Propagant phase in reverberant environments

The phase of the transfer function between two points in an extended system can be easily measured if it is taken to be the accumulated phase obtained by smoothly raising the measurement frequency from zero to the reference frequency. Lyon et al., in an extended series of papers [most recently J. Acoust. Soc. Am. 95, 286–296 (1994)], have examined the behavior of this accumulated phase in systems of two and three dimensions and have elucidated the concept of a reverberant phase which is independent of the separation between the two measurement points, provided they are far enough apart, but which rises sharply with increasing frequency. In some applications, for example, in nondestructive testing of extended structures, it is important to be able to observe simple wave‐propagation behavior and in particular to measure the propagant phase as a function of frequency and position. The conditions under which this is possible are investigated, and are shown to impose constraints on the ratio between the propagation distance and the size of the structure under test, and either the material damping coefficient or the reflection coefficient at the domain boundaries. These results, which represent an extension of those of Lyon et al., are discussed in terms of the distribution of zeros of the transfer function in the complex frequency plane. Many platelike structures of practical interest are found to satisfy these conditions, so that measurement of propagant phase behavior can provide the basis for a useful technique of nondestructive examination.