Menu

Speed of sound

Values for calculation

$ \{γ_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_π $
$ \{τ\in\mathbb{R}\mid τ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ τ $
$ \{γ_{πτ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_{πτ} $
$ \{γ_{ττ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_{ττ} $
$ \{γ_{ππ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_{ππ} $
$ R $ $ \mathrm{J\cdot\ kg^{-1}\cdot\ K^{-1}} $
$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T $ $ \mathrm{°C} $
$ \{π\in\mathbb{R}\mid π>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ π $
$ \{γ^r_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_π $
$ \{γ^r_{ππ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_{ππ} $
$ \{γ^r_{πτ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_{πτ} $
$ \{γ^o_{ττ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^o_{ττ} $
$ \{γ^r_{ττ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_{ττ} $
$ \{δ\in\mathbb{R}\mid δ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ δ $
$ \{φ_δ\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_δ $
$ \{φ_{δδ}\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_{δδ} $
$ \{φ_{δτ}\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_{δτ} $
$ \{φ_{ττ}\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_{ττ} $
$ \text{Region} $

Calculation

Speed of sound

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