The undercutting of toneholes has been practised for centuries with the aim of
improving the tuning and playability of woodwind instruments. The influence of
undercutting on tuning can be understood in terms of linear acoustic theory. Its effect
on other playing characteristics is thought to lie in its reduction of local non-linear flow
phenomena (boundary layer separation and the formation of jets and vortices) at the
tonehole. Particle Image Velocimetry (PIV) is used to examine the oscillating airflow
around a model woodwind tonehole. Velocity and vorticity information is obtained
and compared for a square-edged tonehole and an undercut tonehole at a variety of
sound levels. The upstream, internal edge of the tonehole is found to be the location of
the most significant local non-linear flow behaviour. Undercutting is found to reduce
the strength of local non-linear flow phenomena at a given sound level. Microphone
measurements carried out in a reverberation chamber show that undercutting the
tonehole also reduces the harmonic distortion introduced to the radiated pressure signal
by the non-linear flow. Proper Orthogonal Decomposition (POD) is then applied to
PIV data of oscillating flow at the end of a tube. It is used to approximately separate
the acoustic field from the induced local non-linear flow phenomena. The POD results
are then used to approximate the percentage of kinetic energy present in the non-linear
flow. POD analysis is applied to the case of flow around the two toneholes. It shows a
smaller transfer of kinetic energy to non-linear flow effects around the undercut tonehole
at a given sound level. The dependence of the local non-linear flow kinetic energy on
Strouhal number is considered