  The paper [1] considers a spherical cloak described by three radially varying
acoustical quantities. For a given radial mass density in the cloak the
question posed is whether the remaining two parameters, tangential density and
compressibility, are uniquely determined. A method is proposed in [1] to solve
this inverse question based upon the solution of a Riemann-Hilbert problem
involving spectral properties of a one-dimensional inhomogeneous Schr\"odinger
equation. However, no constructive examples of the solution procedure are
given. This comment provides explicit solutions for any radial mass density
that conforms with the requirements of transformation acoustics [2]. A valid
form of the compatibility condition [1, eq. (22)] for $n=0$ is derived.
