Acoustical impedance measurements by the two-microphone-three-calibration (TMTC) method

A method is discussed for measuring the acoustical impedance of woodwind instruments that is relatively fast and insensitive to the ambient acoustical noise. The apparatus is essentially made of a measurement head, which is an approximately cylindrical cavity fitted with two microphones (in practice often three or more for technical reasons) and, at one of its ends, a loudspeaker; the other end is connected to the acoustical cavity under study (the instrument). The loudspeaker emits acoustical chirps and the signals provided by the microphones are Fourier transformed with the help of a microcomputer, which also extracts from the results the acoustical impedance as a function of frequency. A relatively high dynamic range is needed in order to match the high quality factor of the resonances of musical instruments, especially at low frequencies. To meet this requirement, it was found necessary to take into account the acoustical losses inside the head as well as the mutual perturbation of the microphones or various perturbations arising from geometrical imperfections of the cavity. This can be done automatically and without long calculations by using a calibration method, based on the successive use of three reference cavities, which are described and discussed in detail in this article. The method has been tested with cylindrical cavities and gives satisfactory results in terms of peak positions and heights. Impedance curves of clarinets have also been measured. The three-calibration technique eliminates several sources of systematics and corrects automatically for various perturbations, such as perturbations of the acoustical field by the microphones, and allows the study of instruments of various diameters.