An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave

Question

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?

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Linh Đan 4 years 2021-08-10T20:29:36+00:00 1 Answers 502 views 1

Answers ( )

  1. kimchi2
    0
    2021-08-10T20:31:14+00:00
    Reply

    Assuming constant speeds, the P-wave covers a distance d in time t such that

    9000 m/s = d/(60 t)

    while the S-wave covers the same distance after 1 more minute so that

    5000 m/s = d/(60(t + 1))

    Now,

    d = 540,000 t

    d = 300,000(t + 1) = 300,000 t + 300,000

    Solve for t in the first equation and substitute it into the second equation, then solve for d :

    t = d/540,000

    d = 300,000/540,000 d + 300,000

    4/9 d = 300,000

    d = 675,000

    So the earthquake center is 675,000 m away from the seismic station.

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