# engineering question #5250

James, a 38 year old male from Victoria asks on April 2, 2011,

Q:

I've watched a few videos about sound frequencies altering the geometric pattern of molecules. Some interesting work has been done on the effects of sound on matter. The discipline is called Cymatics. My questions is, how can I find out which frequencies produce which results? In other words, if a certain frequency 'reconstructs" a molecule to a specific geometric pattern, what is the number of that frequency? I want to reproduce those frequencies on my computer with an audio editor I have.

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Quentin Wright answered on April 4, 2011, A:

As a scientific discipline, cymatics is not really about the reconstruction of molecules by sound. Rather, it is concerned with the study of visible sound and vibration. Sound waves can be made visible in many ways. In a typical experimental context, something is coated or covered with fine particles or liquid. When sound frequencies are applied to the item, the coating is displaced by the waves that have been created, making the wave patterns visible.

The 17th Century German physicist Ernst Chladni is regarded as the first person to theorize about sound patterns and experimentally investigate the nature of sound. His work introduced acoustics as a new branch of physics and had a profound influence on the development of wave theory.

In one of his most insightful experiments, Chladni sprinkled fine sand onto plates and rods of varying size, shape and material. He then systematically studied the patterns created in the sand when the plates were vibrated at a range of sound frequencies.

These experiments led to the development of Chladni’s Law. This is an equation which expresses the relationship between the frequency (f) of modes of vibration of a flat, circular surface and the diametric (m) and radial (n) nodes created by that frequency. The equation is as follows:

f = C(m + 2n)p

C and p are coefficients which depend on the properties of the plate. For thin, flat circular plates, p is roughly 2 and C is roughly 1, which simplifies the equation somewhat. Chaldi's law is actually a lot more complicated that this answer suggests. This formula is basically correct but there are other variables based on the properties of the plates, node location and so on. Still as an approximation, if you want to, say, create a cymatic vibration pattern that has 3 diametric and 2 radial nodes on a thin flat circular plate, you could work out the frequency as follows:

f = 1 (3+(2*2))2  or 72 or 49 cycles per second

So to return to the question, the visible wave forms created by various frequencies can certainly be predicted mathematically but it depends upon the size, shape and physical properties of what you are vibrating.

You can conduct your own visible sound wave experiments fairly simply using a Chladni plate. Instructions for building a Chladni plate are available online here: http://www.make-digital.com/make/vol16/?pg=128#pg128