Airborne sound insulation of thick walls

TLDR: In this article, the Euler-Bernoulli plate theory was used to derive approximate analytical solutions for the transmission of airborne sound through a plate between two rooms, where rooms are placed above each other and are of different size.

Abstract: Approximate analytical solutions are presented for the transmission of airborne sound through a plate between two rooms. The rooms are placed above each other and are of different size. The area of the plate is larger than the area of either room. Simple formulas are derived from the Euler–Bernoulli plate theory for the transmission due to the forced as well as the resonant field of the plate. The most interesting result concerns the forced response at coincidence, which is shown to be heavily dependent on the size of the excited area. A “rise length” on the analogy of the rise time in a single-degree-of-freedom system is introduced. Within the rise length, which is often very large, the displacement is proportional to the trace length on the plate of the exciting sound ray. The mean transmission factor due to the forced response at frequencies above the critical frequency is for this reason dependent on the source room area, but not on the loss factor. The coupling between a diffuse sound field and the free waves is, on the other hand, loss factor dependent, but the dependence of the coupling on the angle of incidence is shown to be quite different from that in the corresponding case of an infinite plate.