Brian,
I think we are simply better off with NODENTS.
Amitiés à tous,
Laurent
- Original Message -
From: <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, October 30, 2004 11:36 AM
Subject: [Hornlist] Oddball ebay horn and the resistance duck
> Herb F wrote
>
> This has brought up an interesting discussion. While the standing wave
travels
> more efficiently around a ninety degree bend because it reflects off the
> corner, what happens when there's a node or antinode there? My acoustic
theory
> is weak here. Has anything been published?
>
>
> I think there has, but I am not current on the scientific work.
> Here is what I know about bends in tubing. Suppose you have
> a long straight tube. It will have resonances at certain
> frequencies. The longer the tube, the lower the frequencies
> of the resonances.
>
> Now bend the tube, taking care to maintain the circular cross
> section. You will find that all the resonances have been shifted
> slightly higher. Race car drivers know to drive along the inside
> of a turn to shorten the distance they must drive; so too, the
> path the sound follows through a bend is slightly shorter than
> the path it would take through a straight tube. So the
> acoustical length of a bent tube is slightly shorter than its
> actual length.
>
> You can compensate for this effect by making the tube slightly
> narrower in the region of the bend. Bassoon makers know
> about this. A bassoon's air column goes through a 180 degree turn;
> in that region, the air column is slightly narrower than you would
> predict from the profile of the rest of the instrument. I
> don't know whether brass instrument makers have noticed
> or considered this effect.
>
> There is another effect to consider. First a digression
> about dents. When you play a note on your horn,
> the sound inside the instrument makes a standing wave
> which has displacement nodes and antinodes. If there were
> a wall across the tube, then the wall must be the site of a
> dsiplacement node: you can't displace air through a wall.
> A dent (or a stray blob of solder on the inside
> of the horn, or a rotor port that is slightly out of alignment)
> would act as a partial wall; it wouldn't affect the
> frequency of a standing wave that already had a node
> at the location of the dent. But if a standing wave
> has a node NEAR a dent, that node tends to shift toward
> the dent, changing the frequency of the standing wave.
> In addition, antinodes would tend to shift away from the dent.
> Different notes of the horn will have nodes (and antinodes) at different
> distances from the dent, and so the effect of the dent will
> be different for different notes. An abrupt bend in a
> tube acts like a partial wall, and so affects the horn the
> same way a dent would, shifting some resonances up
> and some resonances down, and leaving some unchanged.
>
> I don't know how large this effect is. I will check out my
> sources and see what they say.
>
> Gotta go,
> Cabbage
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