A Theoretical And Experimental Investigation Of The Parametric Acoustic Receiving Array PDF Download

The parametric reception of a low frequency plane wave by the use of nonlinear interactions between acoustic waves is examined both theoretically and experimentally. The parametric reception of a low frequency wave is accomplished by the use of a high frequency acoustic pump wave which interacts with the low frequency signal wave to produce sound waves at the sum and difference frequencies. These sound waves are received by a second transducer placed on the axis of the pump transducer. This type of parametric array allows for the possibility of narrowbeam detection of a low frequency acoustic signal wave. The interaction of two plane waves is examined theoretically in a manner similar to that considered by Westervelt. Of particular interest is the case in which the pump wave is assumed to be a plane wave originating at and propagating perpendicular to some planar boundary. The low frequency signal wave is assumed to be present over all space. The interaction of two plane waves is of interest for two reasons: (l) This interaction produces a truncated end-fire array (i.e., the parametric receiving array) with a length equal to the spacing between the planar boundary and the observer, and (2) this interaction relates directly to the problem of sound scattered by sound as formulated by Westervelt. Next, the solution for the interaction of a high frequency spherical wave from a point source and a low frequency plane wave is obtained theoretically using a two-dimensional stationary phase solution of Westervelt's scattering integral. The point source solution is in turn used to generate the solution for parametric receiving arrays with various pump transducers including a truncated line source transducer, a rectangular piston transducer, and a circular piston transducer. In each case, the observer is assumed to be in the farfield of the pump transducer. However, the result includes the effects of interaction in the nearfield of the pump transducer. The solution of the parametric receiving array with a point source pump and a truncated line receiver is also found. The theoretical solutions also include the effects of misalignment of either the pump or receiving transducer. With either the pump transducer or the receiver misaligned, the difference frequency beam pattern is an asymetrical beam pattern and is the mirror image of the sum frequency beam pattern. This property is examined in detail in terms of the problem of two sound waves interacting at nonzero angles. A series of experiments were conducted with a 48 ft parametric receiving array with a pump frequency of 90 kHz. In the experiments, an omnidirectional transducer was used with either a rectangular piston transducer or a square piston transducer. Each transducer could be used as either the pump transducer or the receiver so that a variety of parametric receiving array configurations could be realized. A small rotator was used to allow independent rotation of the piston transducer for measurement of the effects of misalignment of the piston transducer. Theoretical and experimental results are compared for the parametric receiving array with several transducer arrangements. The agreement between the theory and the experiment was excellent.