Cylindrical shell structures are used in various constructions such as water drain systems, air conditioning ducts, chemical plants and the fuselages of airplanes. Solid-borne vibrations associated with these structures have to be controlled not only from the point of view of noise radiation but also from that of fatigue. Fatigue is greatly related to the maxmum stresses caused, as well as to the frequency of occurrence. One method of eliminating large vibrational amplitudes is to coat one side of shell surface with a damping material. The pupose of the present paper is to evaluate and estimate the damping capabilities of two-layer cylindrical shells (see Fig. 1). From the practical point of view, the uncoupled five principal modes (see Fig. 2) are disscussed with respect to natural frequency and damping (logarithmic decrement). As was discussed by Oberst, the logarithmic decrements of the extensional and the bending vibrations of two-layer beams are as follows respectively: (δ/π)_<ex. >≈g_<ε2>r_εr_h, (I) (δ/π)_<bend. >≈3g_<ε2>r_εr_h(a+2r_h+4/3r_h^2 (II) provided r_εr_h<<1 and g_<ε2>r_εr_h, where g_<ε1> and g_<ε2> are the loss factors of the two layers respectively, r_<ε> is the ratio of Young's modulus and r_h is the ratio of thickness. The damping is known to be at least three times greater for the bending mode than for the extensional mode. Dampings for various modes of cylindrical shells are sometimes more complicated, because the extensional and the bending vibrations with respect to the shell layers are essentially coupled with each other. The results for different modes are as follows: 1) Torsional mode The logarithmic decrement (L. D. ) is given by the equation of the same form as eq. (I), where g_<ε2> and r_<ε> are replaced by g_<G2> and r_G, i, e. the loss factor of shear modulus and the ratio of shear modulus respectively. 2) Radial mode The breathing motion is coupled with the bending of the shell layers. For a long wavelength, L. D. is given by eq. (I). According as the wavelength becomes shorter, the damping effect increases up to the value given by eq. (II). 3) Longitudinal mode L. D. is given by eq. (I). For a very short wavelength, however, since the motion is dominantly associated with the bending of the shell layers, L. D. comes close to the value given by eq. (II). 4)Non-axially symmetric mode This is a bending motion around the axis, so that L. D. is given by eq. (II). 5) Flexural mode This as a whole is a bending motion along the axis, but an extensional motion is dominantly associated with the shell layers themselves. For a long wavelength, L. D. is given by eq. (I).
A microphone for acoustic measurement in the free field or in other must be samll enough so it does not disturb the original field. For this purpose, a circular tube probe microphone, as shown in Fig. 2, has been often used. However, an exact non-directivity can be expected from this probe microphone only when ka→0, where a is the outside radius of the tube and k is 2π/λ (λ: wave length). For practical pupose, it is necessary to know the directivity and the acoustic center (the end correction) even when ka is small for more accurate measurements. Levine and Schwinger solved the "power-gain function" and the end correction concerning a semi-infinite cylinder with negligible wall thickness by the Wiener-Hopf technique. They have reported that the correction has been calculated pgraphically as a function of ka. The power-gain function, however, is very complicated as shown by Eq. (1) so that it is not suitable for parctical use, therefore, it has been rearranged approximately for the pressure directivity in the range of 0≤ka<0. 5, as shown by Eq. (10). On the other hand, using a turntable, the pressure directivity has been measured in an anechoic chamber as shown in Fig. 3, and the ratio of the directivity (see Eq. (11), Fig. 4 and Fig. 5) between of Θ_1 and of Θ_2 has been measured as shown in Fig. 6, by applying the "interference pattern method" (a method of measureing the complex reflection coefficient of acoustic materials at oblique incidence). Next, the shifts of the acoustic center between two different radius of the tubes (see Eq. (12) and Fig. 7)have been measured at the pressure minimum points (from the first minimum to the fifth minimum counted from the surgace of material) of the interference pattern in front of the reflecting surface. These results are shown in Fig. 8. The acoustic center has been plotted as shown in Fig. 9(see Eq. (13)) by the measurement of the shift of the first pressure minimum in the acoustic tube (for normal impedance measurement) ended by perfectly reflecting surface. The distances were read with a microscope with a reading accuracy of 1/100 mm. Consequently, these experimental results have shown that both the pressure directivity and the acoustic center of the probe microphone can be determined from theoretical results by using the outside radius of the probe tube rather than the inside radius in the range of 0≤ka<0. 5. it is believed that more exact theoretical investigation concerning a finite cylinder with a wall thickness should be carried out, for instance, by means of the technique of Matsui.
