Spherical Sound Source Research Articles

Acoustics for engineers: Troy Lectures

Introduction - Mechanic and acoustic oscillators - Electromechanic and electroacoustic oscillations - Electromechanic and electroacoustic analogies - Electromechanic and electroacoustic transduction - Magnetic-field transducers - Electric-field transducers - The wave equation in fluids - Horn and stepped ducts - Spherical sound sources and line arrays - Piston membranes, diffraction and scattering - Dissipation, reflection and absorption - Geometric acoustics and diffuse sound fields - Isolation of air- and structure-borne sound - Noise control: a survey - Appendices, e.g, complex notation for sinusoidal signals, power and intensity.

Effect of Sound Source Scattering on Measurement of Near-Field Head-Related Transfer Functions

A simple spherical head and pulsating spherical sound source model are proposed to investigate the effect of multiple scattering between the head and the sound source on near-field head-related transfer function (HRTF) measurement. Multipole expansion method is used to calculate HRTFs of the model, then the relationships among the magnitude error of HRTF with frequency, source direction, source size, and the distance between the head centre and the sound source are analysed. The results show that to ensure the magnitude error of HRTF within 1.0dB up to 20kHz, for source distance not less than 0.15m or 0.20m, the radius of the sound source should not exceed 0.03 m or 0.05 m, respectively. The conclusion suggests an appropriate size of sound source in near-field HRTF measurement.

Noise Shielding by Simple Barriers Comparison Between the Performance of Spherical and Line Sound Sources

This study is concerned with the theoretical solution to the problem of sound screening by simple hard barriers on the ground with special emphasis given to the type of wave incidence, namely a comparison between the use of either a spherical or a cylindrical sound source. For a receiver at the shadow of the noise source, the field may be assumed to be due to the edge wave and for this, exact solutions are used. Regarding the wave reflection on an impedance ground, exact formulations are also used, and finally, some calculations are made on the performance of a hard noise barrier on a two-impedance ground. As a conclusion, it is found that although the sound level at the receiver may show some small differences depending on the frequency and on the geometry of the problem, the overall insertion loss of the thin hard barrier is almost the same for the spherical and the line source, and the differences are found to amount to less than 1 dB for geometries of practical occurrence.

Spherical beam-forming and music methods for the estimation of location and strength of spherical sound sources

This paper shows the effect of spherical wave fronts on conventional noise source identification methods which assume a planar wave front. The effects of the array parameters, namely, the distance between the adjacent microphones, the aperture size of a microphone array, and the bearing angle of noise source on the estimation errors have been studied in conditions where the noise field can be considered as the superposition of planar wave fronts. Following these observations, spherical beam-forming and spherical MUSIC methods which incorporate the spherical wave fronts have been formulated and analysed. The validity of these methods in identifying the location and strength of the noise source has been tested by numerical simulations in terms of the various array parameters and also by experiments conducted in an anechoic room. The application and possible extension of the suggested methods for the identification of multiple spherical sources with finite frequency bands are described.

Prediction of a radiation field of a spherical sound source with a local responsive surface from measurements of diffraction field characteristics

A method is offered for the calculation of radiation field using measurements of sound pressure and the vibration velocity normal component on a spherical surface surrounding the sound source and setting it off from extraneous sound sources. The total diffraction field is presented as a superposition of the spead radiation field and the field to be scattered by the source surface (a direct field) as well as standing waves describing a reflected field and a field of extraneous sources. The scattering properties of the emitting sphere are given with the help of modal impedances. The field components are represented as an expansion in terms of the spherical harmonics. The expansion coefficients for the scattered field pressure on the source surface are calculated by solving of the integral equation of the second kind which is derived from the discontinuity properties of the Helmholtz integral on the boundary surface and from the impedance boundary condition. The radiation field is found as the difference of the direct field and the scattered field presented with the help of the Helmholtz integrals calculated over the measured and emitted surfaces. The method is illustrated by calculating the radiation field of a sphere pulsating with the prescribed velocity in the space bounded by the perfect reflecting spherical surface.

