• These two simulations differ only in the driver frequency.

  • The top sim shows how driver frequency and wave tank frequency interact:

    • Notice how small wave bumps appear a few times as resonance builds up

    • This represents slight interference between the driver frequency and resonant frequency.

    • Eventually, the wave shape settles into a unified pattern.

    • Notice that this stable pattern's wave shape is different from the original wave shape.

      • The driver and resonant frequencies are sine waves. This is a very smooth wave shape.

      • The composite wave shape is not as smooth. It is the sum of several simple sine waves.

      • The math which describes this effect is Fourier Analysis.

  • The bottom sim shows how beat frequency works.

    • Initially, resonant energy is built up in the system.

    • After a while, the driver action opposes the action of the resonant waves.

    • The driver decreases the energy stored in the system until the waves die out.

    • The cycle then starts again, and the resonant waves appear again.

• Wavelength and frequency are tightly coupled phenomena. Resonance is a less simple thing.

  • The properties of the wave tank determine resonance:

    • Wave speed (stiffness) and damping (friction).

    • Length of the wave tank.

    • Position and frequency of the driver.

• The frequency of the driver should be close to the natural resonant frequency of the tank or else resonance will not build up energy in the system.

• When the two frequencies differ slightly, the system may stay resonant.

• When the two freqencies differ significantly, other effects occur:

  • Beat frequencies: The difference between the driver frequency and the natural tank frequency produces a third frequency, equal to the difference.

    • This third frequency is generally a much lower frequency than the other two.

    • Sometimes, the third frequency is something other than the simple difference.

  • Destructive interference:

    • Initially the energy builds up in the system.

    • After some time, the energy pattern of the driver frequency opposes the energy pattern maintained by the natural wave tank frequency.

    • When the patterns are opposite, the driver reduces the system energy, rather than increasing it.

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