Klarinet Archive - Posting 000437.txt from 2001/06

From: David Motz <david.motz@-----.net>
Subj: Re: [kl] open tubed vs. closed tube?
Date: Thu, 14 Jun 2001 13:21:04 -0400

At 08:15 AM 6/14/01, you wrote:
>Actually you are pretty close. The clarinet is classified as acting like a
>cylindrical tube closed on one end. Thus it acts exactly like the organ pipe
>closed on one end. That is exactly why it overblows the twelfth. The
>"closed end" is the reed end.

But with an organ pipe it is not the reed end of the pipe which is stopped,
but rather the "bell" end. You can pull the stopper out of the pipe and it
immediately jumps to the octave. So, when I think of a closed tube in
connection with a clarinet I'm picturing one with a cork plug in the end
instead of a bell. I never seen one like that. In any case, the next open
hole up the tube would prevent it from being considered "closed". So, I'm
assuming this analogy is totally off base.

My mental image of a closed pipe is that the wave form starts at the mouth
of the pipe and proceeds to the far end which is stopped, and then back to
the mouth. This accounts for the doubling of the length and hence the
octave lower sound. When you take the stopper off, the wave form goes only
from the mouth of the pipe to the open end, yielding half the length and
twice the frequency.

I just can't make this image fit with a clarinet, or see how there is any
structural difference between the clarinet, flute, sax, oboe, etc. They
all have a means of introducing a vibrating column of air at one end, and
all are open at the other end, with a series of holes to adjust the length
of the tube. I do realize that this is a greatly simplified
representation, but in my ignorance, it seems to be an apt generalization.

So, what am I missing?

Ah, the archives... I just found this interesting post from 1996:

> Acoustically the clarinet behaves as a cylindrical
> tube open at one end with the mouthpiece at the other
> end. Because a pressure antinode forms in the
> mouthpiece it resembles a tube closed at one end and
> open at the other. Therefore its fundamental frequency
> is half that of a tube open at both ends, and of the
> same length. This is why a clarinet sounds an octave
> lower than a flute even though it is nearly the same
> length. Since tubes closed at one end vibrate with
> modes that are odd multiples of the fundamental, the
> next mode of oscillation is three times that of the
> fundamental which is a twelfth. This is why the
> clarinet overblows the twelfth. If the pressure
> antinode did not form in the mouthpiece the clarinet
> would not behave this way. For example the oboe and
> bassoon are also closed at one end but behave
> differently. They are basically tubes with conical
> air columns in which the tip of the cone has been cut
> off and the reed attached. A concical air column will
> vibrate with both even and odd harmonics, therfore
> both instruments overblow the octave. The flute
> behaves as a tube open at both ends and also overblows
> the octave. The saxophone is considered a hybrid
> because while it overblows the octave its fingering
> system is mostly the same as the clarinet. It has a
> wide conical bore. I hope this is helpful. I have
> quoted freely from The Acoustical Foundations of Music
> by John Backus. To further understand nodes and
> antinodes in the vibrating air column I refer you to
> chapter four of the above book. Another good source
> is Fundamentals of Musical Acoustics by Arthur H.
> Benade. These are standard reference books in the
> realm of acoustics so they should be easy to find.

Perhaps I need to read a good book...

Thanks for your help on this.

David

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