In Progress.....

Tonewood

The table below shows calculated properties of resonating plates which have different wood properties but similar resonance frequencies. The calculations are based on the equation for the resonance frequency of an oscillating plate.

For two plates 1 and 2 assuming equal resonance frequency f and length dimension:

\(h2 = h1 \sqrt{(E1d2)/(E2d1)}\) 

where h= thickness of plate, d=density, E = Modulus of Elasticity (in length direction)

The columns h2/h and w2/w compare thicknesses and mass of plates relative to a sitka spruce plate which has the same resonance frequency. (Last column shows ratio between speed of sound (c) and density. The higher this value the more responsive the wood as top.???)

The table explains why the spruces and Western Red Cedar are good choices for the top and Indian rosewood, kauri and rimu are not so good for a top. The weight of a rimu or kauri top would be double the weight of a spruce top of the same resonance frequency. This would result in lower volume of sound and less response for higher frequencies. Reducing thickness and adapting the bracing may be a solution. Western Red Cedar looks good for building instruments producing a big sound. The table doesn't say anything about bracing or damping properties. Individual properties of samples show large variations. Cedar is associated with a warm tone. This could be related to a quicker dissipation (more damping) of higher frequencies or a weaker fundamental associated with a relative low density (nice little research topic). Graphite is included in the table out of curiosity because it can be useful in combination with lighter materials like balsa wood. Balsa by itself is probably not strong enough to take the tension and the low mass is likely to result in a low sustain as well. Sitka and Port Orford Cedar (is actually not a cedar but cypress) are tougher than Engelmann Spruce and Western Red Cedar. This property may make it possible to make a thinner top, which results in a lower resonance frequency. A resonance frequency can be increased if desired by using stiffer bracing and/or increasing the dome shape of the top.