How to Measure Seismic Waves With Trigonometry

Earthquakes produce seismic waves, which are vibrations that travel through the ground. Scientists use wave detectors called seismographs to measure seismic waves. From velocity, time and angle measurements, you can use trigonometry to measure the vertical and horizontal distances traveled by seismic waves. These waves begin on the earth's surface, move diagonally below ground, travel horizontally there and finally travel upward back to the ground surface. It is useful to think of four points that form a trapezoid: the starting point on the earth's surface, the first point on the below-ground line, the end of the below-ground line and the ending point on the earth's surface.

Things You'll Need

  • Scientific calculator
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Instructions

  1. Wave Height

    • 1

      Write down the angle (G) that the wave makes with the normal line. The normal is an imaginary line connecting the ground surface to the center of the earth. Write down the velocity (v1) of the wave as it travels from the ground surface to the first below-ground point. Write down the time (t1) that the wave takes to travel from the ground surface to the first below-ground point.

    • 2

      Convert t1 to the unit (e.g. seconds) in the denominator of v1.

    • 3

      Use a scientific calculator to evaluate v1*t1. The result is the length (B) of the path traveled by the wave from the ground surface to the first below-ground point.

    • 4

      Use a scientific calculator to evaluate Bcos(G). The result is the height of the wave.

    Horizontal Distance

    • 5

      Write down the underground velocity (v2) of the wave and the time (t2) it takes for the wave to travel from the first below-ground point to the second below-ground point.

    • 6

      Convert t2 to the unit (e.g. seconds) in the denominator of v2.

    • 7

      Use a scientific calculator to evaluate v2*t2. The result is the length (C) of the path traveled by the wave from the first below-ground point to the second below-ground point.

    • 8

      Use a scientific calculator to evaluate C + 2Bsin(G). The result is the total horizontal distance traveled by the wave.

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