OT: Visualizing Harmonic Nodes

This is a very neat video of salt on a vibrating surface. The surface is being excited by a transducer of some sort across a range of audible frequencies. The salt reacts to this energy. The pattern of the salt on the surface illustrates the nodal breakdown of the surface into various harmonics. That is, as the frequency increases the surface changes from moving as a single piston to breaking down into ever smaller “nodes.”  This is an excellent visual example of resonance in action.

This link came to me by way of the Twitter feed from The Art And Science of Sound, a project lead by master recording engineer and musician Alan Parsons. The project is a DVD set explaining the many mysteries of modern recording studio techniques.

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  • Very cool!

    In vibrations, a “node” is a spot on a surface (or a string) where the movement is zero (or close to it). In this case, the salt collects along lines of zero displacement, and it rolls away from the parts of the plate that are moving the most. The effect is so pronounced when working with pure tones (single sine waves), since more complex broadband sound will excite minima and maxima overlapping all over the place (resulting in salt in your eyes and on the ground…)

    (Guitar players will recognize this effect when playing “harmonics” on a string — forcing the string to have a zero-movement “node” at some location, while allowing its full length to sound, resulting in the isolated pure tone that has a node at that location.)

    As the frequency of the single tone increases, we see the various “mode shapes” of the plate, or the resonant patterns it naturally wants to vibrate in, each with a corresponding resonance frequency. When driven with a tone in between two resonance frequencies, a mixture of patterns develops (making the salt lines blurry). The sharpest salt lines occur at the natural resonant frequencies of the plate, where the driving signal matches the resonance frequency.

    In a loudspeaker, these higher resonances (which cause the cone to depart from the ideal piston-like behavior) are what cause harmonic distortion — the speaker generates frequencies that aren’t in the input signal. This is why we don’t try to reproduce high-frequency sound with a big woofer, instead using a crossover to deliver that part of the signal to a tiny tweeter (which owing to its size has higher-order resonances that are above the range of hearing).

    • Actually, more accurately, the higher-order resonances in a speaker cause “breakup” of the frequency response, with big peaks and dips at higher frequencies. Harmonic distortion is really caused by nonlinear factors, such as friction and excessive cone displacement. (Just in case my professors ever see this…)

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