Sound Radiation from a Surface Source Located at the Bottom of the Wedge Region

Applying rigorous analytical methods, formulas describing the sound radiation have been obtained for the wedge region bounded by two transverse baffles with a common edge and bottom. It has been assumed that the surface sound source is located at the bottom. The presented formulas can be used to calculate the sound pressure and power inside the wedge region. They are valid for any value of the wedge angle and represent a generalization of the formulas describing the sound radiation inside the two and three-wall corner region. Moreover, the presented formulas can be easily adapted for any case when more than one sound source is located at the bottom. To demonstrate their practical application, the distribution of the sound pressure modulus and the sound power have been analyzed in the case of a rectangular piston located at the wedge’s bottom. The influence of the transverse baffle on the sound power has been investigated. Based on the obtained formulas, the behaviour of acoustic fields inside a wedge can be predicted

Sound Radiation by a Cylindrical Open Cavity with a Surface Source at the Bottom

The rigorous solution describing the sound radiation by an arbitrary surface source located at the bottom of a cylindrical open cavity embedded in a flat baffle has been obtained. The open cavities of different shapes can be found in some architectural structures as well as are components of sensors, musical instruments and vehicles. The presented formulas have been expressed in the form of Infinite sums. To use them, the infinite sums have to be truncated to the finite number of terms. Therefore, in practice, the results obtain based on the proposed solution are not exact and their accuracy is determined by the truncation error. The use of presented formulas is an alternative method for the finite element method (FEM). However, taking into account that the calculation efficiency of FEM rapidly decrease when a volume of considered region increases, the obtained in this study solution can be more useful in some practical cases. The approximated formula of a high computational efficiency has been presented for the sound pressure in the far field. The sound radiation has been analyzed for a rectangular piston as a sound source. The influence of cavity depth ratio on the radiation efficiency has been investigated. The cases for which the cavity radiation efficiency can be approximately calculated from the formula valid for a baffled sound source have been determined

The Acoustic Pressure Radiated by a Vibrating Circular Plate within the Fraunhofer Zone of the Three-Wall Corner Region

The Neumann boundary value problem has been solved for the region bounded by the three perfect rigid infinite baffles arranged perpendicularly to one another. The harmonically vibrating clamped circular plate embedded in one of the baffles is the sound source. It has been assumed that the amplitude of the plate's transverse vibrations is small to use the linear Kelvin-Voigt theory. The Green function has been applied to obtain the asymptotic formulae describing the distribution of the acoustic pressure within the Fraunhofer zone. The analysis of sound radiation has been performed for some selected surface excitations and for some different plate's locations. The acoustic pressure distribution has been examined including the acoustic attenuation and the internal attenuation of the plate's material

Asymptotic Formulae of the Modal Acoustic Impedance for the Asymmetric Vibrations of a Clamped Circular Plate

The asymptotic and approximate formulae for the asymmetric modal acoustic self- and mutual-impedance have been presented for a clamped circular plate embedded into a flat rigid baffle. The formulae have been obtained for the wide frequency band covering the low frequencies, the high frequencies and the middle frequencies. The high frequency asymptotics have been achieved using the method of contour integral and the method of stationary phase. The products of the Bessel and Neumann functions have been expressed as the asymptotic expansions. Further, the approximate formulae valid within the low and middle frequencies have been obtained from the high frequency asymptotics using some mathematical manipulations. The formulae presented are valid for both the axisymmetric vibrations and the asymmetric vibrations

The Acoustic Pressure Radiated by a Vibrating Circular Plate within the Fraunhofer Zone of the Three-Wall Corner Region

The Neumann boundary value problem has been solved for the region bounded by the three perfect rigid infinite baffles arranged perpendicularly to one another. The harmonically vibrating clamped circular plate embedded in one of the baffles is the sound source. It has been assumed that the amplitude of the plate's transverse vibrations is small to use the linear Kelvin-Voigt theory. The Green function has been applied to obtain the asymptotic formulae describing the distribution of the acoustic pressure within the Fraunhofer zone. The analysis of sound radiation has been performed for some selected surface excitations and for some different plate's locations. The acoustic pressure distribution has been examined including the acoustic attenuation and the internal attenuation of the plate's material

The Total Acoustic Power of a Clamped Circular Plate Located at the Boundary of Three-Wall Corner Region