As an effective sound absorbing wall for anechoic room, a flat type sound absobing wall and two types of its modifications, having minimal thickness and simple construction, were examined. Characteristics of the sound absobing wall were evaluated by the normal absorption cofficient using acoustic standing wave tube. The results obtained are as follows; (1) Absorbing properties of the flat type sound absorbing wall of multilayer having different density are as efficient as those of the wall having the taper type sound absorbing element, and the double layered walls are practically sufficient. (2) If we replace the absorbing materials near the hard wall with air space, the amount of the absorbing materials may be saved, but one should take care that the thickness of the air space is not too large. (3) Resonance absorber is not recommended for the sound absorbing wall of an anechoic room because it may impair the absorbing properties except in resonance frequency. On the basis of these results, an anechoic room lined with the double layer flat type absorbing wall was constructed in the Electrical Communication Laboratory N. T. T. . Density of the glass fibre used as absorbing material was 12kg/m^3 in the inner layer and 24kg/m^3 in the outer layer. The inverse square law properties of this room ware measured and presented in Fig. 13. Furthermore, the inverse square law properties of this room ware compared with those of an anechoic room lined with wedge type absorbing wall in natural frequency(Fig. 14), in frequency normalized with the lower limiting frequencies (Fig. 15), and in effective free field area (Fig. 16). From these results, it was verified that this anechoic room as compared with the anechoic room lined with wedge type absorbing walls is superior in taking advantage of the space and by no means inferior in acoustic characteristics.
For the purpose of determining the characteristics of phonetic quality of voewls, the trend in the changes of formants and pitch of vowel with age and sex of speaker has been investigated by analyzing a large number of samples of five japanese vowels. Conclusions obtained are as follows. (1) Most of the formants considerably change with the age of the speaker. Principal articulatory factor in the change of formants is the difference in the vocal tract length. On the other hand, the third formant of /i/ which depends mainly upon the front part of oral cavity, and the first and second formants of vowels /o/ and /u/ which constitute comparatively lip-rounded articulatory configuration do not change so much. For each case of children, youth and female adults the ratio of the measured formant of the open and back vowel /a/ to the mean value of the corresponding formant of male adults is approximately constant. Hence we can estimate the vocal tract length of the speaker from the mesured formants, using Eq. (2). (2) The differences between the first and second formants of male and those of female become distinct after 11 years old, while the difference between the third formant of male and that of female becomes distinct after 9 years old. absolute differences of formants, particularly of the third formant, are useful to discriminate the sex of the speaker. This is important in the case of children since pitch is useless in the distinction of the sex of the speaker before 12 years old (the voice change). (3)There is obvious difference between the pitches of children, youth, female adults and male adults, but it is difficult to infer the age of the speaker from his pitch. (4) Generally speaking, there is a correlation between formant and pitch, but there is no correlation if the speech samples are taken from the speakers of the same age. The correlations of formants and pitch come from the correlations between the age and the formants and the correlation between the age and the pitch. (5) Perfect discrimination of the vowels can not be made by the first and second formants only. There are some confusions between certain vowels (/a/ and /o/, /e/ and /u/) on the first and second formant-plane. But, thre is little confusion between the vowels in the three dimentional space composed of the first, the second and the third formants or of the pitch, the first and the second formants. The pitch or the third formant, not to mention the first and second formant, is an indispensable parameter for the discrimination of the vowels regardless of the age and sex of the speaker.
