Some Perspectives on Wave-Mode Duality in Sea

It is well known that the response of a vibrating system can be viewed either in terms of modes or in terms of elastic wave motion. Both types of description are used extensively in Statistical Energy Analysis (SEA): the fundamental principles which underlie the method are normally expressed in modal terms, whereas wave based arguments are often used to yield practical estimates of key SEA parameters such as coupling loss factors. There has been much previous discussion regarding the relationship between the wave and modal descriptions, and the current view is perhaps best summarised by quoting the following extracts from Lyon and DeJong [1]: “we must emphasise that it is always possible, at least in principle, to arrive at the same conclusions by either [the wave or mode] approach”; “modal bandwidth is a very difficult concept to explain by a wave analysis and spatial decay of vibration is an equally difficult concept to explain by using a modal description”; “the wave-mode duality is useful for mean value estimates. but a wave analysis of variance by its nature disregards spatial coherence effects that are essential to the correct calculation of variance”. To this can be added the following quote from Fahy [2]: “just how pure standing wave fields can be created in any elastic system, by reflection of waves from boundaries of arbitrary geometry, is something of a mystery”. The relationships between the wave and modal descriptions of vibration are explored in the present paper, with the aim of clarifying the extent to which each allows a “physical” insight into the nature of the system response.