Method of calculating the acoustical wave reflection coefficient from a not-sharp boundary of two media

The paper presents a numerical calculation method of the reflection coefficient of a plane, longitudinal acoustical wave from a plane-parallel, non-homogeneous transient layer (not-sharp boundary) positioned between two homogeneous, half-spatial media. Changes in the physical properties of the transient layer, determined by the changes in its material parameters, occur along its thickness and can by described by arbitrary one-variable functions.
Results of theoretical calculations of the reflection coefficient were given for chosen cases of material parameter changes in the transient layer and they were compared with results of measurements conducted on a physical model.
The presented method is accurate, universal and simple. It can be useful for the choice of ultrasonic wave frequency and for the measurement accuracy evaluation in certain applications of ultrasonic level meters, as well as for the determination of the shape of an ultrasonic pulse reflected from a not-sharp transient layer.