Mass Law and Mass Air Mass Resonance

The mass for predicting Sound Insulation.

Looking into sound insulation prediction, you Will most definitely be met with the Mass Law.

While the Mass Law may not offer great accuracy on its own (as sketched below for an acoustically thick plate), it comes into play when utilized as a correction term within comprehensive prediction models.

In short, The mass law is characterized by a 6 dB increase every time mass or frequency is doubled.

Mass Air Mass Resonance

Mass Air mass resonance is another parameter that can really help define the acoustic parameters of the system.

If we solve for the natural frequency of a mass Air mass system, In this case a double Wall, we are able to derive an expression as shown below. Analogous to a mass spring mass system with the airgap between the panels being the spring. 

With this we can derive a lot of knowledge regarding the Sound reduction, as the system Will often showcase a dip at the mass Air mass resonance.