A New Technique for the Rapid Measurement of the Acoustic Impedance of Wind Instruments

The input acoustic impedance of musical wind instruments necessarily has a dramatic variation with frequency. Our technique uses an acoustic current source whose output is calibrated on a purely resistive load, provided by a ‘semi-infinite’ cylindrical pipe. The frequencies, amplitudes and phases of the sinusoidal components in the stimulus are chosen explicitly to provide the desired frequency resolution and range, and also to optimise the signal to noise ratio. A stimulus waveform is then synthesized from this set of frequency components. The acoustic current is produced using a loudspeaker coupled to the system under study via an exponential horn and an acoustic attentuator with a large acoustic impedance. This allows rapid, high precision measurements over a wide dynamic range. This permits us to investigate the air-jet family of instruments, which operate at the minima in impedance, and which require therefore a large dynamic range in measurement. We have conducted a detailed study of some members of this family. Aspects of the sound and playing behaviour of the instrument in any particular configuration or fingering can often be explained by the frequency dependence of the impedance, in particular the frequencies, depths, bandwidths and harmonicities of the impedance minima which together determine a playing regime. INTRODUCTION Acoustic impedance Z(f) is the (complex) ratio of acoustic pressure to acoustic volume flow. The importance of the impedance spectrum of the bore of a wind instrument upon the intonation, timbre and stability of its notes has been known for decades. Until recently, detailed comparative studies have often been complicated by the either the time taken for time domain or swept frequency methods (e.g. Gibiat and Laloe, 1990; Keefe et al, 1992) or inadequate dynamic range. The requirement to measure such a spectrum for every useful combination of keys (several dozens for woodwinds) makes rapid measurements desirable. The air jet family of instruments (flutes, recorders, ocarinas, shakuhachi, quena etc) poses a particular problem for the measurement of acoustic impedance, which may explain why there is very little published material about Z(f) for this family. These instruments are driven by an air jet, so the bore of the instrument is open to the air at the input. Consequently, the minima of Z(f) are of acoustic importance. The variation in Z(f) in a musical instrument is quite large (typically 60-70 dB) and so a large dynamic range is needed. The situation for ‘closed’ instruments such as the reeds (the other woodwinds) and the lip-reeds (brass) is quite different. These instruments operate at impedance maxima, for which the sound pressure is of course