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How to Calculate Resonant Frequency of a Volume

Flutes, pipe organs and whistles are all examples of resonant volumes. The space a volume encloses produces standing wave vibrations at multiples of one particular frequency, and that frequency depends on the volume's length. Short volumes produce high frequencies and long volumes generate low frequencies. The speed of sound in air also determines the volume's resonant frequency, as does the volume's shape. The final factor for calculating resonance is whether the volume has both ends open or has a closed end.

Instructions

Open-Ended Cylinder
- 1
  Key in the speed of sound for air, 1,100 feet per second, into your calculator. Multiply this by .5. You should see an intermediate answer of 550.
- 2
  Press the divide key. Enter the length of the volume in feet. For example, enter 5 feet for an organ pipe.
- 3
  Press the equals key. The calculator computes the result in hertz, or cycles per second. In this example, 550 / 5 = 110, the value for the note A an octave below middle C.
Closed-Ended Cylinder
- 4
  Key in the speed of sound for air, 1,100 feet per second, into your calculator. Multiply this by .25. You should see the intermediate answer of 275.
- 5
  Press the divide key. Enter the length of the volume in feet. As an example, use 5 feet.
- 6
  Press the equals key. The calculator computes the result in hertz, or cycles per second. The example gives 275 / 5 = 55, or the note A two octaves below middle C.

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