# PARAM, SPLRHO

Bulk Data Entry Specifies the density of the acoustic medium in the calculation of the complex acoustic sound pressure and the complex particle velocity vector.

Parameter Values Description
SPLRHO Real > 0.0

Default = 1.0

This parameter is used to specify the density of the acoustic medium in the calculation of the complex acoustic sound pressure and the complex particle velocity vector, as shown below (refer to Radiated Sound Output Analysis in the User Guide):

Sound Pressure Level

Total Complex Acoustic Sound Pressure requested by SPL is:

${p}_{\mathit{total}}\left(f\right)=\sum _{j=1}^{\mathit{np}}\left(\frac{f\rho q}{{r}_{j}}{\left[{V}_{\mathit{flux}}\left(f\right)\right]}_{j}{\text{ie}}^{-\text{i}k{r}_{j}}\right)$

Where,
$f$
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.
${\left[{V}_{\mathit{flux}}\left(f\right)\right]}_{j}$
Velocity flux of the source grid $j$ .
$k$
Wave number as defined in Wave Number.
$i$
Square root of -1.
$np$
Number of source grids
$q$
Value of the scale factor specified using the parameter PARAM, SPLFAC.

Complex Particle Velocity Vector

The complex particle velocity vector is defined for each frequency as:

${\left(\stackrel{\to }{\mathit{pv}}\right)}_{j}\left(f\right)=\frac{{p}_{j}\left(f\right){\stackrel{^}{\text{X}}}_{j}}{\rho c}\left(1-\frac{i}{k{r}_{j}}\right)$

Where,
${p}_{j}\left(f\right)$
Complex acoustic pressure due to source grid $j$ at the microphone location.
${\stackrel{^}{\text{X}}}_{j}$
Unit vector from the source grid $j$ to the microphone grid.
$\left({\stackrel{^}{\text{X}}}_{j}=\frac{{\stackrel{\to }{\text{X}}}_{j}}{|{\stackrel{\to }{\text{X}}}_{j}|}=\frac{{\stackrel{\to }{\text{X}}}_{j}}{{r}_{j}}\right)$
$\rho$
Density of the acoustic medium defined by PARAM, SPLRHO.
$c$
Speed of sound defined by PARAM, SPLC.
$k$
Wave number defined above under Wave Number.
${r}_{j}$
Distance from the acoustic source grid $j$ on the panel to the microphone grid.
$i$
Square root of -1.