A resonator is used practically in an absorbing wall as well as in a rigid wall. In this paper the absorption characteristic of a resonator array in an absorbing wall is studied under the condition of a plane wave incidence normal to the wall. Kosten and Zwikker investigated the absorption characteristic of a resonator array in a rigid wall. Ingard showed the equivalent circuit of a resonator in free space. In these cases, the resonator array in an absorbing wall is assumed to be represent by the equivalent circuit as shown in Fig. 2. The total absorption coefficient, α_<total>, of a wall and a resonator can be calculated by the equivalent circuit as shown in Eq. (4) or Fig. 3. Fig. 3. (a) is the case when μ_2>1. 0 and Fig. 3. (b) is the case when μ_2≦1. 0, where μ_2 is the normalized resistance of the resonator. It is of particular interest that, in Region III of Fig. 3. (b), α_<total> becomes smaller than α_<wall>. The experimental results by the tube method are shown in Figs. 5 and 6 by dashed lines. Fig. 5 is an experimental example in Region I and Fig. 6. is in Region III. Solid line is the calculated absorption characteristic of a resonator array by Eq. (4), where μ_2 is calculated by the experimental equation of Ingard on the resistance of turbulence. This calculated curve agrees well with the experimental result. Consequently, it is found that Eq. (4) expresses well the absorption characteristic of resonator array in an absorbing wall.
A mechanical blowing apparatus was used in a simulation of flute playing for investigating acoustical properties of tones thus generated. Variations of sound pressure level and fundamental frequency with nine kinds of blowing conditions (Fig. 1, Tab. 1) (velocity, width and thickness of an air beam, sectional radius of lips etc. ), which are conceivable in actual flute playing, were measured on a head-joint made by Hermut Hammig attached to a middle- and foot-joint made by Muramatsu. The result is as follows. The sound pressure level (L, dB) is proportional to the velocity (u, m/sec. ) and width (w, mm) of an air beam. (Fig. 2) The other blowing conditions have no noticeable effects on L. ∂L/∂(20 log u)=∂L/∂(20 log w)=1 at the optimum value of u(=u_0) or w(7-10mm). (Fig. 3) With respect to u_0 and fundamental frequency (f, Hz), the following formula was found. log u_0=log 2. 4+1. 5 log(f/f_c^1)m/sec, where f_c^1 is the fundamental frequency of note c^1(=262 Hz). (Fig. 4) The lower soundable limit of u(U min) is usually about u_0/2, and the upper limit (U max) is about 2u_0. When the direction of an air beam is biassed inwards to the mouthhole properly (about 2mm) in the low register(c^1〜c^2) U max rises to about 4u_0, and high sound pressure level can be obtained. (Fig. 5) All the blowing conditions except the width of an air beam (w) have influence upon fundamental frequency f. But the conditions which have noteworthy influence are u and the length of an air beam (h, mm) (Fig. 6, 7). When u≧u_0, ∂f/∂(20 log u)=k. k×100=0. 23%, and the mean value of ∂f/∂h/f×100=0. 7[%/mm]. The level control in flute-playing was discussed on the basis of data obtained and actual observation of flute-playing (performed by P. Rampal, the author and others). The following conclusion has been reached. Permitting of no change in f, the probable dynamic range is about 16 dB [10 dB by width (w) control+6 dB by velocity (u) control] in flute-playing. In both controls (w and u), f is kept constant by adjusting the length of an air beam (h).