Harmonics in a tube closed at one end

Question

I have been learning about sound and how a tube closed at one end only seems to have odd harmonics.

However, I have found that although clarinet follows this and plays only odd harmonics, saxophone does not and can produce every harmonic, while the instrument is almost exactly the same as clarinet. One major difference between saxophone and clarinet is that the saxophone is conical, and the clarinet is cylindrical, but the trombone is a cylindrical tube closed at one end and still can produce every harmonic.

What are other factors contributing to the harmonics an instrument can produce, and does a tube closed on one end realistically only play odd harmonics?

Thanks,

ZaellixA · Answer

The fact that the saxophone can reproduce all harmonics (even and odd) is attributed to its conical shape. You can see a quite simplified explanation here.

The fact that the saxophone is not a tube alters the supported solutions to the wave equation. One can find similar phenomena when dealing with loudspeaker horns. Although the focus there is the limiting frequency and the increase in efficiency, while in your question you are more considered with the frequency spectrum. Nevertheless, if the horns were unable to reproduce the whole spectrum (in their designed frequency range of course) they would be useless, so you can think of them as being a somewhat conceptual counterpart of the saxophone (although many other differences exist between a saxophone and a loudspeaker horn, I believe that for the conceptualisation here, the comparison serves us well).

In addition to that, the last part of the saxophone's tube does resemble a horn and indeed helps with the radiation efficiency.

Harmonics in a tube closed at one end

One Answer

Add your own answers!

Ask a Question