Re: Vibration, damping, and weight


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Posted by John Swensen on August 17, 2001 at 12:56:38:

In Reply to: Vibration, damping, and weight posted by Rick Denney on August 17, 2001 at 11:26:02:

Rick, you have made some excellent observations; to these I would like to add a few on the influences of vibrations of the walls (the brass tubes in our case) to the resonance of the air column. In short, the vibration of the walls can, possibly, affect the response of the horn as much or more than they can rob the horn of "projection".

An interesting experiment to try is to blow across the mouth of an empty, plastic bottle, particularly a bottle that has flat, parallel sides (the wide-mouthed, clear plastic mouthwash bottles in our house work very well). If you just hold the top of the bottle as you blow, it is easy to get a sound from this Helmholtz resonator, even though the mouth is an inch and a half in diameter. However, if the flat sides of the bottle are damped with light finger contact (and without changing the static shape of the bottle), it becomes very difficult to get any kind of sound from the resonator, at least with the air flow that I can produce.

As another experiment, try making the paper cuckoo whistle, linked below. Here, applying light finger pressure to the sides of the whistle dramatically changes the pitch of the whistle.

In each of these cases, the resonance of the air column is affected by the vibration of the walls of the column; in one case wall motion make resonance easier to achieve, in another, it changes the resonance frequency. Benade discusses the contribution of wall vibration in his fascinating, but non-mathematical book,
Fundamentals of Musical Acoustics
. Basically, he claims that the direct contribution of sound from vibrating walls is negligible for most or all wind instruments, but that wall motion can either raise or lower a resonance frequency, depending on the natural resonance frequency of the walls, relative to that of the air column with infinitely-stiff walls, as well as other factors.

It may be that adding a weight to part of the tuba, clamping a belt around the bell, moving a brace or two, or sticking a cork between two tubes slightly alter some of the resonance frequencies of the horn, which may make some stuffy notes a little less so, or may help a horn to slot better, and can help it to project better, because certain important frequencies are resonating more strongly. Benade described several cases where good instruments were transformed into outstanding instruments after subtly adjusting one or more of the instruments' resonance frequencies, allowing each note to speak quickly and clearly. Some of his adjustments involved no more than a strip of lacquer at a specific area in the bore, so they were very subtle (and note that Benade was a physics professor at Case Western University, and was able to verify the effects of these changes through repeatable measurements using his collection of acoustical instruments (the laboratory kind, not the musical kind)).

Although he did a lot of work with brass instruments, Benade's adjustments were most successful with woodwind instruments (which he played relatively well, as an amateur). This may have been because woodwind instruments, essentially, "ignore" the shape of the bore more than few bore diameters past the last open tone hole; thus, he could adjust the lowest note, then open a hole and adjust the next note, and so on, throughout the instrument's range (I am ignoring his treatment of octave and register keys in a futile attempt at brevity).

I believe we are at just the beginning of understanding how to achieve similar successes with brass instruments, where most parts of the bore affect all of the notes, but I am optimistic that great progress in brass instrument design can be made, so that some day we will know how to make a horn as responsive as Arnold Jacobs York, but with the weight of sound of a big Martin BBb, or with the characteristic German sound of an Alexander.



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