Acoustic properties · Light and stiff
Material radiation ratio
What does combining wave speed with density tell us?
Radiation ratio R = c/ρ is a material comparison index. It rewards high directional wave speed at low density, but is not the radiation efficiency of a completed violin.
Try the interactive demoStart with something familiar
When choosing a portable tool, useful capability and the weight carried both matter. Radiation ratio similarly puts directional wave speed beside density. Its name does not mean that a whole violin’s sound output has been measured.
ρ = 400 kg/m³
c = 5400 m/s
ρ = 450 kg/m³
c = 5400 m/s
Notice what changes
At equal wave speed, the lower-density material has larger R. This comparison is not “the lighter loose blank wins”: density already accounts for volume.
Understand why
At equal E′, density affects both inertia in c and the extra division by ρ. That is why the combined expression contains ρ to the third power under a square root.
Connect it to wood and making
A plate still has to move in a pattern that couples to air. Regions moving in opposite phase can partly cancel. Material R helps compare blanks but does not replace the body’s radiation problem.
Put names to the ideas
Three powers of density
Substituting c = √(E′/ρ) gives R = √(E′/ρ³). At fixed E′, density therefore influences R more strongly than it influences c.
Its own SI unit
Dividing m/s by kg/m³ gives m⁴/(kg·s). Keep that unit visible: R is neither a percentage nor a conversion efficiency bounded by one.
Material versus radiation
A vibrating body’s sound radiation also depends on size, wavelength and the spatial pattern of surface motion. Opposing regions can cancel even when the wood has a large R.
R = c/ρ reads “wave speed divided by density.” The expanded expression shows where each input enters. R is not a percentage: a value of 13 does not mean 13% of energy becomes sound.
A worked example
At c = 5400 m/s, densities 400 and 450 kg/m³ give R = 13.5 and 12.0. Equal wave speed does not imply equal radiation ratio or equal mass for an identically shaped plate.
Explore it yourself
Compare R alongside c, density and damping rather than using it as a replacement for the full measurement record.
- c
- 5345 m/s
- E′/ρ
- 28.57 10⁶ m²/s²
- R
- 12.73 m⁴/(kg·s)
- Z
- 2.24 MRayl
- Q ≈ 1/η
- 100.0
- ACE
- 1273 m⁴/(kg·s)
E′ + ρ → c → R, Z η → Q → ACE