Sound Waves in Rooms

Abstract

Eigenfrequencies are found in sound fields in rooms by analyzing wave equations for a rectangular room surrounded by hard walls. The relationship between eigenfrequencies and eigenfunctions holds well for the wave equations as well as for linear equations. It might be quite rare to see a perfectly rectangular room in our daily life, but, room acoustics in rectangular rooms provide a good fundamental basis for better understanding of room acoustics in general. Representation of an impulse response and its frequency characteristics can be derived using the Green function in a rectangular room. Consequently, the wave theoretic representation of a sound field is derived from the expression in terms of geometric acoustics, such as the mirror image theory. Finally, a general solution form of the wave equation is presented using an integration formula in three-dimensional space.