Question

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9000 m/s and an S-wave travels at 5000 m/s. If P-waves are received at a seismic station 2.00 minute before an S wave arrives, how far away is the earthquake center?

Answer 1

Answer:

The distance between earthquake center and the measuring station is 1350 kilometers.

Explanation:

Let the earthquake center be at a distance of 'S' meters from the recording station.

Now from the basic relation of distance, speed and time we know that

$Distance=Speed\times Time$

For a Primary wave (P wave) let us assume that it appraoches the measuring station after $t_{1}$ minutes

Thus making use of the above relation we have

$Distance=V_{p}\times Time\\\\\therefore D=9000\times t_{1}.......(i)$

Now since it is given that the secondary wave (S wave) reaches the measuring spot after 2 minutes or 120 seconds thus the time taken by secondary waves to reach recorder equals $t_{1}+120$ making use of the same relation we get

$Distance=V_{s}\times Time\\\\\therefore D=5000\times (t_{1}+120).......(ii)$

Solving equation 'i' and 'ii' we get

$D=5000\times (\frac{D}{9000}+120)\\\\\therefore \frac{D}{5000}=\frac{D}{9000}+120\\\\\frac{D}{5000}-\frac{D}{9000}=120\\\\\therefore D=\frac{120}{\frac{1}{5000}-\frac{1}{9000}}=1350000meters=1350kilomerers$