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Problem B: Equations for the speed of sound The adiabatic speed of sound is defined as $v^2 = \left(\frac{\partial P}{\partial \rho}\right)_s$. First prove that: $\left(\frac{\partial P}{\partial \rho}\right)_s = \gamma \left(\frac{\partial P}{\partial \rho}\right)_T$, where $\gamma = \frac{C_P}{C_V}$ Using the formula you have just derived above calculate the adiabatic speed of sound in the air at ambient temperature (25 °C) assuming that the air behaves as an ideal gas. Compare your result with values published in the open literature.

          Problem B: Equations for the speed of sound
The adiabatic speed of sound is defined as $v^2 = \left(\frac{\partial P}{\partial \rho}\right)_s$. First prove that:
$\left(\frac{\partial P}{\partial \rho}\right)_s = \gamma \left(\frac{\partial P}{\partial \rho}\right)_T$, where $\gamma = \frac{C_P}{C_V}$
Using the formula you have just derived above calculate the adiabatic speed of sound in the air at
ambient temperature (25 °C) assuming that the air behaves as an ideal gas. Compare your result
with values published in the open literature.

Problem B: Equations for the speed of sound
The adiabatic speed of sound is defined as v^2 = ((∂ P)/(∂ρ))s. First prove that:
((∂ P)/(∂ρ))s = γ((∂ P)/(∂ρ))T, where γ = (CP)/(CV)
Using the formula you have just derived above calculate the adiabatic speed of sound in the air at
ambient temperature (25 °C) assuming that the air behaves as an ideal gas. Compare your result
with values published in the open literature.

Added by Tammy A.

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