In this paper, firstly, a new trial to solve the prediction problem in terms of the lower and higher order cumulants of noise level and the level probability distribution in the general form of statistical Laguerre expansion series is theoretically considered in connection with the internal structure of road traffic noise. More concretely, the above road traffic noise is considered on cases of the arbitrariness of the number of lanes on the road and types of vehicle, the ratio mixture of vehicle types, the average number and the acoustic power level distribution of vehicles running with proper mean velocities on the respective lane of the road, the length of straight interval on the road and the distance from the observation point. Next, the equivalence problem of replacing multilane of road and various types of vehicles with one specific lane and one type of vehicle is discussed in detail. The brief summary of our prediction theory is given below. The moment generating function for the total energy of random noise at an observation point emitted from various vehicles on the road can be derived as shown in Eq. (9) by taking the proper characteristic of noise on an additivity of their sound energy flux density into consideration. Especially in Eqs. (11) and (12) the expressions of lower and higher order cumulants distribution functions are expressed in the general form of statistical Laguerre expansion series (cf. Eqs. (14) and (17)) and the effect of internal structure on traffic noise as mentioned in the above is reflected concretely in two parameters m, S` and expansion coefficient of the above expression (cf. Eqs. (20) and (21)). The equivalent vehicle number in a case when multi-lanes of road are replaced by one specific lane in a sense of equivalence of nth cumulant (or NPL) is given by Eq. (25) (or Eq. (33)) and the equivalent acoustic power of vehicle in a case when various types of vehicles are replaced by one specific type of vehicle on an arbitrary lane in a sense of equivalence of nth culmulant is given by Eq. (26). The validity of the theoretical results is also supported experimentally by use of digital simulation technique.
As shown in previous papers, the beat frequency, its clearness, and duration of remaining tone were freely adjusted by means of local loading and local paring. The research was related only to the fundamental tone. The objective of this paper is to find a method of adjusting the timbre of a Japanese bell. We investigated how the striking rod effected on the timbre of the Japanese bell, in which many overtones were related to the timbre. We tried a kind of model experiment in order to clarify the relation between the material and mass of striking rod and the timbre of the Japanese bell. Namely, we used a block of material in place of the striking rod and striked the bell by changing the material, speed and mass of block. We measured the duration of time that the block was in contact with the bell and the rebound coefficient. From these results the elastic property of the striking rod was obtained. Moreover, the timbre was indicated by the difference of sound spectra by changing the material of the block. In this case, the pattern of sound spectrum was shown by the strength of partial tones, which were divided into three parts, namely the fundamental tone, the first overtone and other tones. These sound spectra were obtained by means of a 1/3 octave analyzer. The results obtained from the above experiments are as follows: (1) The touching time of aluminum is smaller than in order materials. The value is under 10×10^<-3> second and does not change even though the striking speed is changed. The rebound coefficient is smaller than that of other materials, being evaluated under 0. 1. The pattern of sound spectrum is of the roof type, in which the sound level of the first overtone is larger than those of the fundamental tone and the other tones. (2) The touching time of bakelite is almost the same as in aluminum, but the rebound coefficient is large raging 0. 2〜0. 25. The sound level of other overtones is much smaller than that of the first overtone. (3) The touching times of rubber and cork are larger than in the other materials and the values are 50×10^<-3> second and 25×10^<-3> second respectively. The rebound coefficients are large being evaluated at 0. 3〜0. 5. In the sound spectrum, the level of the fundamental tone is higher than in the other tones. (4) The touching time of woods-hemlock-spruce, a kind of cypress, and Japanese cypress and Japanese cedar-is 10×10^<-3> second. The value remains almost constant by changing the speed and mass of the striking block. The pattern of sound spectrum is of the roof type and different from those of rubber and cork. The above experiment is a kind of model experiment, from which we obtained the relation between the timbre of bell and the material of striking rod. Next, we shall investigate how the striking rod in general use effects on the timbre of Japanese bell.
Lamb waves in a solid plate with water loading on its one surface, when their velocity exceeds that of sound in water, take a form of leaky wave which water, propagate with radiation of energy into water (see Fig. 1). It is necessary to know the propagation characteristics of such leaky waves in order to design a fluid-prism coupler (as in Fig. 2) for achieving efficient mode-conversion between the bulk and the Lamb waves. Furthermore, since the radiation angle θ_0 of the leaky Lamb waves depends on frequency (Eq. 1), and ultrasonic-beam steering can be achieved by frequency scanning. It may be applicable to ultrasonic viewing systems and broad-band acoustoopic deflectors. With interest in applications as mentioned above, the propagation and the far-field characteristics of the leaky modes designated by F_<1l>, L_<1l> and F_<2l>, corresponding to the modes of Lamb waves F_1, L_1 and F_2, respectively, are theoretically investigated. Fig. 3 shows the phase velocity v and the attenuation factor ε. The optimum beamwidth W_0 of incident bulk-wave to maximize the conversion efficiency is determined by using these values of ε(Eq. 8). Fig. 4 shows the particle velocity distribution in the modes F_<1l> and L_<1l>, as well as in the modes F_1 and L_1. It is found from Fig. 3 and 4 that the variations of ε are closely related to the velocity distribution. As the frequency is increased, the mode L_<1l> approaches the leaky Rayleigh wave, whereas the mode F_<1l> approaches the free Rayleigh wave. It is clarified by approximate analyses based on the coupled-mode theory that these phenomena are interpreted as result of strong coupling between the modes F_1 and L_1 by water loading. The approximate values of ε calculated by these analyses are also shown in Fig. 3(b). Fig. 5 shows the radiation angles θ_0 for different plate materials. The variation of θ_0 against frequency is larger as the bulk-shear wave velocity v_s of the plate materials is smaller. The far-field characteristics of a single leaky Lamb mode radiating from a finite aperture, such as the radiation pattern and the 3-dB beamwidth θ_B, are shown in Figs. 8 and 9. These indicate that there exists a frequency region in which the very sharp beam can be steered over a considerable wide range without large variation of θ_B. Several results of far-field measurements using the prototype "leaky-wave transducer" of Fig. 10 are shown in comparison with the theoretical ones (Figs. 11-13).
