Abstract
A microphone for acoustic measurement in the free field or in other must be samll enough so it does not disturb the original field. For this purpose, a circular tube probe microphone, as shown in Fig. 2, has been often used. However, an exact non-directivity can be expected from this probe microphone only when ka→0, where a is the outside radius of the tube and k is 2π/λ (λ: wave length). For practical pupose, it is necessary to know the directivity and the acoustic center (the end correction) even when ka is small for more accurate measurements. Levine and Schwinger solved the "power-gain function" and the end correction concerning a semi-infinite cylinder with negligible wall thickness by the Wiener-Hopf technique. They have reported that the correction has been calculated pgraphically as a function of ka. The power-gain function, however, is very complicated as shown by Eq. (1) so that it is not suitable for parctical use, therefore, it has been rearranged approximately for the pressure directivity in the range of 0≤ka<0. 5, as shown by Eq. (10). On the other hand, using a turntable, the pressure directivity has been measured in an anechoic chamber as shown in Fig. 3, and the ratio of the directivity (see Eq. (11), Fig. 4 and Fig. 5) between of Θ_1 and of Θ_2 has been measured as shown in Fig. 6, by applying the "interference pattern method" (a method of measureing the complex reflection coefficient of acoustic materials at oblique incidence). Next, the shifts of the acoustic center between two different radius of the tubes (see Eq. (12) and Fig. 7)have been measured at the pressure minimum points (from the first minimum to the fifth minimum counted from the surgace of material) of the interference pattern in front of the reflecting surface. These results are shown in Fig. 8. The acoustic center has been plotted as shown in Fig. 9(see Eq. (13)) by the measurement of the shift of the first pressure minimum in the acoustic tube (for normal impedance measurement) ended by perfectly reflecting surface. The distances were read with a microscope with a reading accuracy of 1/100 mm. Consequently, these experimental results have shown that both the pressure directivity and the acoustic center of the probe microphone can be determined from theoretical results by using the outside radius of the probe tube rather than the inside radius in the range of 0≤ka<0. 5. it is believed that more exact theoretical investigation concerning a finite cylinder with a wall thickness should be carried out, for instance, by means of the technique of Matsui.
