Chladni Patterns, an introduction
In lutherie, Chladni patterns are used to visualise the -often spectacular- deformations of a resonating plate. A Chladni pattern (after Ernst Chladni 1756 – 1827) is basically a pattern (de)formation in a surface, due to a periodic dissipation of free energy. Somehow I don’t think this cryptic definition makes you any wiser, and since I find it quite hard to describe in words what a Chladni pattern is, especially to someone who has never seen one, I made a video so you can see ‘the magic’ yourself:
This filmclip I made shows the formation of so called Chladni patterns. What you see filmed from above is a plywood plate of 3,5mm thick, 40 x 33 cm² that rests on the cornerpoints, so a loudspeaker can be positioned under the plate. I’ve sprinkled tealeaves on the plate. The loudspeaker that is under the plate, plays a constant tone at a different pitch (frequency) for each pattern.
Tealeaves collect at the nodal lines
Chladni Patterns and harmonics
To understand what is happening here, you first need to know about string harmonics, which you probably already do as a playing technique; a string harmonic can be made to stand out when you slightly touch and let go the (open) string at one of the spots, one of the nodes, that divides the string in an number of equal parts.
Best known are the harmonics or overtones halfway for the octave, on a third of the string length for the octave+fifth, and the second octave at a fourth of the string length etc.
(If you have no idea what I’m talking about, I recommend you read this page on the shape of the tone in the article on string choice).
As also mentioned in that article on string choice, a combination of fundamental frequency and harmonics will ‘automatically’ form in the string; the timbre, the color of the tone is a result of the combination of fundamental and harmonics. Due to this combination we can identify not only the pitch to which the string is tuned, but also if the string is for instance made out of metal or gut or…
The node acts like a ‘hinge’ point; the string amplitude at this point is (almost) zero.
If you add a dimension, and go from string to plate, the collection of hinge points forms a line; a nodal line. Together these lines can form a pattern. In a plate these harmonics also appear ‘automatically’.
Which waves appear and thus which patterns appear, depends on a lot of (boundary) conditions. As seen in the video above, these patterns appeared when the plate that was supported at the four corners was driven into motion with a speaker.
Multiple waves in a plate
Apparently, waves appear in two direction perpendicular to each other, as illustrated in these images:
What you see in these patterns and may seem rather strange, is that while the speaker plays a single (sinus) tone at a constant frequency, two different waves that are perpendicular to each other appear in the plate simultaniously. Do both waves have this same frequency as the driving fequency of the speaker? What’s happening here?
Again, I think it is best explained with a video:
Do the perpendicular waves that emerge when driven by a single frequency both have the same frequency? What’s happening here?
What can be seen in the video and the analysis plot, is that when you tap in the middle and the combined pattern belonging to the resonance of 200Hz appears, both the perpendicular patterns (52Hz and 148Hz) are a lot louder than the actual frequency at which the combined resonance pattern appears.
Most people (including me) are not able to hear the third 200Hz tone in the taptone. This is caused by auditory masking; the two lower frequencies are so loud and relatively close to the third, that their volume masks the third frequency of 200Hz. It is like walking in the sun and having your own shadow, but when you pass a big building that blocks your sun, your shadow is masked.
A little peak in the kitchen of the luthier.
What does a luthier do with this information? what’s the use of all this?
Well, suppose the plate of the video is the top plate of a Bo Diddley cigar box like acoustic guitar like in this picture. The bridge, the driver, is situated at the middle of the plate.
If you play a 200Hz note on this instrument (approx a G3), then this tone will be colored, it wil have a timbre where the frequencies 52Hz and 148Hz, and the range between 52Hz and 148Hz is quite prominent. The 52Hz – 148Hz range lies within the bass – baritone- tenor voice range, probably quite dark and warm, probably also dull and unpronounced due to the lack of sharpness. The tone will also probably not ring out very long, because the vibration at this particular frequency -the resonant frequency- is used up quite fast by the vibrating plate.
If the top plate were totally different, say the area between 250Hz and 1200Hz was quite prominent, the timbre of the 200Hz tone would be more like that of a soprano voice, and the 200Hz tone would ring a lot longer.
Part of the craft of the luthier, is to tune a specific character into the instrument. As demonstrated in the first video in this article on Chladni patterns, one simple rectangular plate that is supported at the corners already has a lot of different patterns.
In the second video that same plate was supported at the intersections of the nodal lines of a certain mode, this introduced boundary conditions that ‘tuned’ the plate.
By tuning the plate, you can influence which frequencies the plate will vibrate ‘by itself’. With ‘by itself’ I mean where the driving force is caused not by an external driver like a loudspeaker or string, but by the energy that is periodically released by the spring-like plate itself. By choosing other support positions, the waves patterns that appear may change.
Actually, apart from choosing another support position, a luthier has a lot of options at his/her disposal to tune a plate; change the shape and position(s) of the driver(s), change the outline, make the plate smaller, or wider, or lighter, or thinner, make it out of another (composite) material, bend /curve it, add supports (soundpost), change the method of support (clamped, hinged, free, spring…), add holes, add sound bar(s), make it a-symmetric etc.
Note that these methods are not only used to tune the overall timbre, other important factor that can be controlled is the dissipation of available energy over time (envelope).
I hope that with this article you now have an idea of what Chladni patterns are and how they can be useful in lutherie.