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.
The acoustic nonlinearity of an orifice in a plate has been investigated by measuring simultaneously the oscillatory flow velocity in the orifice and the acoustic-pressure fluctuations producing the flow. The relation between the pressure and velocity amplitudes, which is linear at sufficiently low pressures, is found to approach a square-law relation at large velocity amplitudes. By evaluating the phase relationship between the fundamental harmonic components of pressure and velocity, the acoustic-orifice impedance is determined. In the square-law region of the pressure/velocity relation, the resistive component of the orifice impedance dominates and is proportional to the velocity amplitude. This method of measurement, which is particularly useful at high amplitudes, is supplemented by measurements of sound transmission and frequency response of the orifice plate so that an impedance curve can be constructed over an extended range of amplitudes. An analogous program of measurements has been carried out to study the influence of a superimposed steady flow on the acoustic-orifice impedance. Finally, as an application of the results obtained, the absorption characteristics of resonator absorbers for high-intensity sound are discussed.
It is shown that the effect of fluid motion past a plane boundary on the reflection and absorption of sound is equivalent to an increase of the normal acoustic impedance of the boundary by a factor (1 + M sinφ), where φ is the angle of incidence of the sound wave, and M is the Mach number of the flow velocity component in the incidence reflection plane of the wave. Similarly, the acoustic energy flux perpendicular to the boundary and the flow is shown to be increased by the same factor. Reflection and transmission coefficients of a thin solid interface between a fluid in motion and one at rest are given. Furthermore, some comments on the problem of transmission in duets are given. For propagation between two plane parallel boundaries with the same acoustic admittance, we find, for sufficiently small values of the admittance, that the sound pressure attenuation constant of the fundamental mode is modified approximately by the factors (1 + M)−2 and (1 − M)−2 for downstream and upstream propagation, where M is the flow Mach number.
In his theory of streaming caused by sound waves, Eckart shows that time independent streams necessarily follow as part of the solution of the complete wave equatoin, taking into account viscosity and second-order terms. His treatment is mainly valid for liquids and it proves that the driving force of the streams is proportional to frequency squared. The effect, therefore, is especially important in the ultrasonic region (crystal winds). However, he suggests that slow streams might also be carried in air at audio frequencies. Studies of acoustical streaming phenomena around orifices have been made by the use of smoke particles in a 3-in. diameter circular tube. These studies covered a range of orifices from thicknesses of 0.5 mm to 19 mm and diameters of 3.5 mm to 20 mm. The frequency lay between 150 to 1000 c.p.s. Velocities in the orifice cover the range of 0 to 700 cm/sec. Close studies of the flow patterns have disclosed that there exist four definite regions of flow as the particle velocity in the orifice is increased. These regions have been represented by “phase diagrams.” Photographs of the various flow patterns in each region of the “phase diagram” have been taken for a number of orifices. Under each observed condition, the acoustic impedance of the orifice is determined by a conventional standing-wave measurement in the tube. It is shown that the nonlinear properties of the acoustic impedance of an orifice is closely connected with the circulation effects. Quantitative check in one of the circulation regions and a good qualitative over-all agreement indicate that the nonlinear properties of the impedance is due to the interaction between the sound field and the circulatory effects.
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.
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