振動するはりから放射する音圧の解析

This investigation is the fundamental study to clear the mechanism of sound radiation from a machine structure and an architecture. In this paper, the sound radiation of an unbaffled beam of rectangular cross section is cleared. The relation between the amplitude of velocity and the sound pressure of an unbaffled beam is theoretically analyzed in consideration of the following cases. 1) The plane wave is radiated from a vibrating beam. 2) The mechanism of sound radiation from a vibrating beam is equivalent to that from two spherical sound sources. The analytic results are verified by experiments. It is concluded that in these experimental results, the sound pressure of an unbaffled beam is influenced by the amplitude of velocity, excitation frequency, the dimension of rectangular cross section of beam, and the distance from origin to observation point. In the latter, an agreement between the experimental results and the numerical results is obtained, but it is not so in the former.

Diffraction Effects by a Rigid Rectangular Plate Near a Spherical Sound Source

Diffraction Effects by a Rigid Rectangular Plate Near a Spherical Sound Source

Sound Wave Distortions Produced by a Spherical Sound Source

Sound Wave Distortions Produced by a Spherical Sound Source

Diffraction Coefficients of Various Shaped Obstacles for Human Mouth and Spherical Sound Source

Diffraction Coefficients of Various Shaped Obstacles for Human Mouth and Spherical Sound Source

Air-Borne and Solid-Borne Noise Discrimination of a First-Order Gradient Microphone Based on the Foil-Electret Principle

A first-order pressure-gradient microphone, which discriminates against air-borne noise as well as against solid-borne vibrations transmitted through the microphone case, is described. The microphone is based on the electrostatic principle and utilizes a foil-electret diaphragm [G. M. Sessler and J. E. West, J. Acoust. Soc. Amer. 40, 1433 (1966)]. For air-borne sound originating from a spherical sound source positioned close to the microphone, the frequency response is flat within ±3 dB in the frequency range 0.1–3 kHz with a sensitivity of about −50 dB re 1 V/μbar in the direction of the microphone axis. In a plane sound field, the sensitivity is lower (by 20 dB at 0.3 kHz) and rises proportional to frequency over most of the mentioned range. The microphone therefore discriminates against plane-wave noise fields in close-talking applications. Rejection of solid-borne vibrations is due to the lightness of the foil-electret membrane. Compared with electrodynamic and electromagnetic transducers, the foil-electret microphone responds 30–40 dB less to solid-borne vibrations referred to equal response for air-borne sound.

First-Order Gradient Microphone Based on the Foil-Electret Principle: Discrimination against Air-Borne and Solid-Borne Noises

Design and performance of a simple first-order pressure-gradient microphone based on the electrostatic principle using foil electrets are discussed. Such a microphone discriminates against air-borne noise as well as against solid-borne vibrations transmitted through the microphone case. For air-borne sound originating from a spherical sound source positioned close to the microphone, the frequency response is flat within ±3 dB in the frequency range 0.1 to 3 kHz with a sensitivity of about −50 dBV/μbar in the direction of the microphone axis. In a plane sound field, the microphone exhibits the typical first-order gradient behavior, i.e., its sensitivity rises proportional to frequency over most of the mentioned frequency range. At 0.1 and 1 kHz, the plane-wave sensitivity is 30 and 10 dB, respectively lower than the sensitivity to sound originating from a nearby source, making this microphone a noise-discriminating device for close-talking applications. Rejection of solid-borne vibrations is due to the lightness of the foil-electret diaphragm. Compared with electrodynamic and electromagnetic transducers, the foil-electret microphone responds 30 to 40 dB less to solid-borne vibrations, referred to equal output for air-borne sound.

Equivalent Network Models of Continuous Media and a Network Representation of Sound Radiators

Simple acoustical systems may often be treated as acoustical networks with lumped elements if the linear dimensions of the elements are small compared with the wavelength. At higher frequencies this circuit theory method becomes less practical, and it is then necessary to use a field theory where the medium is considered continuous. It is sometimes difficult to decide whether to use the circuit theory approach or the field theory approach, because the accuracy obtainable with the circuit theory and lumped elements is not immediately apparent. It is shown in the paper that much uncertainty may be resolved by careful analysis of the elements used in the circuit theory. This is demonstrated by means of a simple example. In the design of sound radiators it is often convenient to represent the radiation impedance as a lumped element network, and such representations are well known for simple sound sources. When an extended definition of radiation impedance is used it becomes possible to find a simple network representation of spherical sound sources of arbitrary order n. Examples are given for n = 0,1,2 … 7. A simple network representation is also possible for the input impedance of exponential and hyperbolic horns. The physical significance of these representations is discussed.