Sonic Grading

BING (Beam Identification of Non-destructive Grading) is a software program developed at the University of Montpelier, France. It uses a single standardized impulse with steel ball to induce the spruce billet to resonate. The wood is flexibly supported at its nodes, allowing the board to vibrate freely. The impulse is induced on one end of the board, and a microphone on the other end captures the resonant frequencies and the sustain of the resulting tone. The program then uses these measurements to mathematically derive the properties of stiffness and damping. The process has been refined, tested, and perfected through several years of research.

The density of the wood is the most straightforward measurement of the criteria we test. Boards are simply weighed and the mass is divided by the volume (kg/m3). The density of our most common product, Sitka spruce, varies widely from 340 to about 560 kg/m3. Density is reported as an important variable in and of itself, but it is also used as a direct input into the mathematical formulas that determine the subsequent properties—stiffness and damping (Q).

The frequencies at which a material vibrates can be used to mathematically determine its stiffness, if the density and dimensions are known. This property, known as the ‘Dynamic Modulus of Elasticity’ or MOE, was originally developed by the forest products industry to determine the structural strength of lumber. It just so happens that these techniques are even better suited to measuring the acoustic properties of tonewood.

The combination of stiffness and density of a top and bracing can help to determine the natural resonant frequencies of a guitar top. In addition, stiffness and density interact in rather complex ways to determine the efficiency by which a guitar top will vibrate, and thus the loudness of given design of guitar. Our studies corroborate what skilled luthiers already know—there is a particular combination of density and stiffness for each guitar design that leads to an optimized tone in the finished guitar. It is thus important to know these variables prior to the build process. 

When a guitar string is plucked, the energy of the string is transferred to the soundboard, and the movement of the wood vibrates the air around it and radiates sound. However, any movement is resisted by the internal friction of the wood itself, a property known as damping.

Spruce in general has rather low damping, but as with stiffness and density, there is a great deal of variability in this property. Guitars built with spruce on the high end of the damping continuum will feature a rather “dull” tone that decays quickly and accentuates the fundamental frequency at the expense of the overtones. Guitars built with low damping wood tend to radiate sound quite efficiently, with a relatively “quick” response, and tend to be preferred in blind listening tests regardless of design or build. By convention, scientists express the damping coefficient as a “Q” factor, which is the inverse of damping – thus, low damping = high Q rating.

When a material such as a soundboard resonates, much of the input energy radiates as sound waves, while some is lost as heat, and some is expended overcoming the inertia of the surrounding air. Radiation ratio (RR) is a theoretical expression describing the relationship between energy input (from the strings, in this case) and the resulting sound amplitude. It varies with the same material properties we measure: stiffness (MOE) and density.

Simply stated, RR is the square root of stiffness (MOE) divided by density cubed. In theory, it describes the potential average loudness of a resonating material. Spruce, in general, exhibits a high stiffness-to-density ratio, and RR helps explain why it has long been favored for highly responsive instrument soundboards – from guitars and violins to pianos. Click here for more.