  In an effective medium description of acoustic metamaterials, the Willis
coupling plays the same role as the bianisotropy in electromagnetism. Willis
media can be described by a constitutive matrix composed of the classical
effective bulk modulus and density and additional cross-coupling terms defining
the acoustic bianisotropy. Based on an unifying theoretical model, we unite the
properties of acoustic Willis coupling with $\mathcal{PT}$ symmetric systems
under the same umbrella and show in either case that an exceptional point hosts
a remarkably pronounced scattering asymmetry that is accompanied by one-way
zero reflection for sound waves. The analytical treatment is backed up by
experimental input in asymmetrically side-loaded wavesguides showing how gauge
transformations and loss biasing can embrace both Willis materials and
non-Hermitian physics to tailor unidirectional reflectionless acoustics, which
is appealing for purposeful sound insulation and steering.
