I am a trumpet player. I actually play 1st trumpet in the college symphonic
band (one perk of being a faculty member at a liberal-arts college). I
often play my trumpet and various "tubes" for my classes, and I often record
the result with a spectrum analyzer.
With a trumpet, all harmonics are there except for the first, which I
understand would require a wider bore in order to sustain.
But when I put my mouthpiece in a straight tube I also get all harmonics.
Notes I am able to play on the straight tube, and what my spectrum analyzier
tells me, is that all harmonics are present (except the first) when I play a
straight tube with my trumpet mouthpiece. Note: When I do this, I use a
glass tube so students can see there are no tricks inside. The tube has
about the same bore and same length as a trumpet, and therefore the lowest
sustainable note is the same as the trumpet. I can then play bugle calls on
the tube and the tube sounds just about the same as the trumpet sounds,
except considerably subdued and slightly different timbre... differences I
attribute to the bell providing better acoustic coupling. But the tube is
definitely cylindrical... not conical... and I definitely get even harmonics
as well as odd.
Now... after Tim suggested the mouthpiece might make a difference, I tried
playing the glass tube without my mouthpiece. I put my lips straight
against the glass (which has been fire-polished). This time I do get just
odd harmonics. So I disagree with Tim that we get only odd harmonics if the
trumpet mouthpiece is placed on a cylindrical tube of dimensions similar to
a trumpet. But I now agree that we get only odd harmonics if we "blow"
directly on the tube... something I had not done before. So the mouthpiece
design is apparently very important... something any trumpet player already
knows quite well on a subjective level.
Yet... and here is where it gets more confusing... another thing I have
often done (as a sort of parlor trick) is play my trumpet without the
mouthpiece (as I suppose many trumpet players have done)... and the even
harmonics are still there in that case. So the mouthpiece is not the total
picture.
I think this is more evidence that trying to transport simple textbook
physics ideas into the realm of musical instruments is a good starting
place, but it gets real complicated real fast.
Also note that intuition about whether the region outside the lips is a
pressure node or pressure antinode is also confusing. The example of
tapping the lips is ambiguous. Viewed one way (as presented by Tim), the
tapping represents pressure fluctuations and the lips can part when the
pressure falls. Viewed another way the lips and pressure in the mouth are
prepared to try to maintain reasonably constant pressure just outside, and
when the fingers are removed the lips part and try to maintain the pressure,
but in this case are unable to do it, so they just remain open. This
behavior is typical of pressure regulators, the valve (often part of a
diaphragm) opens and closes as necessary to maintain constant pressure. The
pressure therefore fluctuates up and down a bit (because the valve has to
open and close) but it doesn't fluctuate very much. So is that closer to a
node or to an antinode?
Further information... we don't need the trumpet tube or mouthpiece to play
tunes with our lips. Just a little bit of practise allows a person to
sustain a particular frequency with vibrating lips alone. So the
oscillation of the lips is not really (or shall we say not totally) caused
by feedback from the reflected waves in the horn. In this regard the horn
simply helps the player get the correct frequency. So... how much help is
needed? Do actually we need pressure antinodes at the lips to force them to
vibrate in phase (like the example of tapping the lips with the fingers at
some frequency) or do we need just a little bit of feedback and the pressure
there could be fairly constant. I guess I just don't know.
I also note that trumpet players who are not scientists use all kinds of
words and talk about all kinds of things I don't understand. They talk
about different back-bores in mouthpieces and different styles of lead pipes
on trumpets and how some situations produce a more centered sound (whatever
that means) etc. They are apparently sensing differences, but don't quite
know how to describe what they are sensing. I've tried to have them explain
to me what this all means, but they are unable to use words that make
scientific sense to me. On the other hand, I am just trying to make sure I
play the right note, at the right time, reasonably in tune, with a
reasonably pleasant timbre. The band director says I do that most of the
time.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817