# Radiated Sound Output Analysis

Radiated Sound Output can be requested for grid points on the structural surface and in the exterior acoustic field. Grid points are used to represent microphones to record the radiated sound, sound power, and sound intensity.

## Request Radiated Sound Output Guide

The following procedure can be considered as a guide for requesting radiated sound output:

- Microphones that record sound levels in the acoustic field can be defined as
grid point sets using the RADSND (
`MSET`field) Bulk Data Entry. - PANELG
(
`TYPE`=SOUND/Blank) can be used to define the sound generating panel(s) which are to be considered for radiated sound output calculations. - The
`PANEL`continuation line in the RADSND Bulk Data Entry can be used to list the panel IDs of the panels defined using PANELG (`TYPE`=SOUND/Blank). This allows the definition of the sound generating panels that contribute to the calculation of radiated sound output at the microphones (Grid points) listed in the`MSET`field of the RADSND Bulk Data Entry. - The value of the speed of sound $c$ required to define the wave number and the
complex particle velocity vector is input using PARAM,
`SPLC`. The density of the acoustic medium $$e$$ used in the calculation of the complex acoustic sound pressure and the complex particle velocity vector is defined using PARAM,`SPLRHO`. An additional scale factor $$q$$ can be specified using PARAM,`SPLFAC`in the Sound Pressure Level calculation. - Various outputs can be requested for this analysis. SPOWER output request can be used to request sound power, SINTENS can be used to request sound intensity and SPL can be used to request sound pressure.

The set up guide for radiated sound output calculation is described in the previous section. The procedure is based on the following set of equations for the calculation of each output type.

## Analytical Background for Radiated Sound Output

The sound radiated from the sound generating panel is reduced to sound generation from discrete point sources. The grid points of the finite element mesh on the surface of the panel are considered as sound sources. Sound power and sound intensity can be requested for both the source grids and the microphone grids.

## At the Microphone Location

### Wave Number

- $$c$$
- Speed of sound defined by PARAM,
`SPLC` - $f$
- Frequency of the sound wave in the medium

### Velocity Flux of the Source Grid

- ${v}_{s}$
- Velocity vector of the source grid.
- $\delta A$
- Area vector associated with the source grid defined as:
(3) $\delta A=A{\widehat{A}}_{s}$

- $A$
- Area associated with the source grid
- ${\widehat{A}}_{s}$
- Unit area vector normal to the panel surface at the source grid (Figure 2).

### Complex Acoustic Sound Pressure (Requested using SPL)

- $f$
- Frequency of the sound wave in the medium
- $\rho $
- Density of the acoustic medium defined by PARAM,
`SPLRHO` - $${r}_{j}$$
- Distance from the acoustic source grid $j$ on the panel to the microphone location grid (Figure 1).
- ${\left({v}_{flux}\right)}_{j}$
- Velocity flux of the source grid
- $k$
- Wave number as defined in Wave Number.
- $i$
- Square root of -1
- $np$
- Number of source grids (Figure 1).
- $$q$$
- Value of the scale factor specified using the parameter
PARAM,
`SPLFAC`.

- $SP{L}_{dB}$
- Sound Pressure Level in decibels
- $\left|SPL\right|$
- Magnitude of the acoustic sound pressure
- $SPLREFDB$
- Reference sound pressure value specified using the parameter
PARAM,
`SPLREFDB`

### Complex Particle Velocity Vector

- $${p}_{j}$$
- Complex acoustic pressure, due to source grid, $j$ at the microphone location.
- $${\widehat{r}}_{j}$$
- The unit vector from the source grid $j$ to the microphone grid (Figure 1).
- $\rho $
- Density of the acoustic medium defined by PARAM,
`SPLRHO`. - $$c$$
- Speed of sound defined by PARAM, SPLC
- $k$
- Wave number as defined in Wave Number
- ${r}_{j}$
- Distance from the acoustic source grid $j$ on the panel to the microphone grid (Figure 1).
- $i$
- Square root of -1

### Total Sound Power (Requested using SPOWER)

- $${p}_{j}$$
- Acoustic pressure at a microphone location, due to the source grid $j$
- ${p}_{j}^{*}$
- Complex conjugate of $${p}_{j}$$
- $np$
- Number of source grids (Figure 1)

### Total Complex Intensity Vector (Requested using SINTENS)

Where, $${p}_{j}$$ is the acoustic pressure at the microphone location due to the sound generated at the source grid $j$ and ${\left({v}_{j}^{p}\right)}^{*}$ is the complex conjugate of ${v}_{j}^{p}$, which is the complex particle velocity vector at the microphone location, due to the sound generated at the source grid $j$.

### Source Grid Location

#### Wave Number

Where, $x$ is the vector from a source grid (1) to the source grid (2) of interest.

Where, $A$ is the area associated with a source grid and ${\widehat{x}}_{r}$ is the unit normal to the area, $A$ associated with a source grid.

#### Complex Acoustic Sound Pressure [at the source grid]

Where,

$f$ is the frequency of the sound wave in the medium.

$\rho $ is the density of the acoustic medium defined by
PARAM, `SPLRHO`.

$${({r}_{s})}_{j}$$ is equal to $\left|{x}_{s}\right|$, for each grid, $j$ ($j$=1 to $np$), as defined in At the Source Grid Location (Figure 3).

$${\left({v}_{flux}\right)}_{j}$$ is the velocity flux of the source grid, $j$ (Figure 3)

$k$ is the wave number as defined in Wave Number.

$i$ is the square root of -1

$np$ is the number of source grids (Figure 2).

$$q$$ is the value of the scale factor specified using the
parameter PARAM, `SPLFAC`.

#### Total Sound Power (Requested using SPOWER) [at the source grid]

- ${\left({p}_{s}\right)}_{j}$
- Acoustic pressure at a source grid, due to the source grid $j$.
- ${\left({p}_{s}\right)}_{j}^{*}$
- Complex conjugate of ${\left({p}_{s}\right)}_{j}$.
- $np$
- Number of source grids (Figure 2).

#### Total Complex Intensity Vector (Requested using SINTENS) [at the source grid]

Where, ${\left({p}_{s}\right)}_{j}$ is the acoustic pressure at the source grid location of interest, due to the sound generated at the source grid $j$.

Where, $${\left({v}_{s}^{n}\right)}_{j}^{*}$$ is the complex conjugate of the normal velocity vector $${v}_{s}^{n}$$ of the source grid of interest.