THE JOURNAL OF THE ACOUSTICAL SOCIETY OF JAPAN

Investigation on the Edge Phenomena of Multilayer Sound Absorbing Panels

Kiyoshi Awaya, Hiroaki Ikeda

Article type: Article
1976 Volume 32 Issue 11 Pages 683-692
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_683

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The authors have indicated in a previous paper (1975) that the increase of sound absorbing power A_p per unit length of the edge is expressed by the next equation almost independently of wave number N and incident angles of sound wave A_p &ampsime 0. 12(r_a-r_b)^2λ where variable λ is the wavelength of the sound wave, and two single-layer sound absorbing panels whose amplitude reflection factors are r_a and r_b, respectively, are supposed. The main purpose of this paper is to expand the previous results to the case of multilayer sound absorbing panels and to clarify how the edge phenomena are formulated in this case. For this purpose, the authors have adopted a group of correlationless continuation of sine-waves of finite length as an incident wave form as in the previous paper. For this incident wave, general expressions for the sound pressure of the edge wave p_e(t, x_0) and for the normal component of the particle velocity of the edge wave v_e(t, x_0) are proposed. Utilizing these expressions general formulation for sound absorbing power density p(x_0) caused by the edge phenomenon has been derived. The authors also discuss the case where the characteristics of two sound absorbing panels are represented only by their dominant reflected waves, respectively. By the numerical integration of p(x_0) the sound absorbing power P_e(θ, φ) per unit edge length has been obtained. It is proved that the sound absorbing power P_e(θ, φ) is valid for the edge phenomena of more general multilayer sound absorbing panels, provided that the wave number N is taken as being sufficiently large. In the case that each of the parameters do not vary in accordance with the incident angles of the sound wave, and that a perfectly defusing sound field is assumed, it is shown that the increase of the sound absorbing power (A_p) is expressed by the equation A_p &ampsime 0. 1λ(r^2_a+r^2_b-2r_ar_bcosφ) where variable φ is the phase difference between each dominant reflected wave.

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Some Vibrational Properties of a Stretched Circular Membrane

Toshio Hayasaka

Article type: Article
1976 Volume 32 Issue 11 Pages 693-702
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_693

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In the electro-acoustic energy transformation mechanism of the electro-static type applied in the condensor microphone, the saturation phenomenon, unavoidable in the electro-magnetic type, does not appear. The electro-static type makes it possible to use an extremely thin diaphragm as far as the material strength and fabrication technique permit. Accordingly a very light weight moving part can be realized in the electro-static type transducer which can operate at high frequency up to several tens kHz if so desired. This electro-static type transducer is expected to be put into practical use extensively. The vibration membrane which is a part of the transducer can be widely applied. From these standpoints, this paper presents the design data for the vibrating membrane. The conventional solution of membrane has been mainly adopting the expansion form by using the normal function method. This solution was very effective in the examination of the physical characteristics of membrane vibration, but it was not suitable for numerical calculation since the convergency was very poor. This paper adopts the direct solution method for the equation of motion not dependent on the expansion form, which becomes effective for numerical calculation. The solution thus obtained was processed by a computer in order to generate detailed design data. Only the principal data were introduced this time among a vast amount of design data.

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Comparisons of Sound Propagation in Rigid-walled and Soft-walled Elliptical Waveguides

Akio Hasegawa

Article type: Article
1976 Volume 32 Issue 11 Pages 703-709
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_703

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In a previous paper, sound propagation in soft-walled elliptical Wave-guides was investigated by employing the solutions of the wave equation expressed in terms of the Mathieu functions and modifie Mathieu functions. In the present paper, the cut-off wave numbers of the rigid-walled elliptical wave-guides are calculated in the same ways in the previous work and compared with the results of the soft-wall. To analyze exactly the sound propagation in the elliptical waveguide with a rigid-wall and a soft-wall the elliptical coordinate system is introduced as shown in Fig. 1. The velocity potentials which are solutions of the wave equation can be expressed in terms of the Mathieu functions Se_m(s, η), So_m(s, η) and the modified Mathieu functions Je_m(s, ξ), Jo_m(s, ξ) (see Eq. (1) for the rigid-wall and Eq. (2) for the soft-wall). Substituting Eq. (1) into the boundary condition Eq. (6) of the rigid-wall, equations of the dimensionless cut-off wave number (Eqs. (9) and (11)) were obtained. The numerical calculation of the dimensionless cut-off wave numbers by a digital computer was carried out for various values of the eccentricity (e), Figs. 6〜9 show the numerical results of k_cB represented as a function of e, where k_c is the cut-off wave number and 2B is the length of the minoraxis. From Fig. 6 for even-wave Φ^e_&ltmn&gt, it seems that the curves starting from k_cB of the circular wave-guide with no nodal circle, one nodal circle and two nodal circles approach 0, π, and 2π, respectively, as the value of e approaches 1. These values of k_cB correspond to those for a palallel waveguide with width 2B. On the other hand, from Fig. 7 (odd wave Φ^0_&ltmn&gt) the curves of k_cB starting from the values of the circular waveguide at e=0 approach π/2 at e=1 in the case of no nodal circle, and 3π/2 in the case of one nodal circle. Experiments were performed by the standing wave method to obtain the phase velocities in air contained in the elliptical waveguides made of aluminum (rigid-wall) and in water contained in the semi-elliptical waveguides made of foam-polystyrol (soft-wall). Examples of the measurement are shown in Fig. 13 for the semi-elliptical waveguides with soft-wall and in Fig. 14 for the elliptical waveguide with rigid-wall. It can be seen from Figs. 13 and 14 that the experimental results are in satisfactory agreement with the theoretical ones.

