This paper describes the vibration of strings and thin plates by warble-tone excitation for a fundamental investigation of the acoustic characteristics of rooms. In the analysises, the equation of motion of strings is solved by the Laplace transformation method, and that of thin plates is solved by the normal function method. In the experiments, permalloy strings and thin plates are excited by means of electromagnetic coils, and the transverse vibration amplitudes of these are measured by a discriminator. First, consider the vibrations of strings. The equation of motion of strings is presented in Eq. (1), and the term of external force is presented in Eq. (2). Equation (1) is solved by the Laplace transformation method under the given initial and boundary conditions (Eq. (3)), then the solution of Eq. (1) is presented in Eq. (5), Eq. (8) and Eq. (9), and then the solution for damped oscillation of strings is presented in Eq. (10). On the basis of these results, the stationary response and the damped oscillation of strings to warble-tone excitation are numerically calculated by a digital computer. Stationary vibration modes, vibration responses and the distributions of mean amplitudes are shown in Fig. (4), Fig. (5), and Fig. (6). Those results indicate that the response of strings to warble-tone excitation repeatedly shows peculiar vibration modes with the modulation frequency of the warble-tone, and that the nodal points tend to vanish and the mean amplitudes distributions along the longitudinal side of the string become flat. Thus, the degrees of flat for distributions of mean amplitudes are expressed by coefficients of variation (δ), and these results are illustrated in Fig. (7). The results of the calculations for damped oscillations are illustrated in Fig. (11), Fig. (12) and Fig. (13). These results indicate that 20dB decay time of strings to warble-tone excitation is longer than the mean value of 20dB decay time for each normal mode which are included in the deviation frequency range of warble-tone. Figures (9), (14) and (15) show the experimental results of the distributions of mean amplitudes and damped oscillations. Next, consider the vibrations of thin plates. The equation of motion is presented in Eq. (11) and the term of external force in Eq. (13). Equation (11) is solved by the normal function method under the given boundary condition (Eq. (14)). The stationary solution is presented in Eq. (22). Such a long time was necessary for numerical calculation that it was given up for want of time. In the experiments with the thin plate the normal vibration modes are illustrated in Fig. (16), and the responses to warble-tone excitation are illustrated in Fig. (17).
A Method of Measuring the Absorption characteristics (Absorption Coefficient and Acoustic Impedance) of Acoustic panels by the Correlate method is studied in this paper. The principles of the Method of Measuring as are follows. Absorption characteristics are derived from the frequency characteristics of Acoustic panels calculated from the relation between the reflected sound wave of Hard board. The reflection coefficient of which is quite near 1, and the reflected sound wave of Acoustic panel, which is regarded as the input signal and the output signal of Acoustic panel function, respectively (Fig. 5), and which are equivalent pulsive sound waves measured by the Correlate method using M-sequence signals (Fig. 1, Fig. 2). The forms of the reflected sound waves depend mainly upon shift pulse time T_m of M-sequence signals and frequency Characteristics of Acoustic panels. In this method, the influence of edge phenomenon (Fig. 4) compounded in the reflected sound waves is taken into consideration so that the measurement may be possible even if the Acoustic panel is not wide enough (Fig. 6). It is derived from the fact that the reflected sound wave measured by the Correlate method contains the influence of edge phenomenon but that the reflected sound wave calculated by Kirchhoff's equation does not contain it. Also, the suitable values of shift pulse time T_m in the measurement of Absorption characteristics are decided by approximating the frequency characteristics by the Correlate method (Fig. 1) to that by the Multi-filter method (Fig. 1, Fig. 7, Fig. 8). This method is to be considered useful for the measurement of Absorption characteristics (α_0, Z_0) of Acoustic panels by comparison between Normal incidence Absorption characteristics of Acoustic panel (Uletan Foam) measured by this method and the Tube method (Fig. 9〜Fig. 14), and by comparison between Statistical incidence Absorption coefficient α_start derived from Oblique incidence Absorption coefficient α_θ (Fig. 15) measured by this method and Reverberation Absorption coefficient α_rev (Fig. 17). Thus, we measured Normal incidence and Oblique incidence Absorption characteristics of Acoustic panel under performance (Wall of unechoic room for high frequence), and it is shown that this method is useful as one of the methods of measuring the Absorption characteristics of Acoustic panels of the spot (Fig. 18, Fig. 19).