How to Calculate the Wavelength of a Water Wave

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To calculate a water wave's wavelength, you need a number of values, including an estimate of the wavelength itself. Calculating therefore requires numerous iterations, which computer programs can manage far more easily than humans. But a slightly simpler formula exists. It determines the wavelength from the wave's period and height.

  • Multiply pi by two.

    π * 2

    = 6.2831

  • Divide your answer by the wave's period. If it has a period of 5;

    6.2831 / 5

    =1.26

  • Square your answer.

    1.26 * 1.26

    = 1.58

  • Multiply your answer by the wave's height, in meters. If the wave is 2 m high:

    1.58 * 2

    = 3.16

  • Divide your answer by the gravitational constant - 9.81

    3.16 / 9.81

    = 0.322

  • Raise your answer to the power of 0.75.

    0.322 ^ 0.75

    = 0.428

  • Find the tanh of your answer, using a scientific calculator.

    tanh (0.428)

    = 0.403

  • Raise your answer to the power of 0.66.

    0.403 ^ 0.66

    = 0.549

  • Square the wave's period.

    5 * 5

    = 25

  • Multiply your answer by the gravitational constant.

    25 * 9.81

    = 245.25

  • Divide your answer by your answer from step 1:

    245.25 / 6.2831

    = 39

  • Multiply your answer by the answer to step 8 to determine the wave's wavelength in meters.

    39 * 0.549

    = 29.4 meters

References

  • Photo Credit D-BASE/Photodisc/Getty Images
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