Approximation to the Diffraction of Sound by a Circular Aperture in a Rigid Wall of Finite Thickness

Abstract

An approximate solution for the diffraction of a plane sound wave incident normally on a circular aperture in a plane rigid wall of finite thickness is obtained by postulating rigid, massless, infinitely thin plane pistons in each end of the aperture, whose motions simulate the movement of the air particles at these positions under acoustic excitation. Plane longitudinal waves are assumed inside the aperture. Numerical solutions obtained on an IBM-7090 computer very closely coincide over a wide range of frequencies with those of much more-complicated existing exact solutions. Furthermore, extensive experiments were conducted on the transmission of reverberant sound through steel pipes of various lengths and diameters inserted individually into a heavy wall between two concrete chambers of 1750 cu ft each. Measured values of reverberant sound-transmission loss through these apertures were found to agree within experimental error with those calculated from the approximate theory. The assumption of plane-wave propagation in the aperture was found to give valid experimental results up to values of d/λ exceeding unity, where d is the pipe diameter and λ is the wave length of incident sound.

Effective impedance boundary optimization and its contribution to dipole radiation and radiation pattern control

“…In the 3-to 11-kHz interval, two transmission peaks are located at l ¼ 10.2d (f ¼ 4,224 Hz) and l ¼ 4.9d (f ¼ 8,832 Hz) for the decorated sample and l ¼ 10.3d (f ¼ 4,160 Hz) and l ¼ 5.1d (f ¼ 8,384 Hz) for the undecorated sample. The high radiation efficiency arises from Fabry-Perot resonances associated with waveguide modes in the centre slit 23 . Figure 2 presents the normalized-to-area transmittance versus the effective length of the centre slit and frequency according to Fabry-Perot resonance theory.…”

Enhanced Transmission of Acoustic Waves Through Subwavelength Holes in Hard Plates

“…Transmission/diffraction by an acoustical grating is an old problem, and the previous investigations addressed some cases: one-dimensional (1D) periodic slits in a rigid screen [31,32], a single hole in a thick wall [33,34], and a 1D grating composed of parallel steel rods with finite grating thickness [35,36]. Here we studied the acoustic transmissions through two structures: (1) a two-dimensional array (square lattice) of subwavelength hole and (2) a single hole surrounded by the surface periodic grooves.…”

Finite Element Modelling of Sound Transmission Loss in Reflective Pipe

“…The presence of the duct walls affects the attenuation of sound and usually causes the attenuation coefficient to be much higher than for plane waves in open space. The problem of steady-state diffraction or transmission of sound energy by an aperture in a plane wall has attracted much attention in the literature for many years (Wilson and Soroka, 1965). Exact solutions are restricted to a few cases where the aperture geometry is simple and may be conveniently described in a coordinate system in which the wave equation becomes separable, or may allow the postulation of a set of velocity potentials that can be made to fit the boundaries.…”

“…The theoretical solution for a circular section curved duct has not been achieved yet due to the mathematical difficulties encountered in the solution of the wave equation. In paper Wilson and Soroka (1965) an approximate solution for the diffraction of a planes sound wave incident normally on a circular aperture in a plane rigid wall of finite thickness is obtained by postulating rigid, massless, infinitely thin plane pistons in each end of the aperture, whose motions simulate the movement of the air particles at these positions under acoustic excitation. In the paper (Chen et al, 2006) the improvement on the acoustic transmission loss of a duct by adding some Helmholtz resonator is discussed.…”