How to Determine Fundamental Frequencies

The fundamental frequency of a wave is the slowest rate of oscillation that still produces a resonance. Resonance is an amplification of vibration caused by reinforcement between waves. Whether in an organ pipe, a violin string or a xylophone block, the fundamental frequency is what’s more commonly known as “pitch.” In a pipe, the fundamental frequency produces peaks of air compression at such a rate that the first peak has bounced back and is just exiting the pipe as the next peak begins entering.

Things You'll Need

  • Pipe
  • Sound-of-speed calculator

Instructions

    • 1

      Determine the velocity of sound based on the air temperature. Use the speed-of-sound calculator to determine the speed by entering the temperature and pressing the “calculate” button.

    • 2

      Measure the length of the pipe, using the same units you chose to measure the speed of sound, so that division will neatly cancel out the length units.

    • 3

      Divide the length by the speed of sound.

    • 4

      Divide the result of Step 3 by four if the pipe is closed at one end and by two if the pipe is open on both ends. The result is the fundamental frequency of the pipe. (If the pipe has nothing to bounce off at one end, it can still reflect off of the air at a second open end, though the fundamental frequency will differ.)

Tips & Warnings

  • To understand why the sound from a pipe is loud at its opening when reflected off a back wall, study the University of Toronto animation listed in References. Interpret the amplitudes not as density but instead as pushing the air molecules left or right out of equilibrium. In this way you can understand how two overlapping waves can cancel each other at the antinodes.
  • Air waves in a pipe are an example of a longitudinal waves, where the vibrations are parallel to the wave motion. String instruments give examples of transverse waves. Their "pitch" is their fundamental frequency, and can be found by matching the pitch to a tuning fork of known known frequency.
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