Klarinet Archive - Posting 000094.txt from 2010/08

From: Richard Sankovich <sanko@-----.edu>
Subj: [kl] Location of antinodes of vibration in an air column
Date: Fri, 13 Aug 2010 22:40:36 -0400

Diego, thanks for your detailed explanation of sound production by
vibrating strings and air columns. I must take issue, however, with
your conclusion that there will be a vibration antinode at the energy
source, or, in your words, a point of maximum amplitude. You wrote:

> For the violin, the player continues providing energy into the same
> position, which is forced to remain one antinode. Playing in different
> positions changes the timber, because it forces the antinode to
> different positions.
Consider, as you did, that bowed violin string. The fundamental mode of vibration will be excited, as well as many higher modes. The fundamental mode always has its maximum vibration displacement at a point that is halfway between the two fixed ends, in other words, at the middle of the string. You can even see this happen if you bow the G string so as to produce a loud sound. This fundamental mode antinode will always be located at that same halfway point *regardless of where the bow (energy source) is placed along the string*. Normal bowing is done close to one of the fixed ends of the string, near the bridge, where there is a vibration *node*. So energy is fed into the string close to one of its nodes. Definitely not at the halfway point antinode.

What happens in a clarinet air column is analogous to the vibrating
violin string. Energy is fed into the system close to one of the
vibration *nodes*. In other words, the tip of the vibrating reed is
close to a *node* of vibration, not to a point of maximum amplitude
(antinode) as you concluded. When we play the lowest note on our
clarinet, there will be a vibration node close to the mouthpiece and a
vibration antinode close to the bell. The distance between the node and
antinode is always one-fourth of a wavelength of the sound that is being
generated.

One more point while I'm at it: antinodes of vibration of the air
molecules are not the same as antinodes of pressure. (Same can be said
of nodes.) Vibration antinodes and pressure antinodes do not occur at
the same places in an air column, in fact, a point where there is
vibration antinode will also be the location of a pressure node, and
vice versa. I point out this distinction because much confusion can
result when people do not make it clear which kind of node or antinode,
vibration or pressure, is being discussed.

---Richard Sankovich
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