The propagation of an acoustic wave is associated with a flow of energy in the direction of the wave motion, the intensity vector I. The sound intensity in a specific direction (through a specific boundary) is defined as the time average of (sound) power per unit area in the direction of the normal to that area.
Knowledge of the intensity is important when characterizing the strength of a sound source — that is, the power emitted by the source. The power is given by the integral of n·I on a surface surrounding the source, where
n is the surface normal. The intensity is also important when characterizing transmission phenomena, for example, when determining transmission loss, insertion loss curves, or absorption.
The acoustic intensity vector I (SI unit: W/m
2) is defined as the time average of the instantaneous rate of energy transfer per unit area (sound power)
pu, such that
where ?∗ denotes complex conjugation. In the frequency domain the velocity is readily expressed in terms of the pressure as
u = −1/(iωρ)∇p. Using the specific characteristic acoustic impedance for plane waves, the intensity can also be expressed in terms of the root mean square (RMS) pressure as
When using the scattered field formulation, by adding a Background Pressure Field feature, the intensity variables for the total, background, and scattered fields are available in postprocessing if the
Calculate background and scattered field intensity option is selected.
This expression is difficult to recover in pressure acoustics and would require the solution of an additional PDE to calculate the velocity from the pressure dependent variable. Only the intensity I (time averaged) is available as postprocessing variable in the frequency domain and can be selected from the expressions menus when plotting. The instantaneous intensity does exists as a postprocessing variable in transient interfaces such as Linearized Euler, Linearized Navier–Stokes, or Thermoviscous Acoustics where the velocity is solved for explicitly, see
Modeling with the Aeroacoustics Branch or
Modeling with the Pressure Acoustics Branch (FEM-Based Interfaces) for details.
The variables are defined in Table 2-3,
Table 2-4, and
Table 2-5. In the variable names,
phys_id represents the interface name, for example,
acpr for a Pressure Acoustics, Frequency Domain interface.
Common to the Pressure Acoustics fluid models (also porous materials) and The Thermoviscous Acoustics, Frequency Domain Interface is that all the interfaces model some energy dissipation process, which stem from viscous and thermal dissipation processes. The amount of dissipated energy can be of interest as a results analysis variable or as a source term for a multiphysics problem. An example could be to determine the amount of heating in the human tissue when using ultrasound. In the Acoustics Module special variables exist for the dissipation.
where * in
Equation 2-6 is the complex conjugate operator.
where |I| is the magnitude of the intensity vector
I and
k is the wave number. This expression is an approximation and is only valid for traveling plane waves (or waves that are close to plane); however, it has many uses as a first estimate of the dissipation since it is easy to calculate in many different situations. The expression is, for example, not valid for standing waves in resonant systems. When the above expression is not valid, the dissipated energy should be calculated using an energy balance approach.
The power dissipation variables are defined in Table 2-6. In the variable names,
phys_id represents the name (
acpr, for example, for a pressure acoustics interface).
where n is the normal to the surface being modeled. The velocity and acceleration are defined in terms of the gradient of the pressure
p as follows
where kn is the out-of-plane wave number solved for,
m is a possible radial wave mode number, and
∇|| is the tangential derivative along the boundary.
The boundary mode acoustics variables are defined in Table 2-7. In the variable names,
phys_id represents the name (
acbm, for example, for a Boundary Mode Acoustics interface).
