Sound Field of a Rectangular Piston

Abstract

The amplitude and phase of the pressure in the field of a rectangular piston, assumed vibrating within an infinite, rigid baffle, are examined theoretically for ranges down to the order of the piston length. Various laws of behavior of this field, both on and away from the acoustic axis, are deduced. An indication is given of the errors introduced by the approximations used. Such experimental evidence as is available supports the theory. Simple means are provided for constructing curves of axial pressure amplitude and phase for any ratio of length to breadth of the radiating surface, and a method is suggested for predicting the long-range axial pressure of a rectangular piston from measurements taken well within the latter's Fresnel region. The near fields of a rectangular and a circular piston are compared. That of the rectangular piston produces the more useful approximation to a plane wave.

Ultrasonic Testing of Materials

“…The sound-field structure depends on the ratios Dj I A and Dz I A and for a general treatment of rectangular radiators it is useful to normalize the distance z in terms of the quasi near-field length Di 14A and the transverse dimensions in terms of D j • This normalization is also used in Fig.4.25 (see also [475,38]). …”

Acoustic Emissions During 3.1 MHz Ultrasound Bulk Ablation In Vitro

“…Stability of array performance was verified by regular measurements of element capacitance between experiments, as well as real-time display of delivered electrical power during each exposure. The measured acoustic powers were converted to in situ acoustic pressure levels by computing the diffracted acoustic field of this sub-aperture using a Fresnel approximation for transducer arrays with rectangular elements (Freedman 1960;Mast 2007), which has previously been shown to characterize array fields accurately . At a distance of 15 mm from the array, the acoustic pressure amplitudes employed were thus estimated as 0.83, 1.10, and 1.38 MPa, corresponding to plane-wave acoustic intensities of 23, 41, and 64 W/cm 2 .…”

Overview of Mathematical Modeling in Nondestructive Evaluation (NDE)

“…A harmonic point source solution was developed by Miller and Pursey (1954). Freedman (1960) solved the near field solution for the rectangular piston in an acoustic field using phase approximations. Zemanek solved the near and farfield of a vibrating circular piston through numerical integration of the double integral.…”