On Apr 4, 2009, at 12:32 PM, Henning Plumeyer wrote:
Therefore, by definition, all blown > musical instruments will
have a fundamental frequency of 2L.
Hi,
not quite: clarinets sound an octave lower than you would expect
when you regard their length.
They behave like stopped organ pipes. I don't know exactly why --
it comes from their cylindrical bore.
(Saxophones have a conical bore and allthough they have mouthpieces
very similar to clarinets they are as long as other wind
instruments.)
I think the _wavelength_ (not the frequency) of non-clarinet wind
instruments is 2 times the length of the instrument.
Henning
There is an excellent tutorial on "lip reed instruments" (i.e., the
brass family) at
<http://www.phys.unsw.edu.au/jw/brassacoustics.html#sound>
The bore of the instrument (conical, reverse conical, or straight)
influences the harmonic content of the sound produced. E.g., a
clarinet and oboe have very different wave forms. I piece of
standard pvc tubing attached to a clarinet mouthpiece produces an
easily identifiable clarinet sound.
A piece of pvc tubing equal to the length of a trumpet can produce
the expected frequency as calculated, using the length as a quarter-
wave (tube closed at one end). A trumpet mouthpiece is unable to
produce this tone due to the mechanics of producing the pressure
"puffs" with the lips. It can be easily done with a reed.
The pressure at the lip end is either high or low. At the open end,
pressure must be equal to atmospheric pressure, i.e., a node.
Therefore, the pressure variation inside the tube is all multiples
of 1/4 wave.
The bell of the instrument is an impedance matching device. Without
the bell, most of the acoustic energy is "trapped" inside. Air
inside the tube feels different to the pressure pulses than air
outside. This results in the internal wave motion (pressure pulses
or vibrations) which make it possible to play the instrument in the
first place. The bell allows a gradual transition from the inside
impedance to the external environment.
A flute is considered an open tube, even though it appears that one
end is stopped. The blow hole is the other open end. Since it is
open ended, the wavelength of the fundamental is twice the length of
the tube.
Constructing instruments from pvc tubing can be instructive and fun!
Stan