Notice that both v(t) and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. The SI units of intensity are W/m2 (watts per square metre).
For a spherical sound source, the intensity in the radial direction as a function of distance r from the centre of the source is:
Here Pac (upper case) is the sound power and A the surface area of a sphere of radius r. Thus the sound intensity decreases with 1/r2 the distance from an acoustic point source, while the sound pressure decreases only with 1/r from the distance from an acoustic point source after the 1/r-distance law.
where p (lower case) is the RMS sound pressure (acoustic pressure).
The sound intensity I in W/m2 of a plane progressive wave is:
|p||pascals||RMS sound pressure|
|ξ||m, metres||particle displacement|
|c||m/s||speed of sound|
|ω = 2πf||radians/s||angular frequency|
|ρ||kg/m3||density of air|
|Z = c · ρ||N·s/m³||characteristic acoustic impedance|
|E||W·s/m³||sound energy density|
|Pac||W, watts||sound power or acoustic power|