Physics Question Waves and Fields?

A sinusoidal seismic wave from an earthquake has a velocity of 5.5 km/s and a period of t=0.5 sec. Suppose one such wave is traveling along the surface of the earth in the east direction. The wave is moving past your location and shaking you (oscillating you) east and west. At time t=0, the wave has you at the westernmost point of your shake (you are as far west as you will ever get).

Someone is standing 1 km to your east (this distance was measured before the wave passed). How long will it be until that person is at the easternmost point of their shake?

1 Answer

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  • NCS
    Lv 7
    2 years ago
    Favorite Answer

    v = λ/T

    5.5 km/s = λ / 0.5s

    so

    wavelength λ = 2.75 km.

    Let's say the wave has amplitude A.

    We're told that where you are standing,

    x(0) = -A

    and in general we can say that for where you are standing,

    x(t) = -Acos(2π*t/T) = -Acos(4π*t) → for t in seconds

    Somebody 1 km to your east is 1km/2.75km = 0.364 wavelengths away, so for them

    X(t) = -Acos(4π*t + 0.364*2π)

    and

    X(0) = -Acos(0.364*2π) = -A*-0.655 = 0.655A

    V(t) = A*4π*sin(4π*t + 0.364*2π)

    and

    V(0) = A*4π*0.756 > 0 which is true (so I've got the signs right)

    SO

    X(t) = A = -Acos(4π*t + 0.364*2π)

    means that

    -1 = cos(4π*t + 0.364*2π)

    3π/2 = 4π*t + 0.364*2π

    0.773π = 4πt

    0.19 = t ◄ in seconds

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