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Volume 19, Issue 1
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Kiichiro MatsuzawaArticle type: Article
1963 Volume 19 Issue 1 Pages 1-8
Published: January 30, 1963
Released on J-STAGE: June 02, 2017
JOURNAL FREE ACCESSTaking the viscosity and heat conduction of air into account, a theoretical study is made on the propagation of a palne sound wave at high frequencies in cylindrical tubes of arbitrary cross-sectional shape. The mean complex density of air ρ and the mean complex bulk modulus of air K may be expressed respectively as, ρ=ρ_0/{1-W(φ_1)}, K=γP_0/{1+(γ-1)W(φ_2)}, where φ_1=(S/L)√<ωρ_0/2μ>, φ_2=(S/L)√<ωc_pρ_0/2λ>, ρ_0 is equilibrium density of air, μ coefficient of viscosity, c_p specific heat at constant presure, γ ratio of specific heats, λ thermal conductivity, P_0 equilibrium presure, ω circular frequency, L and S are perimeter and cross-sectional area of tube respectively, and W(φ) is a function depending upon cross-sectional shape. Solving the fundamental equations, approximate formulae for W(φ) are obtained as follows; i)for a tube having cross section without corners, W(φ)=(1-j)/(2)1/(φ)+(jπδS)/(2L^2)1/(φ^2)+. . . , where δ is 1 or 0 for single or double tubes respectively, and j=√<-1>, ii)for a tube having polygonal cross section with N corners, W(φ)=(1-j)/(2)1/(φ)-(jS)/(L^2)Σ^N_(m=1)K(α_m)1/(φ^2), where K(α) is a constant depending upon the angle of corner α. Thus, in the first approximation, it is found that ρ and K depend only on L/S but are independent of the cross-sectional shape. In the second appoximation, it is found that ρ and K depend on L, S and δ or K(α) but are independent of other quantities concerning the cross-sectional shape. Exact formulae for W(φ) of four simple cross-sectional shapes are compared with the approximate formulae. After numerical calculation, the values of the first approximation are found to be in fairly good agreement with the exact ones, and the valeus of the second approximation are found to be in very good agreement with the exact ones. It is ascertained that the first approximation of the present theory agrees fairly good with the experimental results by Takeuchi and Nakamura for a tube composed of mutually circumscribed circular rods.View full abstractDownload PDF (706K) -
Masaaki AraiArticle type: Article
1963 Volume 19 Issue 1 Pages 9-16
Published: January 30, 1963
Released on J-STAGE: June 02, 2017
JOURNAL FREE ACCESSIn this paper, the electrical circuits equivalent to the porous sound-absorbing materials are discussed. The sound absorption characteristics calculated with an electric simulator are compared with the experimental data obtained with a standing wave tube. The results are summarized as follows: (1)Analogies between acoustical constants and electrical ones make it possible to derive the equivalent circuit as in the case of non-dissipative acoustic filters. There exists a similarity law concerning the size, acoustical constants of materials, and frequencies. (2)A geometrical mean of the input impedances of both T-and π-type approximate lumpedconstant circuit may come near to the input impedance of original distributed-constant circuit, so the sound absorption characteristics determined by an impedance mismatching can be calculaterd in the upper-frequency range without truncation error. (3)The calculation and experimrnt of a thick (or thin) glass wool layer show a satisfactory agreement. It will be easy to unveil the nature of sound-absorbing materials, assuming arbitrary values for acoustical constants. (4)The attenuation characteristic of absorbent-lined duct is also studied as an example of multi-dimentional acoustical systems.View full abstractDownload PDF (722K) -
Masaaki AraiArticle type: Article
1963 Volume 19 Issue 1 Pages 17-24
Published: January 30, 1963
Released on J-STAGE: June 02, 2017
JOURNAL FREE ACCESSIt is known that the sound-absorbing wedges can be simulated with a series of non-uniform electrical transmission lines which acts as an impedance-matching section between a lower impedance side (an open air) and a higher-impedance side (a wall). But, as the numerical calculations are too tedious to practice, the optimum design of wedges has been carried out almost experimentally and their essential aspect is left untouched. This paper describes the influence of the acoustical constants and size on the sound absorption characteristics of wedges, which is verified with an electric simulator and a standing wave tube. Each wedge element, such as a taper, a base and a space, is investigated separately. A tentative "trapezoid" wedge is also mentioned. The following results are obtained: (1)A similarity law holds good for sound-absorbing wedges as well as for the sound-absorbing layers. (2)The pointed head of wedge is not so effective that a flat head is possible. (3)An essential part of wedge is the wedge-shaped air cavity at the bottom of tapered section, a slight adjustment of which may change the characteristics appreciably. (4)The product of effective resistance r and total length l has an optimum value. (5)The ratio of the taper length to the total length has an optimum value. A wedge composed of a taper only may lose its absorptivity below a critical frequency.View full abstractDownload PDF (682K) -
Jun-ichi Saneyoshi, Masao IdeArticle type: Article
1963 Volume 19 Issue 1 Pages 25-34
Published: January 30, 1963
Released on J-STAGE: June 02, 2017
JOURNAL FREE ACCESSFor the elimination of an extra transducer which picks up voltage proportional to the velocity of mechanical vibration for feedback oscillation, a new method to insert a network between the power amplifier and the main transducer is deviced. Three types of the network are proposed and theoretical formulas are derived. Behaviour of the motional feedback oscillators are generally discussed and the ability of automatic frequency tracking and the relation between the amplitude and mechanical load are made clear by graphical representation for the purpose of design. For the experiment, two sets of 50W class oscillator on our principle were built. Experiments proved that the frequency tracking is fairly good even when the transducer has subsidiary resonances, and that the velocity amplitude of the transducer is nearly constant in spite of the variation of the acoustical load if the gain-amplitude character of the amplifier is appropriately designed.View full abstractDownload PDF (849K)
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