Reproducing heads commonly used for magnetic tape recordings are sensitive only to the rate of change of magnetic flux in the tape, so that its most important basic characteristic is the frequency response: as the frequency decreases the output falls off in proportion and reaches zero at zero frequency. The characteristic is shown in fig. 5(a). In order to compensate for the drop at low frequencies, the amplifiers for usual winding heads require a bass-boost amounting to 30〜40 dB at 30 Hz. The winding heads are not suitable for those applications which require very low frequency response, such as data analysis. The output frequency response of the Hall-effect heads is essentially flat from d-c to ultra high frequencies, as in shown in Fig. 5(b). Today, microminiaturization of these heads are required. In this regard, the winding heads are limitative in size and the Hall-effect heads are the most suitable. After all Hall-effect heads are most excellent in respect to frequency response and size miniaturization, but the preparation of Hall-effect heads requires semiconducting thin film Hall elements with very high characteristics comparable to those of semiconductor single crystals. The author has investigated Indium-Antimonide thin films and recently has succedded in obtaining thin films with high physical characteristics(R=200〜300 cm^3/c, μ_e=40, 000〜50, 000 cm^2/Vン). They have been utilized in the preparation of the front gap type Hall-effect heads. In this instance, the most suitable thickness of the film was found to be 0. 9μ. Permalloy was used a the magnetic circuit material. The thin film Hall element which was evaporated on a mica surface is shown in Fig. 8(a), the assembled head is shown in Fig. 8(b) and the microscopic photograph of the gap in the magnetic circuit is shown in Fig. 8(c). Frequency responses of different types of heads are shown in Fig. 9((a) net output of the winding head, (b) output of the winding head after equalizer, (c) net output of the Hall-effct head, (d) the same as (c))
It is wellknown that the spectrum of the noise generated by ultransonic cavitation contains not only numerous harmonics of the ultrasound, but also subharmonics and their harmonics. But the reason why the subharmonics are generated has not yet been clarified. On the basis of a series of experiments it has been thought that they are caused by the radiated pressure waves from either the pulsating bubbles or the cavitation bubbles which are generated and collapse. When the intensity of the ultrasound is weak, cavitation bubbles are generated and collapse in each cycle of the ultrasound. With the increase of the intensity of the ultrasound, there appears an excitation range in which cavitation noise shows the so-called "two-cycle phenomena" or "two-cycleness". In the excitation range we have examined in detail the growth and collapse of cavitation bubbles. Cavitaion bubbles were produced by a nickel transducer of frequency 5kHz and were photographed under the illumination by a micro-flashlight of arbitrary time lag from the standard pulses. The standard pulses with frequency 1/2 of the ultrasound were produced from the sound pressure in the tested liquids (Fig. 2). In our experiments we selected the stable region of the two-cycleness of cavitation noise, so that the phase fluctuation of the pulses was about 1/40 of the period of ultrasound. From our experiments it was verified that in the excitation range in which cavitation noise shows two-cycleness, cavitation bubbles collapse completely in every two cycles. Moreover we found that the so-called "incompletely collapsing cavitation" is only produced in the middle part of the driving surface and that the bubbles produced on the circumference of the surface collapse in each cycle (Fig. 3). From this we may conclude that the component of the first subharmonic contained in the cavitation noise generated under intense ultrasound is due to the cavitation bubbles which are generated and collapse in every two cycles and not to the bubbles pulsating in several or more cycles. It is generally believed that the larger the intensity of the ultrasound, the brighter the sonoluminescence is. But the increase of the brightness of the sonoluminescence is suppressed in the excitation range in which cavitation bubbles show two-cycleness. Analysis of the light intensity scattered from cavitation bubbles by using a frequency analyser showed that the first subharmonic at this moment is very large (Fig. 8). Such phenomena are independent of the kind of liquid tested, so that the two-cycleness of cavitation begins to appear with roughly the same excitation range and has no relation to the kind of liquid tested. From these facts we may conclude that the two-cycle phenomena of cavitation take place in the excitation range determined by the experimental equipment. According to the theory of isolated cavity, cavitation bubbles repeat their growth and collapse in each cycle under the weak ultrasound. With the increase of the intensity of ultrasound, it becomes impossible for the bubbles to collapse within the first cycle and it is in the second cycle of ultrasound that they collapse completely. Thus the initial conditions for the growth of cavitaiton bubbles are different with the cycle, so that their growth and collapse begin to present two-cycleness. With a further increase of the ultrasound, cavitation bubbles become such that they cannot collapse in one cycle and the so called "incompletely collapsing cavitation" is produced (Fig. 10〜Fig. 12). The larger the initial radius of a cavity, the more easily two-cycle phenomena of cavitation are produced (Fig. 13). The above consideration may provide a satisfactory explanation of our experimental results.
