Gravitational frequency shifts in transformation acoustics
1 Instituto de Matemática Multidisciplinar, Universitat Politècnica de València - Camino de Vera s/n, E-46022 Valencia, Spain, EU
2 Institute for Analysis and Scientific Computing, Vienna University of Technology - Wiedner Hauptstrasse 8–10/1152, A-1040 Wien, Austria, EU
Received: 10 December 2012
Accepted: 24 February 2013
In metamaterial acoustics, it is conceivable that any type of fine-tuned acoustic properties far beyond those found in nature may be transferred to an appropriate medium. Effective design and engineering of these modern acoustic metadevices poses one of the forefront challenges in this field. As a practical example of a new covariant approach for modelling acoustics on spacetime manifolds, we choose to implement the acoustic analogue of the frequency shift due to gravitational time dilation. In accordance with Einstein's equivalence principle, two different spacetimes, corresponding to uniform acceleration or uniform gravity, are considered. For wave propagation in a uniformly accelerating rigid frame, an acoustic event horizon arises. The discussion includes a detailed numerical analysis for both spacetime geometries.
PACS: 43.90.+v – Other topics in acoustics (restricted to new topics in section 43) / 03.65.Pm – Relativistic wave equations / 04.20.Fy – Canonical formalism, Lagrangians, and variational principles
© EPLA, 2013