# Sound Intensity

The quotient obtained when the average rate of energy flow in a specified direction and sense is divided by the area, perpendicular to that direction, through or toward which it flows. The intensity at a point is the limit of that quotient as the area that includes the point approaches zero.

Sound intensity is a vector quantity. It describes as a function of frequency the direction and the amount of net flow of acoustic energy at a position in a sound field.

Sound intensity is the time averaged product of pressure and particle velocity. You can measure it using a sound intensity probe, made of two closely spaced microphones.
The pressure may be calculated from the average of the two pressure measurements.
The particle velocity can be related to the pressure gradient using Euler's equation:
This may be integrated to give the velocity:
This is essentially Newton's second law applied to a fluid. If we know the force and mass we can find the acceleration and then integrate it to find the velocity. With Euler's equation it is the pressure gradient that accelerates a fluid of a given density.

The sound intensity is then simply the product of pressure and particle velocity.

Applications:
• Sound power determination.
• Noise source location.

Active Sound Field
A sound field in which the particle velocity is in phase with the pressure. The sound propagates to the far-field.

Reactive Sound Field
A sound field in which the particle velocity is 90° out of phase with the pressure. An ideal standing wave is an example of this type of field, where there is no net flow of energy and constitutes the imaginary part of a complex sound field.

Residual Intensity
This is the sound intensity level measured when the same signal is fed to both channels of a sound intensity measuring system, or it is exposed to a purely reactive sound field.

Effect of Airflow
Turbulence in an airstream can impose non-acoustic pressure disturbances on microphones. This can be reduced using windscreens, but only with limited success. The two microphone probe suppresses the effect of small scale turbulence on the pressure cross spectrum by virtue of the fact that the hydrodynamic pressures have a limited correlation length. However, the resulting intermicrophone coherence is still decreased with the increase in random error. This can be reduced to some extent by averaging. Larger scale turbulence pressures are less well suppressed. The major problems tend to occur at frequencies below 250Hz. Larger microphone spacing will help this considerably.
Usually, there is no direct relationship between sound pressure and sound intensity. However, for a plane wave there is a relationship, this relationship can be used in a free field at a distance from the source.

where
I = Mean intensity [Wm-2]
prms = RMS sound pressure level [Pa]
ρ0 = Equilibrium density of air [kgm-3]
c0 = Speed of sound in air [ms-1]
ρ0c0 is the characteristic specific acoustic impedance, 415 rayl (N s m3) for air at 20°C
Sound intensity can also be quoted in dB:

LI = Sound intensity level in dB
Iref = Reference sound intensity level 10-12 Wm-2

For a plane wave:
Lp dB re 2x10-5 Pa = LI dB re 10-12 Wm-2

This relationship is used within ISO 3744:1994(E) to determine sound power from sound pressure levels. The sound intensity level is combined with an area term to determine the sound power of an object.