Steve's Clinic: Solving Low Register Issues

[peterbas]

Read Nick Drozdoff's blog, he' a physisist and trumpet player, and he points out very good the difference who things work as a player and as a scientist.

https://www.nickdrozdoff.com/single-pos ... -Trumpeter

[peterbas]

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[Matt G]

So when do we solve the wave equation here?

Right now I think your mental model is of a static system. In that model, the lips, since they are an impedance mismatch, reflect sound waves (and I think out of phase). But then they are also the source function. A source using wind energy and muscular tension to create vibration, or acoustic energy. So there’s some time invariant and time dependent stuff going on.

[timothy42b]

Steve has coined a new meaning for impedance – meaning – deep breath - ‘the effect on the sound wave produced by the lips of the flow and spatial volume of air as configured by the throat and mouth cavity and tongue position all being controlled by the degree of muscular relaxation or tension and arching or lowering of the tongue’.

Impedance in general and a bit oversimplified is "frequency dependent resistance." In purely electrical terms, impedance is caused by reactance (capacitance or inductance) and therefore is different from pure resistance. The term is used for more than just a wave flowing in a wire! but as far as I know it always varies with frequency.

[timothy42b]

There are forward and backward travelling waves.

When you buzz your lips, there is propagation of sound into the oral cavity from the lips. Basically, the lips smacking together create a pressure front that is effectively omnidirectional. Anyhow, keeping an open throat and oral cavity allows the backwards propagating sound to resonate better in the part of the air column that is in the human. The resonance will be then reflected back into the tuba and support the resonance there.

I don't think so. I don't want to speak dogmatically, because I don't know. But here's what I think happens.

The lips generate signal. It travels both directions - down the horn towards the bell, and backwards in the mouth and throat. There are frequency dependent impedance mismatches that generate reflections from both ends that end up back at the lips.

Remember that the horn is several feet long depending on how many valves are down, and the mouth is a few inches - so the harmonics in the mouth have to be different and very much higher than in the horn. (the mouth may be a Helmholtz resonator in some shapes, not sure)

As pressure peaks and troughs return to the lips from both directions, there is a mechanical effect that helps them to close and open at the right time. Most of that assistance comes from the reflection at the bell (or that point on the flare where frequency dictates). But a little bit of that assistance comes from the reflection in the mouth and throat, and that is why the throat cavity must be shaped just right.

At any rate, I don't think the effect of the mouth resonances is reflected into the tuba. I think instead it has a direct mechanical effect influencing the buzz of the lips.

[Matt G]

The lips generate signal. It travels both directions - down the horn towards the bell, and backwards in the mouth and throat. There are frequency dependent impedance mismatches that generate reflections from both ends that end up back at the lips.

Remember that the horn is several feet long depending on how many valves are down, and the mouth is a few inches - so the harmonics in the mouth have to be different and very much higher than in the horn. (the mouth may be a Helmholtz resonator in some shapes, not sure)

Agreed. Impedance mismatch is kinda off, I think. There is a continuous drop in impedance along the entire bugle. The only "mismatch" is when the cross-sectional area goes to ~inf at or near the end of the bugle. Also agreed that this is a discrete variable as a function of valves.

The mouth would work as a Helmholtz resonator. Certainly, due to the vast difference in volume, the resonant frequencies will be much higher there. But I think some do escape (as forward propagating waves that sneak through the aperture into the bugle and help color the term. n.b. This isn't a fact, merely a suspicion.

As pressure peaks and troughs return to the lips from both directions, there is a mechanical effect that helps them to close and open at the right time. Most of that assistance comes from the reflection at the bell (or that point on the flare where frequency dictates). But a little bit of that assistance comes from the reflection in the mouth and throat, and that is why the throat cavity must be shaped just right.

Just pointing out that the peaks and troughs are fixed as a function of frequency. They do not move: https://www.youtube.com/watch?v=-gr7KmTOrx0" target="_blank

I think instead it has a direct mechanical effect influencing the buzz of the lips.

It likely does this as well. I'm just trying to point out how complex the whole system is.

[timothy42b]

Per Matthew:

Just pointing out that the peaks and troughs are fixed as a function of frequency. They do not move: https://www.youtube.com/watch?v=-gr7KmTOrx0" target="_blank

We're both right, I used sloppy terminology so it isn't apparent.

I'm in the time domain, you're in the frequency domain. The difference is just a z-transform. Well, for us mechanical engineers it is; for Steve it's probably a Laplace transform.

What I meant was looking at longitudinal waves reflecting from the end of the tube; what you meant I think was what I would call nodes and antinodes.

And again, it illustrates how complicated this stuff is.

[peterbas]

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