Posted by Rick Denney on October 22, 2001 at 10:50:37:
In Reply to: Re: Re: Re: Re: Re: OK, I did it - update posted by js on October 20, 2001 at 01:08:23:
I think your math may be off by a couple of orders of magnitude. (That's a joke for the mathematicians.)
I'm not prepared to agree completely with your assertion that vibrating brass has no effect on vibrating air. I do agree that it is vibrating air that the audience hears out front, and not vibrating brass. But it would be foolish to think that the two are completely unrelated.
If I initiate a vibrating air mass into a brass cone, the air will vibrate, and the brass, being elastic, will vibrate. At some points, the vibration of the air and the brass will be in phase, and at some points it will be out of phase, unless they are both vibrating at exactly the same frequency throughout the instrument. This is, of course, impossible, because the modes of vibration in brass are radically different than in the air within it. So, at some points within the instrument, the vibrating brass will add to the energy of the vibrating air, and at other points it will subtract from that energy. This much cannot really be refuted. The question is, how much effect does the vibrating brass have on the vibrating air?
The resonant frequency of brass instruments is much higher than the fundamental tone of a tuba sound. A low Bb is about 58 Hz, but when I ring the bell of a tuba, I hear a metallic ringing noise that is a composite of frequencies ten or twenty times higher. The resonance of a mouthpiece is likewise much higher.
So, it is unreasonable to think that the vibrating brass could have much effect on the fundamental tone. But as I have shown in my own work (and as others have shown with greater precision and understanding), tuba sounds include extremely important information in the high harmonics of the fundamental. No tuba playing a low Bb sounds like a 58-Hz sine wave. Those high harmonics are what give the instrument its characteristic timbre.
I measured significant harmonic information up to the 500-1000 Hz frequency band. At these frequencies, the vibration of the brass could have a subtle effect, it seems to me. When I tried the Monster Weights, for example, I was utterly skeptical of their potential, yet the results were so clear that my wife, who is anything but a tuba-sound sophisticate, noticed without being prompted which was which, and commented without being asked.
And I think we are being simplistic when we look only at the steady-state sound vibration. The response of the tuba, which to me means the ease of intitiating a given note, may be profoundly affected by mass, because the extra mass deflects less with a given vibrational energy. That means more sound goes into the initiation of the note. Once the note is started, then that effect doesn't mean as much, because it only takes a tiny amount of energy to maintain a resonant vibration.
A heavier mouthpiece might well provide a noticeable effect in initiating the notes, because it will vibrate less for a given amount of energy. Some seem to notice this effect and others don't--that's for you guys to argue about. But I don't think science has an opinion on the matter until we know more.
But it isn't an issues of damping, and I emplore everyone to understand this term. Mass requires energy to initiate movement. More mass takes more energy. Once moving, however, it takes more energy to stop it. Also a stiffer structure requires more energy to create a given amount of movement (called deflection). A heavy mouthpiece is both heavier and stiffer. But it may be just as resonant or elastic as a thin-wall mouthpiece of similar material, it will just require more energy to initiate that resonance. Damping would occur if the mouthpiece were made from soft plastic (like a pencil eraser), caused by the absorption of energy rather than by changing the way that energy is reflected back into the structure. All mouthpiece are well-damped in any case, because they are pressed up against our highly plastic lips.
Now, let's talk about magnitude.
The volume inside a mouthpiece is small compared to the horn. Every bit of the acoustical energy amplified by the tuba passes through a hole about a third of an inch in diameter. The molecules of air are moving in two respects. One is the linear flow caused by the air movement from our lungs. The other is the three-dimensional vibration, in all directions, caused by the acoustic energy. The mouthpiece moves, because it is made of an elastic material. But the movement is kept to tiny magnitudes, as a result of mass and stiffness. How tiny are the movements of air molecules resulting from acoustic energy? I don't know, but they are at least a small fraction of the diameter of the mouthpiece throat, yet they are big enough when amplified by the tuba to snuff out your match.
If the mouthpiece deflects 0.0001 inches because of vibration (which I'd bet is on the high side), and the air molecules are more like .1 inches in their movements, then it's hard to imagine what effect mouthpiece stiffness and mass could have on the sound. But vibration is a funny thing, and tiny input forces can cause huge effects because of how little energy it takes to maintain a resonant oscillation. And the high-frequency movement of the molecules will be much smaller than the peak movement, though not by as much as at the bell, after having been overwhelmed by resonance at lower frequencies.
And people routinely report differences between mouthpieces that are supposed to be identical, showing that even the tiniest differences resulting from normal manufacturing tolerances are noticeable to some players on some tubas.
So, while science should make us skeptical, it should not close our minds, it seems to me. I've never done the test you describe, so I don't have an opinion. But I have tested Monster Weights, and their effect was pronounced and noticeable. I'm therefore unwilling to take limited knowledge of the science of adding mass and build walls around our understanding. There is more here than meets the eye (or ear).
Rick "thinking Joe's test is too narrow and his conclusions too broad" Denney