Studies in acoustic pulse propagation
A theoretical study is made of the transient response in two acoustic systems. Each system consists of an ideal fluid in contact with an elastic solid. In one case the interface is plane, in the other case it is cylindrical. In the plane case it is found that an exact algebraic solution can be ob...
| Summary: | A theoretical study is made of the transient response in two acoustic systems. Each system consists of an ideal fluid in contact with an elastic solid. In one case the interface is plane, in the other case it is cylindrical.
In the plane case it is found that an exact algebraic solution can be obtained on the axis of symmetry. The vertical displacement at axial points is composed of the acoustic, afterflow, and correction terms. In solids for which Poisson's ratio is greater than one third the initial variation of the correction is toward positive values (corresponding to motion directed toward the interface). In solids for which Poisson's ratio is less than one third the initial variation may be either positive or negative depending on the magnitude of the compressional velocity ratio. An interface wave is shown to exist regardless of the choice of elastic parameters. It is found that the reflected wave has a forerunner in the region of the fluid in which the refracted wave is the first arrival.
In the cylindrical case the initial pulse shape is distorted upon reflection. It is found that as the wave approaches the axis of the cylinder the leading edge steepens. If, at the source, the initial slope of the pressure-time curve is finite the amount of steepening is infinite. An exact expresson for the transient response at points off the axis is obtained which can be evaluated by numerical means.
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