Klarinet Archive - Posting 000194.txt from 2010/08

From: Jennifer Jones <helen.jennifer@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Tue, 17 Aug 2010 04:17:56 -0400

I am still thinking about the wave patterns within clarinets.

On Sun, Aug 15, 2010 at 4:35 AM, Diego Casadei <casadei.diego@-----.com> wr=
ote:
> Tony Pay wrote:
>>
>> I think I see where the 8cm problem is. =A0Diego has made the assumption=
that the 'speed of sound' in the clarinet tube is the same as the speed of=
sound in open air.
>> But we know that that speed can vary according to other parameters
>
> This is indeed interesting. =A0However, the only explicit statments about
> the sound speed in air which I've found can be summarized this way:
> 1) the temperature is the most important parameter
> 2) in air, the humidity plays some minor role
> 3) no dependence on pressure (obviously: the sound waves are the
> perturbations of the pressure and they do not depend on the average
> value, unless the density is also affected)

The speed of sound is higher at higher air pressures. c=3D(adiabatic
index*pressure/density)^(1/2). At high pressures, there are more
molecules per unit volume. The speed of sound is higher in deep water
(http://en.wikipedia.org/wiki/Speed_of_sound), where pressures are
very high. The pressure in the clarinet must vary along its length
with a high pressure in the mouthpiece and the lowest at the bell.
So, I would expect there to be variation in the speed of sound from
the mouthpiece to the bell. Keith mentioned a change in the speed of
sound at the end of the bell.

> I made my measurement without warmup, to be sure that the temperature
> was the same as for the room, which I was able to measure within 0.1 C.
> =A0Humidity inside the clarinet is by necessity higher, but it should be
> really a very small correction, which compared to the precision of my
> measurement is completely negligible.
>
> (Needless to say, I did not insert anything inside my clarinet during
> the test.)
>
>
>
>
> Jennifer Jones wrote:
>>
>>> On section 6.1 the plane acoustic waves in air are treated and it is
>>> shown that the variations in pressure and particle velocity are in
>>> phase. =A0Plane waves are a good approximation for any real acoustic wa=
ve
>>> in a homogeneous medium far away from the source (more precisely, at
>>> distances of many wavelengths or greater). =A0However, this approximati=
on
>>> is not valid inside a clarinet.
>>
>> This seems odd to me. =A0The reed is vibrating and driving vibrations of
>> the air column within the clarinet. =A0So I would think that the
>> vibrations within the clarinet would be like a section of a spherical
>> wave and essentially behave like a planar wave. =A0Why is this not a
>> valid approximation?
>
> Section is 6.1 is about parallel waves in an infinite medium. =A0This
> means that all fronts are parallel planes orthogonal to the direction of
> propagation and that there are no edge effects because the boundaries
> are at infinity. =A0Quite significantly different from the inner bore of a
> clarinet, I would say.

OOPS. Yes. There is interaction with the walls of the bore, tone
holes, register tubes as well as with reflected waves.

> Note that inside a cavity there are many more possible modes than
> parallel waves (which anyway are still there). =A0The include rotation
> modes in addition to purely oscillatory modes. =A0Depending on the
> frequency and the cavity parameters, only a few modes can propagate for
> decent distances: the other are local effects which are dumped in a
> short distance.

Interference results in a pattern much more complex than the parallel
planar waves. Like the wave pattern in the bore is much more complex
than the simple diagram of one node at the mouthpiece and an antinode
at the bell. One particular we have discussed is the node placed 8 cm
from the mouthpiece...

I take it the oscillatory modes are the waves generated by the
vibrating reed? Why would those be any more oscillatory than the
waves themselves. All the modes should be oscillatory, because they
are composed of waves. What are the rotational modes?

So, we have local variations in pressure (sound waves); standing
waves, a result of the constructive and destructive interference of
the sound waves and an overall pressure gradient that follows the
direction of air flow, with high pressure in the mouthpiece and lowest
pressure at the end of the bell. In particular, the highest pressure
is relatively localized in the tapered region of the mouthpiece and
serves as a barrier of sorts that acts as the closed end of the tube,
a pressure wall that sounds waves refract through and reflect off of.
This wall would be formed by a node, where destructive interference
creates an absolute minimum in dP/dt (it has to be an absolute minimum
because it is acting as the closed end of the tube, if there were any
lower dP/dt nodes, they would act as stronger barriers). Do nodes
occur at the levels of open tone holes such that they favor reflection
of higher frequency waves?

