# Speed of sound

## Values for calculation

$γ_π$
$τ$
$γ_{πτ}$
$γ_{ττ}$
$γ_{ππ}$
$R$ $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$T$ $\mathrm{°C}$
$π$
$γ^r_π$
$γ^r_{ππ}$
$γ^r_{πτ}$
$γ^o_{ττ}$
$γ^r_{ττ}$
$δ$
$φ_δ$
$φ_{δδ}$
$φ_{δτ}$
$φ_{ττ}$
$\text{Region}$

## Calculation

### Speed of sound

$\text{if }\ \text{Region}= 1$
$$w=\sqrt{\left(\cfrac{γ_π^2}{\cfrac{\left(γ_π-τ\cdot γ_{πτ}\right)^2}{τ^2\cdot γ_{ττ}}-γ_{ππ}}\right)\cdot R\cdot\left(T+273.15\right)}$$
$\text{else if }\ \text{Region}= 2$
$$w=\sqrt{\cfrac{1+2\cdot π\cdot γ^r_π+π^2\cdot {γ^r_π}^2}{\left(1-π^2\cdot γ^r_{ππ}\right)+\cfrac{\left(1+π\cdot γ^r_π-τ\cdot π\cdot γ^r_{πτ}\right)^2}{τ^2\cdot\left(γ^o_{ττ}+γ^r_{ττ}\right)}}\cdot R\cdot\left(T+273.15\right)}$$
$\text{else if }\ \text{Region}= 3$
$$w=\sqrt{\left(2\cdot δ\cdot φ_δ+δ^2\cdot φ_{δδ}-\cfrac{\left(δ\cdot φ_δ-δ\cdot τ\cdot φ_{δτ}\right)^2}{τ^2\cdot φ_{ττ}}\right)\cdot R\cdot\left(T+273.15\right)}$$
$\text{else if }\ \text{Region}= 5$
$$w=\sqrt{\cfrac{1+2\cdot π\cdot γ^r_π+π^2\cdot {γ^r_π}^2}{\left(1-π^2\cdot γ^r_{ππ}\right)+\cfrac{\left(1+π\cdot γ^r_π-τ\cdot π\cdot γ^r_{πτ}\right)^2}{τ^2\cdot\left(γ^o_{ττ}+γ^r_{ττ}\right)}}\cdot R\cdot\left(T+273.15\right)}$$
$\text{else}$
$$w=0$$