Sound Field in Rooms: Zeros by Multiple Reflections and Eigenfrequencies for Reverberation

Sound field would be a representative of linear systems where poles and zeros might be the key to identify the systems. Sounds in rooms may be a superposition of the direct sound, followed by early reflections from prominent walls around the source, and reverberation after repeating successive collisions with surrounding walls in the environment. Early reflections may be characterized by zeros, while reverberation identifies the poles from a perspective of the linear system theory. The poles of sound fields correspond eigenfrequencies which the wave equation governs. This chapter exemplifies frequency characteristics of sound fields, which may reveal noticeable signatures due to the poles and zeros. Most prominent properties of poles or eigenfrequencies of sound fields would be non-harmonics in contrast to one-dimensional systems like musical instruments. The non-harmonic eigenfrequencies make density of the eigenfrequencies to be frequency dependent such that the density may increase in proportion to the square of frequency. Dense eigenfrequencies may make spectral fine structures of frequency responses of sound fields, which might smoothly fill under the spectral envelopes. Spectral envelopes give macroscopic spectral dynamics that are constructed by the early reflections, because of zeros or interference between the direct sound and reflections.