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On the Role of Temporal Information in the Pitch Perception of Complex Tones

Kengo Ohgushi

Article type: Article
1976 Volume 32 Issue 11 Pages 710-719
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_710

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An experiment was carried out in which subjects adjusted the frequency of pure tone to match the pitch of a complex tone consisting of short pulses. The experimental results shown in Fig. 5 indicate that the frequency of a pure tone having the same pitch as the complex tone was slightly lower than the fundamental frequency of the complex tone in the frequency range between 200 Hz and 2000 Hz and slightly higher than the fundamental frequency at 100 Hz. The following hypothesis was proposed for the purpose of accounting for the results: "As a cue for pitch perception, temporal information provides a different value from what is given by spatial information, especially it provides a lower value than spatial information above 200 Hz". In order to verify the hypothesis, experiments on the pitch of complex tones were carried out. If the hypothesis is reasonable, the pitch of the complex tone consisting of short pulses without the fundamental component is expected to become lower because of rejection of spatial information. The experimental results shown in Fig. 7 support the hypothesis. In the second experiment, the pitch of complex tones consisting of two frequency components (f_1, f_2) was investigated. Three kinds of complex tones were used as follows: (1) f_1=400 Hz, f_2=800 Hz. (2) f_1=800 Hz, f_2=1200 Hz. (3) f_1=1200 Hz, f_2=2800 Hz. Since spatial information is expected to show a decrease in order of the above number, the pitch of two-component complexes should become lower in this order according to the hypothesis. The experimental results shown in Fig 8 also support the hypothesis. On the other hand, interspike interval histograms of primary auditory neurons published by Rose et al. (1967) were examined in detail. As a result, the interspike interval was found to be longer than a period of a tone stimulus waveform above 200〜300 Hz as shown in Fig. 10. This may be physiological evidence to show that the hypothesis is reasonable.

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Resonant Frequency and Vibration Mode on U-Type Vibrator

Hisashi Nakamura, Seiji Hirose

Article type: Article
1976 Volume 32 Issue 11 Pages 720-727
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_720

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This paper deals with an analysis of a U-type vibrator restrained by arbitrary supporting stiffness at the center of the circular part of the vibrator, and presents some diagrams of the frequency constants and vibration modes, which are very convenient for design. As symmetric vibration on the U-type resonator is treated in this paper, it is possible to analyze by only a half section of the vibrator, and the center of the circular part is analogized for a roll-end binding with arbitrary stiffness s_s (Fig. 1). From eqs. (3), (4), equations of motion on a circular bar, a characteristic equation (7) is derived and its solutions are obtained as eqs. (8)〜(16). The conditions of connection are given as eqs. (17)〜(26), so the characteristic equations on the U-type vibrator are obtained as eqs. (28)〜(45) by using those mentioned above. The calculated results of the frequency constants α in relation to the dimension ratio l_a/l and some experimental results are shown in Fig. 2, and each curve demonstrates in order (a), (b), (c) the values on the first mode in the case of a clamped end (s_s=∞), roll end (s_s=0) and those of the second mode in the case of a clamped end (s_s=∞). Fig. 3 illustrates deviations of the frequency constants of the vibrator in the case of a roll end in relation to those of the clamped end on the first mode. It is evident that the values obtained in the case of roll end approach those of the clamped end in the region of practical use, about l_a/l≧0. 7, so that either value can be use in designing the vibrator. Fig. 4 and 5 illustrate the characteristics of frequency constant α to normalized supporting stiffness ζ as the parameter of the dimension ratio l_a/l, the diagrams demonstrate coupling resonance occurred with vibration of elastic symmetrical mode and rigid-vibration at a certain point of ζ. This indicates that spurious vibrations occur in the neighborhood of the coupling resonance, so that in designing, a suitable value of supporting stiffness must be chosen except the coupling resonance in accordance with the figures given above. The vibration modes at points numbered by the ○ mark in Fig. 4 are shown in Fig. 6 (a)〜(c). These figures indicate shifting aspects of modes from the rigid-vibration to the first mode of the clamped vibrator and from the vibration of the roll-end to the second mode of the clamped one. These results are convenient for use in the design of the U-type vibrator to the supporting system.

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Edge-Enhanced Acousto-Optic Bragg Imaging

Masayuki Yamazaki, Isao Kato

Article type: Article
1976 Volume 32 Issue 11 Pages 728-
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_728

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Effect of Rectified Diffusion on the Cavitation Bubble

Hideo Kimoto, Ken Ikuno, Tatsuzo Hirose

Article type: Article
1976 Volume 32 Issue 11 Pages 729-731
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_729

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The 1st Meeting of the WORLD FEDERATION FOR ULTRASOUND IN MEDICINE AND BIOLOGY/3rd World Congress of Ultrasonics in Medicine

Masao Ide

Article type: Article
1976 Volume 32 Issue 11 Pages 732-735
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_732

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[title in Japanese]

[in Japanese]

Article type: Article
1976 Volume 32 Issue 11 Pages 736-
Published: November 01, 1976
Released on J-STAGE: June 02, 2017

DOIhttps://doi.org/10.20697/jasj.32.11_736

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