Beam Behavior within the Nearfield of a Vibrating Piston

A numerical investigation of the nearfield region of a vibrating piston was conducted. While existing literature is not exactly clear about how close to a transducer a regular beam pattern is formed, the results of this investigation show the limits of operation one can expect. From one interpretation of literature, a −3-dB beam with a minimum spot size equal to the transducer diameter would be expected to form beyond an axial distance z = 3.89 a2/λ. This investigation shows that such a beam forms at z = 0.75 a2/λ and has a minimum spot size equal to one-quarter the transducer radius. These results are verified for transducers with a/λ's ranging from 1 to 20 and can be extended with confidence to higher a/λ's. Similar results are also obtained for −1.5-, −4.5-, −6.0-, −7.5-, −9.0-, −10.5-, and −12-dB beams.