Uno Ingard

On the Theory and Design of Acoustic Resonators

Absorption and scattering from resonators in a free field as well as in walls are discussed. The effect of different aperture geometries on the resonance frequency of resonators is considered and illustrated by examples. Considering losses due to viscosity, heat conduction, and radiation, the optimum design for maximum resonance absorption is analyzed, and the results are expressed in terms of design charts. Nonlinear effects on the absorption and resonance frequency are also included, and a discussion of the onset of turbulence is presented.

On the Reflection of a Spherical Sound Wave from an Infinite Plane

The reflection of a spherical sound wave from a wall with the boundary conditions expressed in terms of a normal impedance independent of the angle of incidence is treated. It is shown that the integral for the reflected wave can be evaluated exactly in closed form under certain conditions. The solution given for an arbitrary normal impedance involves a slight approximation of the integral. The reflected wave is brought into a form such that it can be considered originating from an “image source” having a certain amplitude and phase. Graphs for determining this amplitude and phase are given in terms of a “numerical distance,” which depends on the normal impedance and the position of the field point. Pressure distributions around point sources for different wall impedances are shown. The limitations in simulating plane wave conditions at a boundary and the corresponding effect on free field methods of measuring acoustic impedance are discussed.

A Review of the Influence of Meteorological Conditions on Sound Propagation

The study of the different atmospheric effects indicates that in short‐range sound propagation the attenuation by irregularities in the wind structure (gustiness) often is of major importance in comparison with humidity, fog, and rain, and ordinary temperature and wind refraction. However, the ground attenuation can be of equal importance to the gustiness, in particular, when the sound source and the receiver are sufficiently close to the ground. The effect on the attenuation of the height of the source and the receiver off the ground is presented as a function of frequency for a typical ground impedance. The attenuation curve exhibits a maximum which in most cases lies at a frequency between 200 and 500 cps.

Sound propagation into the shadow zone in a temperature-stratified atmosphere above a plane boundary

The sound field in the “shadow zone” (diffraction region) formed over a plane boundary in an atmosphere with a constant vertical temperature gradient is analyzed both theoretically and experimentally. The boundary condition at the plane is given by a normal acoustic impedance independent of the angle of incidence. As in the corresponding problem of underwater sound where the boundary is a pressure release surface, it is found that the major portion of the sound pressure in the shadow zone decays exponentially with distance at a rate proportional to the one‐third power of frequency and two‐thirds power of temperature gradient. The effect of boundary impedance enters mainly through its resistive component. The rate of sound decay for a pressure release boundary (zero impedance) is found to be 2.3 times that for a rigid boundary (infinite impedance).Sound pressure measurements in the shadow zone in a laboratory chamber in which a large temperature gradient was created were made for both hard and absorbing bo...

Scattering of Sound by Sound

As a preliminary to an investigation of the scattering of sound by turbulence, the scattering of one sound beam by another is studied using the Lighthill formulation. The scattered sound is predicted to be composed in part of components with frequency equal to the sum or difference of those in the primary beams. These components of the scattered field have been isolated in measurements using a selective receiver and their angular distributions are compared with those predicted. This work was supported in part by the NACA.

Perforated Facing and Sound Absorption

In the analysis of the absorption characteristics of a porous layer with perforated facing, it is usually assumed that the facing contributes only a mass reactance to the total impedance. In the present paper it is shown that the facing also causes an additional acoustic resistance which is often larger than the acoustic resistance of the porous layer itself. This resistance obtained only when the porous material is in close contact with the facing and becomes practically zero when the air space between facing and material exceeds approximately one perforation diameter. The effect is due to the near field (higher mode) losses in the porous material around the perforations. The resulting effect on the absorption characteristics considerable, as demonstrated in some examples, and may at least partly explain reported disagreement between measurements and previous calculations.

On the Radiation of Sound into a Circular Tube, with an Application to Resonators

The radiation from a plane piston into a rigid circular tube is treated. Consideration is given to the propagation of higher order sound waves. Curves of radiation impedance and pressure distribution are given together with an analysis of the elements of the equivalent impedance circuits. In addition to the closer study for special values of the tubes end impedance, some outline of the general case is given. Simplified measurements verify the calculations in the case of a tube closed by a rigid wall. Finally, the resonance frequency of cylindrical resonators is discussed.

Effect of a Reflecting Plane on the Power Output of Sound Sources

The presence of a reflecting plane boundary will affect the power output of a sound source located above it. This effect may be expressed as a “power amplification factor” which has been calculated for a number of elementary sound sources (monopole, dipole and longitudinal quadrupole) as a function of the distance between the plane and the source. Special attention has been given to evaluation of the source height yielding minimum power output and to the ratio between the maximum and minimum power radiated.

The Impedance of a Resistance Loaded Helmholtz Resonator

The impedance of a Helmholtz resonator damped by a thin porous layer in the form of a screen or cloth is calculated as a function of the distance between the aperture and the screen. It is shown that the input resistance of the resonator decreases very fast as the distance between the screen and aperture increases, whereas the aperture mass reactance passes through a maximum. The importance of these results with regard to design of resonators and perforated facings is discussed.

The Near Field of a Helmholtz Resonator Exposed to a Plane Wave

The near field of a spherical Helmholtz resonator exposed to a plane wave is computed and shown to be in good agreement with measurements. Comparison is made with the near field of a resonator terminating a cylindrical tube. A discussion of the calculation of the dissipation in the resonators is included.