Klarinet Archive - Posting 000789.txt from 1998/12

From: Tony@-----.uk (Tony Pay)
Subj: Re: [kl] Clarinets, saxes, octaves, and the trumpinet....
Date: Mon, 21 Dec 1998 12:21:31 -0500

On Mon, 21 Dec 1998 15:31:19 +0000 (GMT), roger.shilcock@-----.uk said:

> Let's not forget that this is about so-called "standing waves" (which,
> nonetheless, can move) and (more or less) equilibrium cnditions.
> Roger Shilcock

Quite right, Roger. So when I wrote:

> > Now, the wavelength is the distance after which the wave is the
> > 'same' -- the distance between two wave-crests, or two wave-troughs
> > at sea, for example. So because 'open' and 'closed' are
> > 'different', the tubelength can only correspond to the distance
> > between a crest and a trough. (The distance between two crests, or
> > two troughs, would be the distance between two things that are 'the
> > same'.)

...there's a danger of confusing the issue -- exactly the issue that I
was trying to make clear in the other thread.

But it requires further clarification.

Inside the clarinet, the wave is a standing wave. It has a certain
frequency, to do with the fact that initially waves of compression are
propagated down the instrument and partially reflected on contact with
the open air; and the reflected waves interact with the reed so that a
steady state is achieved.

This steady state is achieved very quickly.

Then, outside the clarinet, the wave is a travelling wave, just like a
wave on the sea, but longitudinal rather than transverse (it consists
of increases and decreases in pressure, rather than increases and
decreases in height).

The wave equation for a given material describes what must be true about
the behaviour of the material when it vibrates. In this case the
material is the air inside the instrument, and the equation applies to
any wave, or combination of waves, inside the instrument.

The steady state, or standing wave, can be thought of as a combination
of travelling waves; the boundary conditions (closed at the top, open at
the bottom) defines the allowed frequencies of these waves.

When broadcast, they are generally heard as one sound: a fundamental
pitch plus a timbre, though in more complicated steady states we may
hear them as a chord.

I'll talk about the trumpinet another time:-)

Tony
--
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