Precision measurement of the reverberant sound absorption coefficient has always been drawing attentions in the history of architectural acoustics. In Europe and North America, the round robin tests were carried out repeatedly to standardize the method of measurement. Results of these investigations were collected in the ISO Recommendations or ASTM Standards. However, it seems that some essential problems remain unsolved, such as diffusivity in the reverberation room, edge effect of test materials and so on. In Japan, the 3rd round robin test was carried out from 1965 to 1966 by the cooperation of 13 research laboratories. Details of reverberation rooms used for this round robin are shown in table 1. Glasswool board (50 mm thick, 25kg/m^3) was used as test materials. Test areas and the number of suspended diffusing plates were varied in nearly the same manner as in the European round robin (1959). Other Specifications of measurement conformed to the ISO Recommendation R 354. Test results are illustrated in Fig. 1〜Fig. 7. Deviations of measured absorption coefficients were fairly large. Thus, investigations into the precision measurement of absorption coefficient have been pursued for these two years. In general, measurement of sound absorption coefficient in a reverberation room assumes a diffuse sound field in the room. Diffusivity in a room is connected with the room volume, room shape, various diffusers put in the room, area of test materials and so on. Among these factors, the room volume would have influence mainly upon the diffusivity in the low frequency region. Test materials used in this investigation have relatively small absorption coefficient in low frequencies and it would be inadequate to discuss the requisite volume of reverberation room only through this investigation. Thus, the primary object of this research was to obtain the diffuse conditions in the middle and high frequency region. In the European round robin test, the diffuse condition in a room was specified by the ratio of the total area of suspended diffusing plates to the floor area of the room. However, this specification does not determine uniquely the sound field for different shapes or volumes of rooms. It would be desirable to introduce the index of diffusivity which can be measured directly in the room. Various methods and quantities have been proposed, such as fine structures of decay curves, directional distribution of sound energy, cross correlation in the sound field and so on. Through preliminary investigations, elevational diffusivity or ratio of horizontal to vertical mean energy during decay process was adopted for the evaluation of the sound field. So far as measurement of the absorption coefficient is concerned, it was concluded that the diffusivity in the reverberation room is sufficient, if the ratio of horizontal to vertical meanenergy during decay process is less than 3. 0 (Fig. 14). From the measurement of this ratio, the sound fields of all the rooms shown in Table 1 (except 13) could be regarded as of the same order of diffusivity, when the total area of suspended diffusing plates in each room attains about 80 percent of the floor area of the room. Important factors in the disagreement of the absorption coefficients in the 3rd round robin test would have to be sought in other items.
In order to investigate the fluctuations of absorption coefficient related to the reverberation time measurement, experiments were conducted in the following ways. (1) Reference decay curves were recorded in two reverberation rooms with and without test materials. Copies of these decay curves were sent to 13 research laboratories and were read by 25 persons. Absorption coefficients calculated from these data are shown in Fig. 2. Deviations of coefficients are fairly large. Statistical analysis showed a significant difference among readers or decay curves. Fig. 1 illustrates the typical decay curves which cause relatively large deviations. From these results, it would be reasonable to think that the personal difference in reading the decay curves plays an important role in the precision of absorption coefficient measurement. (2) The absorption coefficient of identical test materials was measured by using the same instruments in 11 reverberation rooms. From the recorded decay curves the reverberation time was read by a single person. The absorption coefficients thus obtained are shown in Fig. 5. Compared with the results of the 3rd round robin test, deviation of absorption coefficients measured in different rooms are relatively small, i. e. , within ±10% in most frequencies. (3) To check the effect of dynamic characteristics of a high speed level recorder, decay curves were recorded by each level recorder in respective laboratories. These records were read at first by a single person and then by the respective persons in each reserch laboratories. The absorption coefficients thus obtained are shown in Figs. 6 and 7. From these results, it was concluded that the dynamic characteristics are sometimes connected with errors in absorption coefficients. Following this, the 4th round robin tests were conducted using the same test materials as in the 3rd round robin, but the specifications of measurement were supplemented by referring to the above investigations. Major items are as follows: adjustment of writing speed and linearity of a high speed level recorder, proper setting of writing speed and paper speed, determination of adequate number of decay curves for each frequency and exclusion of unfit curves. Results of this round robin showed fairly small deviations among different laboratories (Fig. 10). Fig. 11 shows the maximum deviations of absorption coefficients obtained in the successive steps of this investigation. Corresponding results of the European round robin tests are also shown in this figure. In conclusion, the accuracy of measurement is sufficient for usual purposes, as long as the deviation is kept within the range of this 4th round robin test. This is expected from the application of the specification of measurement derived from this investigation.