THE RELATIVISTIC DOPPLER EQUATIONS FOR ATTENUATED WAVES.
Abstract
A uniform plane electromagnetic wave which is attenuated as it travels through a dispersive medium is demonstrated to have a phase which is not Lorentz invariant. The attenuation can be caused by dissipation in the medium, or because the frequency of the wave is below the cut-off frequency of the medium. The relativistic Doppler equations for the attenuated plane waves are derived, and used to study some of the general properties of this wave, including the geometry of the field vectors. It is shown from the Doppler equations that an attenuated wave which is time-harmonic in one inertial reference frame is not time-harmonic in all other inertial reference frames. This result has important consequences in the formulation of the constitutive relations which characterize the medium. The Doppler equations are also utilized as a basis for studying the drag effect for attenuated waves in moving media. The basic method of analysis in this paper utilizes the rigorous electromagnetic field equations in conjuction with Minkowski's extension of the theory of Special Relativity for material media. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 30, 1966
- Accession Number
- AD0837200
Entities
People
- H. Berger
- J. W. E. Griemsmann
Organizations
- New York University Tandon School of Engineering