The energetic aspect of the sound radiation has been analyzed in the case of the three-wall corner region. This region is the part of space bounded by three baffles arranged perpendicularly to one another. The Neumann boundary value problem has been solved assuming that the sound source is the vibrating circular plate embedded in one of the baffles of the three-wall corner region. The Kelvin-Voigt theory of a visco-elastic plate has been used which allows to include internal attenuation existing in the plate material. It has been assumed that the sound source is excited to vibrations by the external pressure asymmetrically distributed on the plate surface. The modal coefficients of the acoustic impedance have been obtained in the form of the expressions containing single integrals only. The formula describing the acoustic power of the analyzed sound source has been presented as a fourfold infinite series containing the modal coefficients of the acoustic impedance. The influence of some asymmetric excitations on the acoustic power has been analyzed. The possibilities of the modelling some uniform excitations located on the plate fragment of the small area by the point force excitation has been examined. The influence of the transverse baffles on the acoustic power has also been investigated. It has been determined for which frequency the baffles influence on the acoustic power is the greatest

The acoustic power radiated by a circular membrane excited for vibration both by means of the edge and by external surface load

In this paper the acoustic power of the circular membrane, excited both by the edge and external exciting forces uniformly distributed over the whole surface, is examined. Some different amplitudes of exciting factors and some differences between the phases of excitations were considered. It has been assumed that the source of a sound is located in a flat, rigid and infinite baffle and is sourrounded by a lossless and homogeneous fluid medium. The vibrations are axisymmetric and time-harmonic. Employing the Cauchy's theorem of residues and asymptotic formulae for the Bessel functions, the asymptotes for active and reactive power consisting of elementary functions are obtained. The acoustic power radiated by the membrane was shown graphically in terms of the parameters describing both kinds of excitations

The Radiation Efficiency Measurements of Real System of a Thin Circular Plate Embedded Into a Thick Square Baffle

Most of sound sources are complex vibroacoustic objects consist of numerous elements. Some coupled vibrating plates of different shapes and sizes can be easily found in urban environments. The main aim of this study is to determine the sound radiation of coupled plates system of practical importance. The investigated vibroacoustic system consist of a thin circular plate coupled with a thick flat baffle with a circular hole. The circular plate has been mounted to the baffle’s hole using screws and two steel rings. The measurement setup was located inside a semi-anechoic chamber to assure the free field conditions. It was necessary to take into account the whole system surface to obtain the radiation efficiency based on the Hashimoto’s method. Such an approach can be troublesome and time-consuming. Therefore, the criterion has been proposed which allows the vibration velocity measurements and calculations to be performer only for the thin plate’s area. An alternative approach has been proposed based on the classical Rayleigh integral formula. Its advantage is a simpler implementation in a computer code. The obtained results have been compared with the theoretical results obtained for the elastically supported circular plate. A good agreement has been obtained at low frequencies

Acoustic Pressure Radiated by a Circular Membrane Into the Quarter-Space

The Neumann boundary value problem for the Helmholtz equation within the quarter-space has been considered in this paper. The Green function has been used to find the acoustic pressure amplitude as the approximation valid within the Fraunhoffer’s zone for some time-harmonic steady state processes. The low fluid loading has been assumed and the acoustic attenuation has been neglected. It has also been assumed that the vibration velocity of the acoustic particles is small as compared with the sound velocity in the gaseous medium

The Low Frequency Approximation of the Sound Radiation Power of Two Vibrating Circular Pistons Embedded in Two Different Rigid Planes of a~Three-wall Corner

The problem of sound radiation by a system consisting of two vibrating circular pistons embedded in two of three different planes perpendicular to one another forming a three-wall corner is considered. The earlier published results dealing with the sound radiation by sources vibrating in a three-wall corner are the basis of analysis. According to the earlier studies, the exact formulae for acoustic power of radiation of two circular pistons are used. The formulae are expressed as double Fourier integrals. The active and reactive, self and mutual, components are separated from them as well as the corresponding expressions of the acoustic power of mirror images of the piston sources. The acoustic power of the two sources are expressed in the form of the Rayleigh formulae whereas, in the case of the mirror images, it is expressed in the form of the single series expansion containing spherical Bessel and Neumann functions. In the case of the mutual acoustic power of the sources, approximate formulae are presented for low frequencies. On the basis of the results obtained, the corresponding formulae valid for a two-wall corner are presented as the limiting transitions. All the results presented can be useful, e.g. in designing the room acoustics and outdoor system everywhere the free field conditions are disturbed by the acoustic waves reflected at rigid vertical walls for the wavelengths being considerably shorter than the geometric sizes of the walls