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Outside Comments



I forwarded many of the recent e-mails on the physics of musical
instruments to a physicist friend of mine who has had a long-standing
interest in the physics of music and musical instruments. I thought the
contributors to the discussion might be interested in his comments.

Ken Morgan
Physics Department
Michigan Technological University

His comments:

Tone production in wind instruments is governed by non-linear
differential equations. Trying to discuss it using a driven
harmonic oscillator (a linear system) is bound to lead one
astray. The actual driving force for the instrument is D.C.,
and the non-linearities lead to oscillations. It is self-driven.
Similar considerations apply to brass instruments with the lips
being the reed. What is going on is a lot more than just
noise (or tone) production followed by a filter.
In simple terms, the reed (or lips) act as a pressure-controlled
valve. The pressure difference across it opens or closes the valve
allowing air to flow. On one side of the valve, the pressure is
(more or less) constant. On the other side it varies - largely
due to the time delay for a "pulse" of air to be reflected from
the end of the instrument back to the mouthpiece. When the
pulse returns, it opens the valve allowing more air to be added
to the pulse (and at the same time, the pulse is reflected back),
thus reenforcing the pulse. This positive feedback leads to
an instability and oscillations.
Flutes act in a similar manner, except they can be considered
as being "flow controlled," rather than pressure controlled, valves.

In addition to Chapter 13 in Fletcher and Rossing, which is
difficult reading, see:

M. E. McIntyre, R. T. Schumacher, and J. Woodhouse,
J. Acoust. Soc. Am. 74, 1325 (1983)
and/or
A. Barjau, V. Gibiat, and N. Grand,
J. Acoust. Soc. Am. 102, 3023 (1997).

(Benade's book, "Fundamentals of Musical Acoustics" is also a good ref.)