  A recently proposed analogue transformation method has allowed the extension
of transformation acoustics to general spacetime 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 do not leave
its form invariant. It is in these cases that ATA shows its true potential,
allowing for building a transformation acoustics method that enables the full
range of spacetime 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.
