Question

A seismographic station receives S and P waves from an earthquake, separated in time by 17.3 s. Assume the waves have traveled over the same path at speeds of 4.50 km/s and 7.80 km/s. Find the distance from the seismograph to the focus of the quake.

Answer 1

Answer:

184 Km

Explanation:

given,

speed of S wave = 4.50 Km/s

speed of  P wave = 7.80 Km/s

reading time difference = 17.3 s

we know,

distance = speed x time

 time taken by s-wave

$t_1 = \dfrac{x}{4.50}$

time taken by the P-wave

$t_2= \dfrac{x}{7.80}$

now,

t₁ - t₂ = 17.3 s

$\dfrac{x}{4.50}-\dfrac{x}{7.80} = 17.3 s$

$\dfrac{(7.80-4.50)x}{7.80\times 4.50} = 17.3$

 3.3 x = 607.23

    x = 184 Km

distance of the focus from the station is 184 Km.

Answer 2

Answer:

184 Km

Explanation:

given,

speed of S wave = 4.50 Km/s

speed of  P wave = 7.80 Km/s

reading time difference = 17.3 s

we know,

distance = speed x time

time taken by s-wave

time taken by the P-wave

now,

t₁ - t₂ = 17.3 s

3.3 x = 607.23

   x = 184 Km

distance of the focus from the station is 184 Km.