Investigations of musical instrument tone are classified into three categories, (1) mechanical study of the musical instrument and generation of tone, (2) analysis of acoustical wave generated by musical instrument, and (3) study of the correlation between acoustical wave and human sense of hearing. In the first part, are reviewed briefly the results of the latest digital processing of musical instruments. Then, the physical features of musical instruments are reported for the first time which are derived from the author's short-time spectral analysis. In a previous paper, prior to the experimental analysis, mathematical considerations were made with regard to the analytical error when DFT was applied to the musical instrument tone. Here, a new analytical method with examples are presented with regard to the "inharmonicity" of musical instrument tone, which could not be dealt with by the method proposed earlier. Eleven kinds of musical instruments are used -violin, viola, cello, flute, clarinet, oboe, bassoon, trumpet, trombone, guitar and piano. To save the space, only representative notes of analytical results for these instruments are shown (Figs. 1〜14). In these figures, the ordinate shows the amplitude of each harmonics in a linear scale, and numerical figures and alphabet signs show each harmonics. The changes of fundamental frequency are shown by a percentage scale using P or %. It is an outstanding feature that string tones of violin, viola and cello have long attack transient time, in general. The amplitude of each harmonics presents complicated behavior in a pseudo-steady state and especially so in case vibrato is applied to violin and cello. It is also a characteristic feature that flute and clarinet show the attack transient as S-form. The attack transient time of the two instruments are relatively long of the order of 100 msec, while their decay times are of the order of 200 msec. The attack transient time of bassoon and oboe are very short of the order of 20 msec. The pitch variation of bassoon is very easily recognized. Change of pitch of -2% at the attack transient and that of +2% at the decay part are recognized, when the steady state part is regarded as 0% change. In case of oboe, the vibrato and the amplitude variation of each harmonics are regular in the steady state part, and the pitch variation is synchronized with the change of amplitude. When the instruments are normally played at a given dynamic marking, mf, the attack transient time of trumpet tone A_4 is very short, while that of trombone tone A_3 is considerably long. The attack transient time of piano and guitar are very short. And, the max. spectral density lies in the region of max. amplitude. With regard to decay, the low order harmonics show gradual exponential function, while the high order harmonics show more fast decay. As for the analysis of inharmonicity, in order to improve the resolving power of frequency, DFT analysis was applied to the sum of zero of three times that of data window and the waveform which is A/D converted at sampling frequency, in which the fundamental frequency of musical instrument tone is pitch synchronized with data window. Fig. 17 shows the peak value of each spectrum obtained by this method approximated by quadratic function, and accurate amplitude and frequency are calculated. The inharmonicity of grand piano tone can be calculated by the frequency of each harmonics obtained as stated above, and in the actual measurement, constant B is 0. 00008 at note A_2.
Prediction of noise distribution in the surrounding of airports is very important for the adequate measures of aircraft noise control in these areas. We made a large-scale survey of noise in the surrounding areas of air bases in Japan mainly caused by F-104J, F-4EJ, and F-86F, that is, the main fighters of the Japanese Air Force, and on the basis of the results obtained, the basic data on noise were arranged by the relation between the peak noise level and the distance to aircraft i. e. slant distance (Fig. 7), and the relation between the peak noise level and the duration of noise (Fig. 10). In this paper, we discuss the procedures of drawing out forecast contours for WECPNL in the surrounding areas of air bases by use of the basic data on noise. Here, we drew out a contour in the following order. (1) The surrounding area of the air base was divided into 500-m meshes with the runway as the center and expressed by the coordinate system. (2) Flying courses were set up by referring to the standard course diagrams, etc. (Figs. 12 and 13). The sectional shapes of the flying courses in the distant areas could be almost approximated to be elliptical. Several typical flying courses were selected in the section set up in this way, and projected on a plane expressed by the coordinate system. The location (X, Y, Z) of the aircraft in an arbitrary space was expressed by taking the distance (D) moving on the plane along their respective flying courses from their respective reference points (take-off or landing points) as parameter. (3) The shortest distance from the flying course numerically expressed for each flying pattern to the intersecting points on the mesh was calculated (Fig. 14). As for the sides and rear of the runway at the time of take-off, the slant distance was obtained as the distance from the take-off point. (4) Then, peak noise levels at all intersecting points on the meshes were calculated from the slant distances obtained in this way and by use of the formulas of regression ((1)〜(7)) corresponding to the basic data on noise. (5) The duration of noise was calculated from the peak noise levels calculated as above by use of the formulas of regression ((12)〜(17)) corresponding to them. There are big differences in the number of daily flights in air bases ; there are 10 days or so in a month when there is no flight (Refer to Fig. 16). We calculated the number of flights per day, excepting the days in which there was no flight or only several aircrafts took off and landed. The contour obtained by calculation in this way showed a good agreement with the actual contour with a slight allowance of ±1〜2 dB (Fig. 17 and 18). It is considered that this good agreement is attributable to the following three reasons : (1) The basic data on noise were obtained from our tests on many aircrafts and therefore have a high reliability. (2) We expressed the flying courses of aircraft as of an elliptical section taking variations in flying courses into consideration, and in consequence could reproduce the actual flying condition more accurately. (3) As for the take-off noise on the sides and at the rear of the runway, we considered that the noise of aircraft at a position where it can be confirmed by eyes has an effect, and from this viewpoint calculated the slant distance by choosing the taking-off point (not taking-off run starting point) as reference point.
