Double Wall Resonance Frequency Calculation
The resonance frequency of a double wall system is calculated using the mass-spring-mass model. In this model, the cavity acts as the spring, and each wall is treated as a lump mass. The formula used to calculate the resonance frequency is:
\[
f_{\text{msm}} = \frac{1}{2\pi} \sqrt{\frac{s'_g}{\frac{\rho_{s1} \rho_{s2}}{\rho_{s1} + \rho_{s2}}}}
\]
Where:
- \( s'_g \) is the dynamic stiffness per unit surface of the gas, measured in \( \frac{N}{m^3} \)
- \( \rho_{si} \) is the mass per unit surface of material \( i \), measured in \( N/m² \)
Dynamic Stiffness Formula
The dynamic stiffness \( s'_g \) is calculated using the formula:
\[
s'_g = \frac{\gamma P_0}{L_z} = \frac{\rho_0 c_0^2}{L_z}
\]
Where:
- \( \gamma \) is the specific heat ratio, equal to 1.4 for air in adiabatic compression, and 1 if the cavity is filled with fiber materials due to heat conduction by the fibers.
- \( P_0 \) is the atmospheric pressure, and \( L_z \) is the cavity depth.
- \( \rho_0 \) is the air density, and \( c_0 \) is the speed of sound in air.
Reference: Sound Insulation - Carl Hopkins
And to calculate the complete transmission loss of materials, use
AcouVApp Insul