Sound transmission of a spherical sound wave through a finite plate

For an incident plane wave on an infinite plate, a doubling of mass or frequency adds 6 dB to the sound transmission loss (TL), but for an incident spherical wave on an infinite plate, a doubling of mass or frequency adds only 3 dB to the TL. In reality, the discrepancies of the sound transmission due to plane wave and spherical wave incidence might not be so huge, since the influences resulted from the plate size and the distance between the source and the plate cannot be ignored. In this article, the sound transmission of a spherical wave through a finite plate is theoretically analyzed through the modal expansion method. The transmission losses for typical plates are illustrated and as well are compared with that of the mass laws due to normal and spherical wave incidence, respectively. The effects of parameters such as the size of the plate, the distance between the source and the plate, and the horizontal shift of the plate are investigated. An indicator for the estimation of the TL through a finite plate due to a point source is given for the potential of practical applications.