 The Clarinet BBoard
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Author: krawfish3x
Date: 2003-08-30 23:17
im interested in clarinet acoustics and im trying to learn about it on my own, but im not exactly sure what some of these formulas mean. in the site below, about 1/3 down the page there is a formula with wavelengths and then it begins to talk about the harmonic series. can anyone explain what this formula they have means?
http://www.phys.unsw.edu.au/~jw/clarinetacoustics.html
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Author: Synonymous Botch
Date: 2003-08-31 00:49
When you play a given note, other notes are present in the sound, with less volume contributed.
Squeaks are an example of a harmonic overtone to the intended note.
In other words, the reason clarinets sound like clarinets is the additional accoustic energy supplied with the fundamental tone.
Also, the sounds illustrated in the 'au' or 'wav' file are overtones in the harmonic series above the first note played.
When the first note is played solidly, and with stability, the next notes you hear should be present, although at considerably lower sound pressure.
It's a really good site!
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Author: Terry Horlick
Date: 2003-08-31 01:12
Krawfish3x,
Those formula are really a bit silly to have put there. They are covered by the text anyway.
First: they use something they are calling L. Look at the graph, L is just a length they picked on the graph. If you look carefully L is 1/4 of a full wave, or 1/4 of the wavelength. The usually accepted symbol for wavelength is the Greek letter Lambda: λ What they are doing is just defining λ = 4L Simply put they are saying we are calling a new parameter L and it is to be 1/4 the wavelength. Fine. Why do that? No reason, they just needed to fill space on the page, L isn't used anywhere else on this page or in the real world to my knowledge.
Second: in the text they define frequency. They just repeat that frequency is the Speed of the wave divided by the wavelength in the formula:
f = v/λ
The frequency or f is the pitch of the note. The speed used is the speed of sound (v) for your particular temperature, pressure, air density etc.
The series of graphs and formulae just repeat the same thing for different frequencies. In this case the frequencies are those for a given length of pipe so you are comparing the frequencies for standing waves with similar nodes.... all this is a fancy way of saying he is showing how to figure the pitch of the overtone series obtainable from a given length of pipe (clarinet).
Often writers like to throw in formulas to impress you. In this case they are there if you want them, but are not needed for the discussion. That gooney λ = 4L doesn't need to be in there at all!
IMHO TH
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Author: Dan Shusta
Date: 2003-08-31 02:54
krawfish3x, I suggest you get a copy of "The Clarinet relealed" by Ernest Ferron.
Wavelength = 4L means that a full cylce of a particular note must travel 4 times the lengh of the tube for that note. It starts out at the mouthpiece, travels to the end of the bell, is reflected back to the mpc and then heads back to the end of the bell. (This is for all holes closed.)
As each finger if lifted, the subsequent length of the tube is shortened which, of course, means the wavelength is shortened and therefore the pitch is higher. The longer the wavelength (all of the holes closed), the lower the tone (frequency). The shorter the wavelenth (as when playing Bb with the left thumb, 1st finger), the higher the tone or frequency.
I highly recommend this book if you want to understand the acoustical nature of clarinet design.
Dan
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Author: Matt Locker
Date: 2003-09-02 12:23
Krawfish:
Try this website for clearer information
http://www.phys.unsw.edu.au/music/pipes.html
MOO,
Matt
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Author: Phat Cat
Date: 2003-09-02 14:25
In the prehistoric era, I took classes in math and physics at Case Western University when Arthur Benade taught there and at the same time took classes at the Cleveland Institute of Music where Robert Marcellus was on the faculty. Eventually I concentrated on mathematics and went on to Columbia for my doctorate but I still insult the clarinet repertoire and have maintained a keen interest in clarinet acoustics. The article originally referred to in this post is an excellent introduction to the acoustics of the clarinet, in fact one of the nicer I have seen. I’ll add my own explanations to those already posted.
The formula is not silly and is not there just to full up the page, and the quantity L is not just the arbitrary width of the graph. Simply, L is the effective length of the cylindrical pipe for the note being generated down the interior of the clarinet bore. The pressure wave starts at the point where the tip of the reed (nearly) closes the tip of the mouthpiece when you blow enough air to produce a sound. The other end of the pressure wave is where the pipe is “open” to the outside atmosphere...either the end of the tube or the first open tone hole. The distance between these two points is (to first approximation) the effective length L.
The physics of such a vibrating column of air indicate that only waves of certain length and shape will resonate in the tube and produce an audible sound. Such waves are called standing waves. The author is demonstrating graphically that the waves must take the mathematical form of a cosine graph whose top (maximum) occurs at the mouthpiece/reed closed end of the pipe, and whose 0 point occurs at the open end of the pipe. In order understand why this is so, remember that the sine/cosine waves are mathematical representations of the relative pressure of the air column at each point along the clarinet bore. The pressure maximum occurs at the closed end and the pressure zero occurs at the open end. Makes perfect sense.
In the figures with the formulas you ask about, the author is superimposing the graph of each of the possible cosine standing wave solutions along the horizontal axis of the clarinet tube. You’ll notice that each graph has a maximum at the mouthpiece end and a 0 at the open end. Using the Greek lambda to represent the full wavelength of each standing wave, the author translates the graphics into a simple equation for how lambda relates to the effective length L of the tube. These standing waves together make up the harmonics of the sound; each is present in the final sound wave produced, although the strength decreases as lambda gets smaller.
The author uses the formula relating frequency to wave length (or, equivalently, L). The frequency of the longest standing wave, called the fundamental, is the pitch our ears perceive because it resonates much stronger than any of the other standing waves. In the far right hand formulas of this graph, the author relates the frequency of each standing wave to that of the fundamental. Note that the frequencies of all the harmonics’ standing wave solutions turn out to be precisely the odd multiples of the fundamental. This is unique to the clarinet amongst orchestral instruments and accounts for its characteristic sound.
As to the usefulness of L, observe how the frequency of the note produced is related to the effective length L of the pipe multiplied by 4. Comparing these formulas to similar ones for the flute, oboe or sax, you can now understand why a clarinet produces a note an octave deeper than the other instruments of the same length. This is because where the clarinet formula has 4L, the others have 2L. (In physics parlance, the 4L makes the clarinet a quarter-wave resonator, whereas the others are half-wave.) Thus the wavelength of the clarinet fundamental is twice as long and the corresponding frequency, or pitch, is only half as great. Since doubling of frequency is perceived by our ears as an octave, the clarinet sounds an octave lower.
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Author: Mark Charette
Date: 2003-09-02 15:32
Phat Cat wrote:
>The pressure wave starts at the point where the
> tip of the reed (nearly) closes the tip
Don't be scared  \
Sometimes completely closing the tip opening. The pictures exist ...
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Author: Phat Cat
Date: 2003-09-02 21:23
Mark is right. You can see the effect of the tip closing in the graphs (of the referenced article) regarding playing at different loudness levels. The right-most graph shows the clipping that happens when the read actually touches the mouthpiece tip and momentarily closes the air column during a ff note. The wave form changes drastically, effectively adding many higher frequencies to what was formerly a relatively pure sine wave fundamental. These (often non-harmonic) partials can give a thicker or "dirty" sound, as they do in the case of an amplifier or loudspeaker that clips.
Personally, I only play Mozart and never beyond mf, so my reed doesn’t actually touch the mouthpiece tip.![[tongue]](http://test.woodwind.org/clarinet/BBoard/smileys/smilie6.gif)
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Author: BobD
Date: 2003-09-03 15:41
The above exchange is a good example of the value of having a private tutor....vis a vis just trying to do it yourself.
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The Clarinet Pages
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