Space–time transformation acoustics

• We derive the mappings under which the acoustic wave equations are form invariant.
• We thoroughly compare Standard (STA) and Analogue (ATA) Transformation Acoustics.
• We show that the pressure wave equation is not suited for an ATA approach.
• We design an acoustic frequency converter via ATA that cannot be obtained with STA.

A recently proposed analogue transformation method has allowed the extension of transformation acoustics to general space–time transformations. We analyze here in detail the differences between this new analogue transformation acoustics (ATA) method and the standard one (STA). We show explicitly that STA is not suitable for transformations that mix space and time. ATA takes as starting point the acoustic equation for the velocity potential, instead of that for the pressure as in STA. This velocity-potential equation by itself already allows for some transformations mixing space and time, but not all of them. We explicitly obtain the entire set of transformations that leave its form invariant. It is for the rest of transformations that ATA shows its true potential, allowing for building a transformation acoustics method that enables the full range of space–time transformations. We provide an example of an important transformation which cannot be achieved with STA. Using this transformation, we design and simulate an acoustic frequency converter via the ATA approach. Furthermore, in those cases in which one can apply both the STA and ATA approaches, we study the different transformational properties of the corresponding physical quantities.