question

P and S waves from an earthquake travel at different speeds and this difference helps in locating the epicenter (point of origin) of the earthquake. (a) Assuming P waves travel at 10.3 km/s and S waves travel at 4.2 km/s, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 3.25 minutes apart

Answer 1

x = 1382.9 km

Step-by-step explanation:

The speed of the wave is constant, so we can use the uniform motion relationships

p wave

`v_p` = x / t₁

t₁ = x /v_p

S wave

v_s = x / t₂

t₂ = x / v_s

indicate that the time difference between the two waves is

t₂ - t₁ = 3.25 min (60 s / 1 min)

t₂ -t₁ = 195 s

let's substitute

`(x)/(v_s) - (x)/(v_p)` = 195

x (
`(1)/(v_s) - (1)/(v_p)` = 195

let's calculate

x
`( (1)/(4.2) - (1)/(10.3) )` = 195

x (0.1410) = 195

x = 195 /0.141

x = 1382.9 km