The authors devised a detection method of pipes buried underground by applying a pulse-echo method using impulsive sound and studies on its practical use are proceeding. In this method, an electromagnetic induction type sound source is used to radiate an impulsive sound with wide directivity into the ground. The echo signals from buried pipes are received by four receivers arranged symmetrically with respect to the sound source. A proper delay time is given to each of the four received outputs. These outputs are processed by a technique similar to a polarity correlation. Then, the output signals give an image along a line in a particular direction. Two-dimensional image pattern of pipes are drawn by varying the direction of directivity and scanning the ground. In this paper, the results of experiments performed in two model sand baths are described. Fig. 1 (a) and (b) show model sand baths (I) and (II) together with the location of the buried pipes. In the model sand bathes, a small electromagnetic induction type sound source was buried at 1. 0 m in depth. Using the buried sound source and a receiver placed on the ground surface, the values of sound velocity in the model sand baths (I) and (II) were measured at about 153 m/s and 155 m/s respectively. Fig. 2 shows the arrangement of the sound source and four receivers on the ground surface and a block-diagram of the measuring equipment. In the measurement for the detection of pipes, the sound source was placed just above the pipes and the four receivers were arrayed perpendicular to the pipes and symmetrically with respect to the sound source at intervals of 50 cm. The outputs of the four receivers were recorded in a magnetic tape. The signal processing and image pattern display were made at our laboratory. Delay time given to each receiver output was set so as to compensate the transmission time of sound from an imaginary position of the buried pipes to the four receivers. Then, the four delayed received outputs were divided into two pairs and summed in each pair, leading to two outputs, and the signal processing was carried out. The output of the signal processing circuit was memorized once in the WAVE MEMORY and reproduced at a time conversion of 0. 0l by a pen-recorder on a recording paper. Fig. 4 and 6 show a bock-diagram of the signal processing device and the displaying process of output waveform after signal processing respectively. In Fig. 7, (b) shows the output waveforms of four receivers which are arrayed perpendicular to the pipe axis. The measurements were made at point C in Fig. 1(a). The sound source was placed just above the poly-vinyle chloride (P. V. C. ) pipe of 8 cm in diameter buried at the depth of 1 m. In Fig. 7, (c) shows four output waveforms after signal processing obtained by setting delay times corresponding to four different depths as shown in Fig. 7, (a). The figure illustrates that the amplitude of the output signal from the pipe buried 1 m deep decreases only a little when setting delay times corresponding to the depths of 0. 8 m and 1. 2 m, but the amplitude decreases by about one-half when setting them corresponding to the depth of 0. 6 m. This fact explains that by setting the delay times corresponding to the position of 1 m in depth, the received output represents reflective wave pattern of pipe buried 0. 8 m to 1. 2 m deep. Accordingly, in order to obtain the entire image patterns over a wide range of depth, it is necessary to synthesize some displayed patterns in each effective range. Fig. 8 through 19 show underground cross sectional patterns for detection of buried pipes in model sand bathes. Fig. 10 and 11 show image patterns obtained by setting delay times corresponding to the depth of 0. 6 m and 1. 0 m respectively. Fig. 12 shows the synthesized pattern of these two patterns in each effective range of 0. 8 m to 1. 2 m in depth and of 0. 5 m to 0. 8 m in depth. The figure illustrates that the clear image patterns of a steel (S. A. ) pi
A new method of measuring the distribution of vibration amplitude on an ultrasonic transducer has been developed by using the concept of ultrasonic holography. The basic idea is to measure the complex amplitude of a sound field at some distance apart from the transducer, and to reconstruct the vibration amplitude on the transducer by using the holographic reconstruction formula with the aid of a computer. If the complex amplitude of the sound field (denoted by P(γ, θ)) generated by the ultrasonic transducer is measured for a fixed value of the distance γand for the angle between O to θ_0 (see Fig. 1), then the vibration amplitude on the surface of the transducer can be calculated by using Eq. (12), where V_c(ρ) is the reconstructed vibration amplitude on the transducer and ρis the radial component of a polar coordinate system taken on the transducer. However, it is necessary to satisfy Eqs. (8) and (10) in order to use Eq. (12), whereγ', γ'_0 and ρ' show γ/λ, γ_0 /λand ρ/λrespectively, in which λis the wavelength of ultrasonic waves and γ_0 is the radius of curvature of the transducer. Results of analysis of the resolving power of this method are shown in Figs. 2 and 3. In Fig. 2, the half-power width of the reconstructed line source is shown as a function of maximum scanning angle θ_0. It is seen that a linear relation exists between 1 / sin θ_0 and half-width. Fig. 3 shows the relation between the radius of transducer and the distance between transducer and measuring point. The parameters in the figure show the half-width required for the measurement. Experimental apparatus is shown in Fig. 4, where the transducer to be measured is mounted on a rotating table and scanning of the angle is performed by rotating the transducer. Consequently, only a small water tank is required for the measurement. For experiments, a P. Z. T. ultrasonic transducer of radius 25 mm was divided into four rings concentrically whose radii were given by 12. 