Question

Earthquakes produce several types of shock waves. The most well-known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, the P-waves travel at around 6.5 km/s while the S-waves move at about 3.5 km/s. The actual speeds vary depending on the type of material they are going through. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away the earthquake occurred.

Answer 1

The given question is incomplete. The complete question is as follows-

Earthquakes produce several types of shock waves. The most well-known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, the P-waves travel at around 6.5 km/s while the S-waves move at about 3.5 km/s. The actual speeds vary depending on the type of material they are going through. The time delay between the arrival of these two waves at a seismic recording center tells geologists how far away the earthquake occurred. If the time delay is 73 s, how far from the seismic station did the earthquake occur?

Answer:

553.6 km

Explanation:

Given that,

speed of P-wave = 6.5 km/sec

Speed of S-wave = 3.5 km/sec

Delay time is given to be = 73 seconds

Distance is needed to find,

Since, the distance covered by P wave in 't' seconds, and S wave in "t + 73" seconds

Now, Distance = Speed × Time

⇒ Distance = Speed × (t+73 sec)

For P wave, distance is, D = Pt   ...... equation (1)

and for S wave, distance is, D = S(t+73) ...... equation (2)

As, both the distances are the same, means equation (1) and (2) being equal,

Pt  = S (t + 73)

Pt = St + 73 S

Pt ₋ St = 73 S

t (P ₋ S) = 73 S

t = $\frac{73 S}{P - S}$

Putting this value of t in equation (1), we get,

D = Pt = $\frac{73 PS}{P - S}$

Now, by substituting the values of speed of P and S waves in it, we get-

Distance = \frac{73 \times 6.5 \times 3.5 }{6.5 - 3.5}

Therefore, distance = 553.6 kilometers.