Acoustic Field of a 1-D Array Element

Abstract

As discussed in Chap. 1, an ultrasonic phased array is composed of many small acoustic sending and receiving elements, each of which acts as an individual sending or receiving transducer. In this Chapter we will develop models of the acoustic waves generated by a single element and describe how the nature of this wave field depends on the size of the element and its motion. Models that simulate the radiation of a single array element will be generated explicitly in MATLAB®. The superposition of a number of these single element models with different driving excitations will then give us a complete model of a multi-element phased array transducer, as shown in Chap. 4. To keep the discussion as simple as possible in this Chapter the single element will be treated as a 1-D source of sound radiating two-dimensional waves into a fluid or through a planar interface between two fluids. Although both linear and 2-D arrays are composed of 2-D elements which produce sound waves traveling in three dimensions, the physics of wave propagation is similar for both 1-D and 2-D elements so that we can learn much of the fundamentals of sound generation with these simplified models. In Chaps. 6 and 7 we will discuss the corresponding three-dimensional models and wave fields of single elements and phased arrays.