Visualization of resonance phenomena for acoustic education

Shinichi Sakamoto, Kanako Ueno and Hideki Tachibana

Institute of Industrial Science, University of Tokyo [email protected]

Abstract used in the model 1, a digital delay was connected to adjust the phase condition of the sound. Visualization of sound field is very effective for comprehension of acoustic phenomena and various kinds of visualization techniques have been devised. The Time delay Driver unit of authors are also interested in these techniques and have loudspeaker Function Amp. been contriving physical experiment and numerical generator simulation methods as the educational tools for architectural acoustics. Among them, some applications Cork dust of Kundt’s dust figure method to the visualization of

is scattered resonance phenomena such as normal modes in a 2- dimensional room, active noise suppression in the room and Helmholtz resonance are introduced and thick demonstrated in this presentation. 100 mm Primary source 480 mm Acrylic plate 15 mm 1. Introduction Secondary source 300 mm 80 mm It is very effective to visualize a sound field for intuitive 120 mm understanding of various acoustic phenomena, (a) Model 1: (b) Model 2: especially for acoustic education. The most famous and Normal mode Helmholtz resonance classical visualization technique is the Kundt’s dust-tube method contrived by August Adolph Kundt (1839-1894). Figure 1 Experimental set-up He devised this experimental technique to determine the sound velocity in the air by observing the mode pattern 3. Active Model Control of a standing wave excited in a glass tube. The technique Using the model 1, visualization of normal modes in the can be applied to various other acoustic resonance rectangular room sound field and that of the active mode phenomena. In Japan, Sato and Koyasu applied this control was performed. At first, the experiment was technique to 2-dimensional room acoustic model made by exciting the primary sources. When the experiment in which the effect of shape of a frequency of the sound coincides with the modal reverberation room on the normal modes was frequency of the sound field, the scattered dust is examined[1,2]. Referring these experiments, the authors intensively excited and makes a figure corresponding have made experiment to visualize normal modes in a with wave pattern of each normal mode. As one of the room, the active mode control and the effect of examples, the pattern of the 1-1 mode (640 Hz) is shown Helmholtz resonator. in Fig. 2 (a). In this figure, it is clearly seen that high and dense pleats are excited in the midst of each side where 2. Instrumentation for the Visualization the particle velocity is maximum, and that the cork dust is settled down at the four corners where the sound For visualization of sound field, two models with the pressure is maximum. In the next experiment, both of the size of 48 cm x 30 cm and 5cm thick were made of primary and the secondary sources were driven with the acrylic plates as shown in Fig. 1 (a) and Fig. 1 (b). The same frequency in phase. As a result, the pattern of the model 1 is for visualization of the normal mode of the 1-1 mode was much degenerated as shown in Fig. 2 (b). room and the active noise suppression and the model 2 is The mode excited by the primary source has been for that of the Helmholtz resonance. In the models, even- canceled by adding the secondary source. This is very sized cork dust was uniformly scattered on the floors. As simple and basic experimental presentation of the the sound source, driver units of loudspeakers were principle of the active mode control. mounted at the corners of the models and a pure tone sound was radiated from them. For the secondary source

We.P1.3 III - 2311 Primary source : ON intensively excited for both of the resonators. The frequency is 1,250 Hz which coincides with the first (n=1) resonance frequency calculated as follows.

nc (2) f n = 2 ⋅le

Secondary source : OFF (a) 1-1 mode excited by the primary source Primary source : ON

(a) Helmholtz resonance for the (b) Helmholtz resonance for the large resonator (170 Hz) small resonator (240 Hz)

Secondary source : ON (b) both of two sources are excited at the frequency of 1-1 mode

Figure 2 Visualization of the active mode control (c) Open pipe resonance which occurs in the neck parts of 4. Visualization of Helmholtz resonance both resonators (1,250 Hz)

The Helmholtz resonance is one of the most basic Figure 3 Visualization of resonance phenomena using acoustic resonance phenomena and various absorption the model 2 constructions based on this principle are used in architectural acoustics. Using the model 2, in which the 5. Conclusions two Helmholtz resonators with different sizes were Two examples of the visualization of acoustic resonance installed, the resonance was visualized. When the phenomena using the Kundt’s dust figure method have excited frequency coincides with the resonance been introduced in this paper. This kind of the frequency, the cork dust in the neck parts of the presentation based on the physical experiment is very resonator is excited. Figures 3 (a) and 3 (b) show the impressive and effective to understand acoustic Helmholtz resonance for each resonator. As shown in phenomena intuitively. Such a presentation method is these figures, the cork dust in the neck part is uniformly much effective for acoustic education. excited. It means that the particle velocity in the neck part is uniform. The resonance frequencies are 170 Hz 6. Refferences and 240 Hz, respectively, and these are almost the same [1] Sato, K., Koyasu, M.,“The effect of room shape on as the f0 calculated by the following equation. the sound field in room”, J. Acoust. Soc. Jpn. (J), c S Vol.13, No.3 (1957) f = (1) 0 [2] Sato, K., Koyasu, M., Nakamura, S., Kubo, K., 2π le ⋅V Miyahara, Y.,“The illustration of sound field where, c is the sound velocity, S is the section area of the distribution in a model room by means of dust neck, le is the efficient length of the neck and V is the figure”, J. Acoust. Soc. Jpn. (J), Vol.16, No.1 (1961) volume of the cavity. In addition, open-pipe resonance also can be observed by increasing the frequency further as shown in Fig. 3 (c). In this case, the cork dust in the vicinity of the neck is

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