Abstract
The choice of the dimensions of capillary tubes used for acoustic impedance measurements (with applications to wind musical instruments or materials) depends on the frequency and impedance ranges. It is shown that there is an optimum range for the ratio of the length of the tube to its area, in order to have a flat amplitude response over a wide range of frequency. Several shapes of capillaries, in particular a narrow slit with arbitrary shape, such as a hexagon inscribed in a circle, using an approximate theory of viscothermal effect are studied. The upper limit of frequency does not depend on the shape, but only on the length of the capillary. Therefore, the choice of the dimensions starts with the frequency range, and our study allows one to deduce successively the length, the transverse dimension related to the width of the slit, and finally, from the impedance range, the transverse dimension related to the number of capillaries.
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