Fluid–fluid interface and equivalent impedance plane

In the domain of outdoors sound propagation, the prediction of the monopole field is generally performed by replacing the porous ground by an impedance plane, i.e. a plane boundary with an impedance independent on the angle of incidence. An air–porous medium interface can be replaced by a fluid–fluid interface if the porous frame is motionless. In the present work, comparisons are performed around grazing incidence between the monopole fields above semi-infinite fluid–fluid interfaces, and above impedance planes. It is shown that the monopole field above an impedance plane satisfies an impedance condition which is the same as for a plane field, the ratio of the pressure to the normal velocity on the plane is equal to the constant impedance. It is shown that a similar impedance condition can be satisfied with a good approximation above a semi-infinite fluid–fluid interface. In this case, the impedance is the impedance at the angle of incidence where the pole is located. Some results have been obtained by transposing to acoustics a previous study by Baños of the electromagnetic Zenneck wave. An illustration is given with a semi-infinite porous layer having a small porosity.