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Dimensionless solutions of the wave equation | | J. Blas
; J. L. Gutiérrez
; E. J. Abril
; | | Date: |
1 Aug 2022 | | Abstract: | Plane waves are regarded as the general solution of the wave equation.
However the plane wave expansion of standing waves by means of complex phasors
leads to a theory in which the time coordinate does not receive the same
treatment as the three space coordinates. An equal treatment is possible using
our alternative approach built upon the dimensionless version of the wave
equation. As a result, the usual standing wave solution written as sum of plane
waves is just one of the available geometrical projections and therefore
removes a part of the available information. The existence of these alternative
projections and the constraints that they introduce, produce verifiable
consequences. We present an experimental verification of one of this
consequences by means of acoustic waves. In particular a resonant cavity is
radiated from an external source through a squared aperture. The predicted
flows of phase based on P’olya potentials allow us to find the direction of
arrival without using temporal coordinates. Although this work is limited to
the wave equation, the background concept is the relationship between space and
time and therefore could have far reaching consequences in other physical
models. | | Source: | arXiv, 2208.00551 | | Services: | Forum | Review | PDF | Favorites | |
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