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The double wall frequency in Hz is calculated considering a mass-spring-mass system. The cavity has the role of spring and each wall as a lump mass.
The formula used is :
$$ f_{\text{msm}} = \frac{1}{2\pi} \sqrt{\frac{s'_g}{\frac{\rho_{s1} \rho_{s2}}{\rho_{s1} + \rho_{s2}}}}$$
with :
- \( s'_g \) the dynamic stiffness by unit surface of the gas \( \frac{N}{m^3} \)
- \( \rho_si \) the mass per unit surface of the material i (N/m²)
The formula of \( s'_g \):
$$s'_g = \frac{\gamma P_0}{L_z} = \frac{\rho_0 c_0^2}{L_z} $$
with :
- \( \gamma\) the Specific Heat Ratio that is equal to 1.4 in air in adiabatic compression and
1 in the case where the cavity is filled with fiber materials due to heat conduction by the fibres
References : Sound Insulation - Carl Hpokins