There are problems with this web site.
The biggest one is that the first paragraph which lays the theme out is flat out WRONG!
An open ended wind column instrument is indeed a flute or a pennywhistle as it is open at both ends, yeilding a pressure node at both ends.
However, trumpets and trombones are most definitely NOT open at both ends! You clog up one end with your face - lips. There is a pressure node at the bell but a pressure ANTINODE at the mouthpiece.
This is a popular mistake, as trumpets play a series that appears to be an all integer harmonic series. This is NOT the result of the instrumet being open at both ends. It is the result of the instrumet being tapered - NOT cylindrical. In fact, the "series" produced on a trumpet is NOT perfect becuase it is tricked out like this. The "fundemental" is NOT the low C on a trumpet, because the next note up ought to be a C one octave higher, but instead we hit a G a perfect fifth higher. There must be one note lower. Indeed that is pedal C, but on a trumpet, the pedal C is extremely flat - quite out of tune unlness you lip it up. This is becasue this note is not part of an all integer series of an open ended system. Let me explain.
Consider a simply cylindrical pipe - like a PVC didjeridoo. If you try to play all of the notes on this, you only get the odd multiple harmonics, just like a closed end pipe. Adding taper to the pipe causes the odd series to collpase together to appear to form an all integer series. This is called a variable acoustic length. This is why cheap trumpets play out of tune - special care to build a proper bell and leadpipe wasn't taken so the horn plays out of tune.
Next, it is physically impossible for a pressure antinode to occur at an open end! A DISPLACMENT antinode occurs at an open end! A pressure antinode can only occur at a closed and where the pressure variations can be contained - or in the middle of the tube with no openings.
Finally, a wind chime can't be a wind column instrument at all! It is a vibrating bar. The frequency goes as one over the square root of length whereas for a wind column the frequency goes as one over the length. There was a pair of nice articles on this in the Physics Teacher a few years ago. They can be found in the archives.
I will email the web master with these corrections. These are common mistakes and even fairly competent teachers can fall into them. Here is some suggested reading that has got it correct.
The Acoustical Foundations of Music by John Backus
The Science of Sound by Tom Rossing
Any of the writings of the late Arthur Benade
The Lectures of Tom (I think that is his first name) Holmes
The Writings of Thomas Moore - Science editor of the International Trumpet Guild.
You should in fact contact professor Moore. He'll bear me out on this. He is at Rollins College in Florida.
The rest of the web page is OK, except for confusing pressure waves with displacment waves. The cylindrical series is outlined well. Of course what happens with tapered pipes is left out.
I have been doing lectures on brasswind acoustics for many years and this is a special passion of mine and was represented in my masters thesis for my physics masters (my music masters just had a recital and interiew attached to it).
Thanks Nick. I have read Benade, which made this particular site confusing.
I did contact the author. I first apologized for seeiming brusk here. I didn't mean to come off as a hard guy. Actually, the web site is quite nice. It's just that this particular page had some significant slip ups.
"...examples include the brass instruments such as the flute..."
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