Several of our customers have asked about radiation ratio. Here, we’ll describe the concept, discuss its limitations as a grading tool for tonewood, and provide the information needed to calculate this value using data supplied by PRT.
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.
However, when this formula is used to “grade” one spruce top against another, its limitations become clear. Moderate- to higher-density wood will yield a disproportionately low RR, yet experienced luthiers know that some of the loudest “banjo-killer” dreadnoughts are built with denser spruce. Actual instrument loudness depends as much on design variables – body size, bracing, string choice, and construction – as it does on material properties alone.
That said, some builders (particularly those making classical or smaller-bodied guitars), do find RR useful when selecting wood. Lower-density tops (and therefore higher RR values), when paired with a high Q factor, can produce highly responsive instruments that require relatively low energy input, as is typical with nylon strings. For this reason, we include the formula so you may calculate and interpret this ratio as you see fit.
For further discussion of RR and related acoustic theory, we recommend “Wood for Sound,” a widely cited paper by Ulrike Wegst, published in the 2006 Journal of Botany and readily available online.
