The Acoustic Impedance of the Flute

How were these Results Obtained?

Impedance Spectra

The spectrometer injects an acoustic current with several thousand different but precisely known frequency components, all with the same amplitude, into the system to be measured. The pressure spectrum then gives the acoustic impedance spectrum directly. For these measurements, 2801 sine waves from between 200 Hz and 3000 Hz were injected simultaneously. Because the frequency spacing is 1 Hz, each measurement takes 1 second (the reciprocal of 1 Hz) to do. The impedance spectrometer is described in the first of the articles cited below. Another article gives more details of the measurements on the flute.

It is important to remember that these are measurements on the flute itself, not of a flute being played. The spectrometer does not "play" the flute. Rather it exposes the flute to several thousand different frequencies at once and measures the instrument's response. For these measurements the spectrometer was attached to the lip plate in a way that aims to reproduce the acoustic loading of the flute when a player is partly covering the hole with his/her lower lip. The flute was held in a rigid ("sound-proofed"), acoustically damped box in order to minimise the effects of the external sound. It was at room temperature (19.5 +/- 0.5 C) and low, uncontrolled humidity.

The flute we used for the measurements of impedance spectra was a Pearl PF-661 closed hole C foot model. This is a widely available, production-line model and is relatively cheap. It was chosen so that any other scientists who want to compare /music/flute/results or calculations with ours can do so easily on a nearly identical instrument. It has the further advantage (from the scientific viewpoint) that the scale appears to be identical in the closed- and open-hole versions.

Sound Spectra

The main results page shows the sound files and sound spectra made by an eminent professional flutist, using his own flute. These were made in a room with relatively dead response, so room resonance effects should be small. The flutist is Geoffrey Collins of the Australia Ensemble, resident at the University of New South Wales. We thank Geoffrey most sincerely for his help and advice with the flute project.

Geoffrey's flute is a hand-made, sterling silver Brannen-Cooper flute with a Nagahara head made of Brittania silver with a 14 ct gold lip-plate and platinum chimney. It has a "donut" insert to facilitate E6. It has a B foot.The acoustic impedance spectra of flutes with B feet are different from those of flutes with C feet. Further, the fingerings used are different in some cases, especially for high notes. For this reason, the notes with sound files and those used for impedance spectra have different fingerings in some cases.

For serious study, the effects of impedance spectra on the spectra of the sound produced, the comparison should be made on similar flutes. To compare the impedance measurements with sound spectra made on a production line flute with a C foot, go to Cfoot results. For these spectra, the flutist was one of the researchers who, when asked about his flute playing, claims to be a competent saxophonist.

Relative Tuning of the Impedance Spectra and the Sound Spectra

First and quite importantly, the flute used for the sound spectra was being played by a human player. It was therefore full of warm, humid air. The speed of sound, and therefore the frequency of the notes produced by the flute, increases with temperature and humidity. (It is actually proportional to the square root of the ratio of the absolute temperature to the air density. Water molecules are less massive than oxygen or nitrogen, so humidity reduces the density of the air at any given pressure.) For the measurements of Z, the flute was not being played and was filled with dry air at room temperature (19.5 +/- 0.5 C). In future experiments we shall control these variables differently.

Secondly, the acoustic properties of the flute depend on how much of the embouchure hole is covered by the player's lower lip. This varies among players, and for the same players under different conditions. Greater occlusion of the hole (rolling the embouchure hole towards the face) is used when the pitch is to be lowered, and conversely. We had to simulate the occlusion in the impedance measurements and therefore we needed to decide what fraction of the hole was typically covered, and what fraction of the solid angle above was blocked by the player's face. These were both set arbitrarily at 0.5 and kept constant for this initial series of measurements. The relevant parameters will probably be revised in future measurements.

Finally, although the resonances are mainly quite sharp, in the flute they are driven by an air jet with its own characteristic frequency, and which is also coupled to resonances in the mouth and vocal tract of the player. Further, more than one minimum contributes to any given oscillation regime. For these reasons, the frequency of the note produced need not coincide exactly with the impedance minimum under playing conditions.

References

• Wolfe, J., Smith, J., Tann, J. and Fletcher, N.H. (2001) "Acoustic impedance of classical and modern flutes" Journal of Sound and Vibration , 243, 127-144.
• Wolfe, J., Smith, J., Tann, J. and Fletcher, N.H. (2001) "Acoustics of classical and modern flutes: a compendium of impedance spectra, sound spectra, sounds and fingerings" JSV+. Electronic supplement at "http://journals.harcourt-international.com/journals/jsv/supplementary/suppindex.htm

Research team

• Nathalie Henrich (student in 1996)
• Elizabeth O'Connor (student in 1998)
• John Smith
• John Tann
• Joe Wolfe

Industrial Collaborator

• Mark O'Connor of Lehner Flutes Australia and The Woodwind Group.

Flutist

• Geoffrey Collins of the Australia Ensemble, resident at the University of New South Wales.
  You can hear Geoffrey play a signature.

Acknowledgements