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Trombone Physics

posted May 1, 2012, 2:28 PM by Fr. Kevin Vogel
I began to play the trombone in fifth grade, but it took a while before I had developed the skills to make playing it enjoyable. So I am glad that my mom made me practice. I really do enjoy music, and there is something about creating music that feeds the soul.

Anyway, I wanted to put something up about the physics of music as it applies to the trombone (actually it applies to other brass instruments as well). The trombone is basically a closed cylindrical air column, closed at one end (the mouth) and open at the other.

This means that it produces resonant standing waves at a fundamental frequency (the lowest resonant frequency of a vibrating object) and then at odd harmonics (integer multiples of the fundamental frequency). This is because the air at the closed end has to remain in place, forming a node. Open ended air columns, on the other hand, can produce all harmonics because they are not restricted to having a node at one end.

The problem with only producing odd harmonics is that one wants the instrument to be able to produce all harmonics. The technique is to force a full harmonic sequence by forcing the upper and lower odd resonances together to form all the harmonics. This is done by altering the shape of the ends of the cylindrical column. The mouthpiece forces the high resonances down while the bell forces the low resonances up.

Now the trombone can play a full chromatic scale. After all this, I am sure you would like to actually hear this in action. Here is a short piece recorded a few years ago called "Chorale and Allegro" with my sister Rachel on trumpet and I on trombone.
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Or if you want to get in the Christmas mood early, here we are playing a short version of "Jingle Bells" with star appearance by my brother Adam on the bells.
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But is music simply vibration of air? Not necessarily applying the following to the previous humble tunes, John Henry Newman wrote about great music in general:

    "Can it be that those mysterious stirrings of the heart, and keen emotions, and strange yearnings after we know not what, and awful impressions from we know not whence, should be wrought in us by what is unsubstantial, and comes and goes, and begins and ends in itself? It is not so; it cannot be. No, they have escaped from some higher sphere; they are outpourings of eternal harmony in the medium of created sound; they are echoes from our Home; they are the voice of Angels, or the Magnificat of Saints, or the living laws of Divine Governance, or the Divine Attributes ..." (as quoted in Thomas Dubay's The Evidential Power of Beauty, p. 57)

You can read more about brass instruments here, other musical instruments here, and about sound here all from the HyperPhysics website.