5 mm, 17. 7 mm, 21. 7 mm, and 25. 0 mm from inner to outer. But this division was made for the electrode only and the ceramic portion of the transducer was not divided at all. The driving high-voltage signal was applied to the central and second electrodes independently, and in each case the vibration amplitude on the whole circular transducer was examined. In Fig. 5, the amplitude and phase of the measured ultrasonic field are shown where the central and second rings are excited. In Fig. 6, the reconstructed amplitude and phase of the vibration amplitude on the transducer are shown where only the central rings is excited. The dotted lines in Figs. 6 show the calculated curves on the assumption that the excited region of the transducer vibrates uniformly and the other part of the transducer does not vibrate at all. In Fig. 7, the reconstructed amplitude and phase are shown when the second ring is excited. The dotted lines in Fig. 7, also show the calculated curves for the ideal case. By comparing these curves it can be said that the amplitude and phase of the excited region is almost uniform and the other part of the transducer radiates a considerable amount of sound energy.
In a previous paper, we investigated the statistical properties of road traffic noise based on a model of traffic flow, in which vehicles of the same acoustic power are distributed on a road of infinite length so that the spacing between successive vehicles has a probability density function (pdf) of a negative exponential form. In this paper, the outline of the results of the previous work is described introductorily, since the results are closely related with the subjects of the present investigation. It was found out that the cumulant generating function, K(u), of acoustic intensity at an observation point given in equation (4) can be well approximated by the function, K_1(u), given in equation (10), where S is the average spacing between successive vehicles and d is the perpendicular distance from an observation point to the road. This K_1(u) satisfies the conditions that K_1(u)=K(u) at d=0 and d→∞, and I^^-_1=I^^-, where I^^-_1 and I^^- are means of acoustic intensity determined by K_1(u) and K(u) respectively. From this approximated K_1(u), the pdf, mean and variance of sound pressure level (SPL) are derived as equations (16), (20), and (21). The correspondences between the results of simulated calculations and the values obtained from above equations are given in Fig. 2, Fig. 3, and Fig. 4. In the present study, an exponentially distributed model with the same acoustic power is modulated into a more realistic model. First, we introduce an exponentially distributed model in which two kinds of vehicles with different power levels are distributed independently on a road. The cumulant generating function of sound intensity I^^- is expressed by equation (28), and the mean and variance are given by equations (29) and (30). When d is 0, K(u) is expressed as shown in equation (31). In this case, one can find an exact expression for the probability density function (pdf) of sound intensity and of sound pressure level (SPL). As an approximate expression for K(u) , K_1(u) as shown in equation (32) is adopted, where S_0 and d_0 are given by equations (33) and (34) respectively. K_1(u) satisfies the conditions that K_1(u)=K(u) at d=0, and I^^-_1=I^^- for all the values of S_0 and d_0. Then the mean of SPL can be calculated from equation (20) by using S_0 and d_0 instead of S and d in equation (20). The correspondences between calculated values and the results of simulated calculation by means of the Monte Calro method are given in Fig. 6 and Fig. 7. In the next step, we deal with a model in which the power level of each vehicle is assumed to be a random variable having a pdf of normal distribution. The cumulant generating function of sound intensity is expressed as equation (46), where σ is a standard deviation in dB of power level. The mean and the variance of sound intensity are given in equations (48) and (49) respectively, where A is defined by equation (47). When d is zero, K(u) is given by equation (50) and in this case we can obtain an exact pdf of sound intensity and of SPL. K_1(u) in equation (51) is used as approximate expression for K(u) in equation (46). This K_1(u) satisfies the same conditions as are shown previously. Then the mean of SPL is given by equation (54). Fig. 8 shows the correspondence between the results of simulated calculation and the values from equation (54). In Figs. 9, the values of "mean of SPL minus energy mean level" are indicated as a function of d/S for the cases where σis 0, 5, and 10 dB.