This paper presents a method to estimate excess attenuation of noise by an absorptive barrier, i. e. a barrier covered with sound absorbing materials. The approximate theory of the diffraction by an absorptive barrier is derived by the procedure that the second term of the theoretical solution of diffraction by a hard barrier is multiplied by the complex sound pressure reflection coefficient, because the solution of diffraction by a hard barrier is composed of two terms, the first term presents the combined fields of an incident wave and a diffracted wave caused by the incident wave and the second term presents the combined fields of a reflected wave and a diffracted wave caused by the reflected wave (see Eqs. (1), (2) and (3)). "Effect of Absorption" [EA], i. e. the increase of the excess attenuation caused by the absorbing treatment of the barrier, is defined as the difference of sound pressure level in the shadow zone resulting from the replacement of the hard barrier by the absorptive barrier (see Eqs. (5p) and (5s)). It is found by the numerical calculations of Eqs. (5p) and (5s) that the effect of absorption for a plane sound wave _p [EA] is not so much different from that for a spherical sound wave _s [EA](see Figs. 2, 3 and 4). A single chart, which may be very convenient for quick estimation of the effect of absorption in the practice of noise control, is offered under the conditions that the imaginary part of the acoustic admittance ratio of the absorbing materials is neglected and that source point and receiving point are symmetric with respect to the barrier (see Fig. 9). The validity of the method presented here is confirmed by comparing the estimated values with the measured values, consequently, this method may be useful to estimate excess attenuation of noise by a barrier with absorbing treatment in the shadow zone of the barrier (see Figs. 10, 11 and 12). It is also discussed that the excess attenuation by an absorptive barrier may be calculated for an incoherent line source (see Eqs. (8) and (9)).
Using a 5 MHz crystal-controlled ultrasonic interferometer and a pycnometer, the sound velocity and density are obtained and the adiabatic compressibility is computed in the systems of water-urea, water-urea-valeric acid, and water-urea-acetone. The water-urea-system exhibits a rather common behavior in the sound velocity vs. concentration curves (Fig. 1), having a common intercept for curves of different temperatures. The concentration dependence of the density is monotonous (Fig. 2), and the behavior of the adiabatic compressibility curve with a common intercept is also similar to many of the aqueous systems (Fig. 3). As different from usual aqueous solutions, the dependence on mol fraction is completely linear for both Rao's molecular sound velocity and Wada's molecular compressibility (Fig. 4), presumably indicating that the urea molecules freely replace the water molecules in the framework of the ice-I like structure of water and the single water molecules in cavity sites. The solution obtained by dissolving valeric acid in a 6 Mol urea aqueous solution is not so different from usual aqueous systems in its sound velocity behavior: The peak-sound-velocity temperature (T_p) of pure water shifting to the lower side under the influence of both urea and the valeric acid (Fig. 5). The sound velocity in the solution obtained by dissolving valeric acid in a 10 Mol urea solution, however, is rather peculiar (Fig. 6), being sensibly constant up to 4 wt-% urea, and decreasing sharply beyond this concentration. The dependence of density on the concentration being monotonous and nearly linear (Fig. 7), and the behavior of the adiabatic compressibility curves (Fig. 8) are nearly the inversion of sound velocity curves. The molecular sound velocity, on the other hand, is quite linear in its dependence on the mol fraction of valeric acid as indicated in Fig. 9. The temperature dependence of the sound velocity is independent of concentration up to 4 wt-% valeric acid, but increases in its absolute value) with concentration beyond 4% (Fig. 10). By applying the empirical formula of Lagemann et al. on the dependence of dv/<dT> on the molecular weight for this system, we can obtain the mean molecular weight in dependence on the concentration. Circles in Fig. 11 show this result. The solid curve in this figure, on the other hand, corresponds to the hypothesis that a molecular cluster of size 21×(3 water molecules+1 urea molecule) persists in the solution up 4wt-% valeric acid, each cluster adapting up to 1 voleric acid molecule. At 4%, all clusters adopt valeric acid molecules each. Beyond this concentration, however, further addition of the valeric acid increases the number of clusters, each valeric acid forming a new cluster around it by depriving water and urea molecules from existing clusters. Water-urea-valeric acid system is known to produce urea-aduct as precipitation and we may expect some cluster structure in the aqueous solution system, too. On the other hand, water-urea-acetone system does not show this peculiar sound velocity behavior (Fig. 12). The density behavior is nearly linear also in this case (Fig. 13), and the adiabatic compressibility (Fig. 14) behaves itself quite monotonously. As this system does not produce ureaaduct, the absence of specific sound velocity-behavior is to be expected.