In this paper, a numerical method is derived for Helmholtz equations in unbounded domains of the type arising in the analysis of acoustic transmission system with radiation. The given problem on an unbounded domain is replaced by an approximate problem on bounded domain with an approximate radiation boundary condition on the artificial boundary. In order to obtain a reasonable solution, it is necessary to make this boundary sufficiently far from the sound source. The domain is divided by an internal boundary surrounding the source into two domains, Ω_1 adjacent to the source and Ω_2 adjacent to the external domain. In Ω_2, first the phase term e^<ikr> of the spherical wave is factored out of the solution and then the finite element method (f. e. m. ) is employed with non-uniform mesh sizes, and in Ω_1, the f. e. m. is employed directly with uniform mesh size. Since the behavior of the solution may be much different from that of the spherical wave in a domain close to the source, the direct application of the f. e. m. solves the problem with a smaller error, and the adoption of non-uniform mesh sizes results in a great reduction in the number of equations to be solved. This method is applied to the practical problems, 3-dimensional acoustic field analysis of a rectangular horn and that of a rectangular speaker cabinet, to get satisfactory results.
This paper describes that the network theory for an electric network with loss elements characterized by resistance r and conductance g is also applicable to the estimation of sound attenuation through a chamber with compliant walls in the lower frequency region and it is verified by the experiments. For the lumped constant system, when the ratio d_r of resistance r to inductance L is equal to the ratio d_g of conductance g to capacitance C in a network, the poles and the zeros for "Betriebsubertragungsfaktor" of the network on a complex plane move toward the left side along the real axis by the distance d, which is the average of ratio d_r and d_g, and accordingly we may directly learn the attenuation characteristic of the network in the lower frequency region. However, the ratio d_r is not equal to the ratio d_g in acoustic filter in general. Even in such cases, we can estimate the attenuation through a chamber lined with absorbing material by assuming both ratios to be equal to each other and by taking Mayers law into consideration. In the distributed constant system, we apply the same concept as mentioned above to an acoustical filter and assume both ratios d_r and d_g per unit length to be equal to d. Calculated results and measured ones show a good agreement with each other for an absorbent chamber. The same method of estimating TL is found to be a good approximation in a lined duct, too.
Paired comparison experiments were carried out on the pitch of 18 computer-generated complex tones synthesized by slight modification of frequency structure of Shepards endless scale sounds. The results were analysed by multidimensional scaling technique, and simple helixes were obtained in which two components of pitch (tone height and tone chroma) were represented. Some personal differences in perception of pitch were observed based on weights of subjects attention to each components.
The comlexity of vibration in acoustic vibrating systems and its measures have been studied by introducing and modifying the concept of entropy. Here, entropy H and energy-entropy product K by our definition are found to be naturally derived from thermodynamic entropy, from the thermodynamic point of view. Consequently, four measures of efficiency (i. e. , η, κ, γ, δ) are deductively obtained, and are applied to string and rectangular plate vibrations excited randomly. It is now essential to deal with thermodynamic adaptability and with relationships between complexity of vibration and thermodynamic work against fields around vibrating objects. Therefore we analyze (as a consideration), using all the above measures along with the concepts of essergy and exergie efficiency, experimental data from R. M. Fand et al. , meauring thermoacoustic vibration of a heated aluminum beam inserted in stationary sound fields consisting of plane waves. Throughout the present paper the mode theory is employed as a theoretical means of analyzing vibrations. The results show that the efficiencies in string and plate vibrations increase as the driving frequency increases, and that more complex vibrations tend to produce more thermodynamic work. Furthermore, it is concluded that γ is a technological measure because of comprising Shanon'S redundancy as a special case, and that thermodynamically well matched measures are K and κ.
This paper proposes saddle-like bending vibrators of a single square-plate of piezoelectric ceramics, in which interdigital electrodes are formed on the plate face and used for both poling treatment and excitation of vibration. There are two saddle-like bending vibrators, anti-symmetric and symmetric modes. For excitation of anti-symmetric or symmetric mode, interdigital electrodes are set in parallel to a diagonal or a side line of the plate, respectively. Both of piezoelectric transverse and longitudinal couplings, k_<31> and k_<33> contribute to excitation of the vibration. These bending vibrators have several merits of no bonding layer, easy mechanical support, very small spurios responses and relative small capacitance ratio. The resonance frequencies and distributions of vibrational displacement and strain are calculated for anti-symmetric and symmetric modes by using the finite element method. The caluclations also clarify the electrode-configuration dependence of the capacitance ratio and spurious responses of vibrator, and give the condition of electrode configuration for suppression of spurious responses. These are confirmed experimentally.
Surface displacement excited by a SH wave sources in an inhomogeneous elastic medium is represented in alternative forms: 1) Love wave modes and a continuous spectrum, 2) geometrical SH waves (virtual waves) and an interference wave expressed in an integral form, and 3) geometrical SH waves and Love wave modes. Followings are discussed with numerical evaluation results : a) the accuracy and the physical interpretation of these representations, b) the interrelation between geometrical SH wave and Love wave modes, c) the influence of the SH wave source location on the amplitude of Love wave mode, d) interference regions in which the interference wave or lower order Love wave modes is (are) significant. The surface displacement is expressed by a few geometrical SH waves for sources in a deep location, and by the combination of a few geometrical SH waves and one or several Love wave mode(s) for shallow sources.