In this paper an active multimodal beam vibration reduction via one actuator is considered. The optimal actuator distribution is analyzed with two methods: an exact mathematical principles and the LQ problem idea. It turned out that the same mathematical expressions are derived. Thus, these methods are equivalent.
The cuboidal room acoustics field is modelled with the Fourier method. A combination of uniform, impedance boundary conditions imposed on walls is assumed, and they are expressed by absorption coefficient values. The absorption coefficient, in the full range of its values in the discrete form, is considered. With above assumptions, the formula for a rough estimation of the cuboidal room acoustics is derived. This approximate formula expresses the mean sound pressure level as a function of the absorption coefficient, frequency, and volume of the room separately. It is derived based on the least-squares approximation theory and it is a novelty in the cuboidal room acoustics. Theoretical considerations are illustrated via numerical calculations performed for the 3D acoustic problem. Quantitative results received with the help of the approximate formula may be a point of reference to the numerical calculations.