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How to Calculate Harmonic Oscillations

An oscillation is change in a system. Waves are oscillating systems that change in predictable ways. Oscillations are measured by way of frequency, which is the number of cycles of the wave per second (hertz, or Hz). Harmonic oscillations are the smaller waves based on the fundamental frequency. The harmonic frequencies of any given wave system can be found by considering the integer multiples of the fundamental frequency.

Things You'll Need

  • Ruler
  • Calculator
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Instructions

    • 1

      Measure the length of your system. Measure in units of length that will correspond to the speed for your system. For example, if you are calculating the harmonics of a string on a musical instrument or other sonic system, the speed of sound is typically measured in meters per second. Therefore, record your length in meters.

    • 2

      Record the speed of your wave. For a sound wave, the speed of sound in air at 20 degrees celsius is approximated to be 344 meters per second.

    • 3

      Divide the speed of your wave by its wavelength. For a tube or string, the wavelength is twice the length of the system (for a tube closed at one end, the wavelength is four times the length of the system). For example, if you are calculating the harmonics of an organ pipe of length 1m, the fundamental frequency is:

      344 m/s / (2 * 1m) = 172 Hz

    • 4

      Multiply the fundamental frequency by positive integers, beginning with 1. These correspond to the harmonics. For example:

      First harmonic: 172 Hz * 1 = 172 Hz

      Second harmonic: 172 Hz * 2 = 344 Hz

      Third harmonic: 172 Hz * 3 = 516 Hz

      Fourth harmonic: 172 * 4 = 688 Hz

      ...and so on.

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