Flute acoustics: measurement, modelling and design - School of ...

1.4. HOW FLUTES WORK 5
Figure 1.3: The flute may be approximated as a pipe open at both ends. Pressure modes corresponding
to the first three harmonics are shown.
several dozen fingerings without hogging the flute maker’s computer and wasting too much
of his time, and accessed through a user-friendly interface, with most of the physics removed
from view.
1.4 HOW FLUTES WORK
A brief introduction to the relationship between music and physics is given in Appendix C. To a
physicist, the zeroth order model of a flute is that of a pipe open at both ends. When a jet of air
is directed across one of the open ends at the appropriate speed, pulses of air set up a standing
wave within the pipe. Some of the energy from the standing wave escapes and propagates to
the ear, where it is perceived as sound. Holes in the side of the flute can be opened or closed
by the player’s fingers, which changes the effective length of the pipe and the frequency of the
notes that can be played.
A flute with all the tone holes closed has a long column of air, open at both ends. When the
flute is played, sound waves travel up and down the flute, producing a standing wave. The air
column in the flute resonates at particular frequencies—these different modes determine the
notes that are possible. The first three modes for all holes closed are shown in Figure 1.3. These
produce the notes C4 (middle C), C5 and G5.
A flutist plays a flute by directing a stream of air across the embouchure hole. This creates
an acoustic disturbance that propagates the length of the flute, is reflected back by the open
end and interacts again with the jet. If the length and speed of the jet are such that oscillations
of the jet are in phase with a resonance of the air column, a sustained note is produced.