The Acoustics of a Tenor Recorder

The study of acoustics is rooted in the origins of physics, yet the dynamics of flue-type instruments are still only qualitatively understood. Our group has developed a measurement system, the Acoustic VNA, which can precisely determine acoustic wave amplitudes of the lowest mode propagating in a cylindrical waveguide. I used the AVNA to study a musical oscillator, the tenor recorder. The recorder consists of two components , an air-jet amplifier driven by the player's breath and a cylindrical waveguide resonator with an effective length that may by varied by covering or uncovering finger holes. Previous research on the recorder has focused on understanding the resonator frequencies in some detail, but has only provided a rough understanding of the air-jet. In particular, there is not yet a quantitative understanding of how the pitch varies with blowing pressure for a given fingering. I designed several experiments to provide a quantitative picture of how the air-jet behaves at different blowing pressures and discovered that higher blowing pressures lead to stronger amplification at higher frequencies. Later, using a dimensionless quantity known as the Strouhal number, I showed that maximum amplification always occurs when the oscillating air-jet is allowed approximately one wavelength between the duct exit and the labium. This physical situation is corroborated by Schlieren imagery done by M.P. Verge and my approximate efficiency calculations based on the power spectra.