The critical frequency is a key parameter in building and material acoustics. It occurs when the bending wavelength of a panel equals the acoustic wavelength in air. At this point, the bending wave speed equals the speed of sound in air, leading to a drop in sound insulation performance.
The critical frequency (fc) can be calculated using the following equations:
$$ f_c = \frac{c_0^2}{2\pi}\sqrt{\frac{\rho_s}{B_p}} = \frac{c_0^2}{\pi} \sqrt{\frac{3\rho_s(1-\nu^2)}{E h^3}} $$
When designing walls, floors, or partitions, accounting for the critical frequency helps optimize sound insulation performance depending of the frequency radiation of the noise source. Near this frequency, sound transmission increases due to coincidence effects.
Reference: Sound Insulation – Carl Hopkins
For complete transmission loss calculations of various materials, try our interactive module: AcouVApp Insul.