> I don't know the exact details, but my guess that the situation is
> different from plane waves in an open space should not be completely
> wrong :-)
>
>
>> I am thinking of antinodes as locations of relative high pressure
>> (force per unit area and number of air molecules per unit volume)
>> within the clarinet.

>> I am thinking of nodes as locations of low
>> pressure (equal to atmospheric pressure).

OOPS. That is not correct and it is not how I've been thinking. The
image I use is a gradient in pressure high in the mouth, lower in the
mouthpiece decreasing to the bell and then atmosphere outside. This
is a result of the air blown from the mouth into the tube, which
escapes through the tone holes and bell and represents the mass
transit of air molecules. As wind in earth's atmosphere is driven by
variations in atmospheric pressure, so should mass transport of air in
the clarinet be driven.

Superimposed on that is the sound waves which reflect on the walls and
interfere with one another to produce nodes and regions of maximal
variation in pressure.

>
> Please make sure you think in terms of fluctuations dP sperimposed to an
> average pressure P. =A0Acoustics in air is all about the evolution of the
> dP term. =A0Unfortunately, people simply omit to write dP+P everywhere and
> simplifies the notation with dP -> P (which may be difficult to
> interpret correctly) when writing equations. =A0Even more confusingly, the
> often obtain expressions containing P and implicitly assume that such
> symbol means "the root-mean-square measurement of the fluctuation dP on
> top of the average pressure value P". =A0Quite easy to get lost!

Well, then what is dP? I guess it would have to be dP/dt. This is
starting to feel like my calculus class.

If P is a sine function of t, then dP/dt is cosine t.

>> What is meant by maximal pressure variations?
>
> The amplitude of the variations of dP is locally maximal in that position.
>
>
>
>> (...) since several sources
>> indicate that the reed is a point of maximal variation in pressure, my
>> impression is that there must be some variation in the central
>> tendency (overall pressure).

OOOOH. I don't think this follows at all... dP/dt is incidental; we
have to adjust our embouchure and air speed to make reed vibrate as we
send air past it. There can be air flow without reed vibration. Can
there be reed vibration without air flow?

> The reed is the generator of the sound, which is the source from which
> all the power of the wave comes from. =A0For this reason, it must
> correspond to the absolute maximum of the amplitude. =A0Again, we are
> speaking about the amplitude of the small variations dP superimposed
> with the constant pressure field P, which is the same everywhere (the
> clarinet is open).

What happens in the case of resonance or constructive interference?
When there is constructive interference, don't regions of
"supramaximal" variation in pressure occur? Regions that may have a
larger amplitude of variation, above that directly driven by the reed
itself?

It seems that would be required, since the instrument amplifies the
sound... Maybe the instrument does not amplify the sound, my
mouthpiece played alone is rather loud and comparable to the volume of
altissimo notes... Is that the case for a trumpet? That the sound
made from the mouthpiece has a lower volume than the sound made when
attached to the trumpet itself. I don't have a trumpet here to check.

>> When it is says that there is an antinode at the reed, it seems that
>> there should be a high pressure point there (because of the
>> displacement of the node 8 cm away from there, into the barrel as
>> Diego pointed out). =A0Is this pressure linked to the pitch played?
>
> The reed is _not_ a point of high pressure. =A0The pressure is the same as
> in the room. =A0The oscillating reed is the source of the _perturbations_
> of the pressure. =A0It is the amplitude of such perturbations which is
> maximum.

How can the top of the mouthpiece not be a relative high pressure
point. There is mass transfer of air molecules out of the mouth into
the mouthpiece. Those molecules have to go somewhere. So there
should be some pressure gradient through the instrument from the
mouthpiece to the bell... How big the gradient is, I don't know and
whether it falls to atmospheric interior to the bell, I am not sure,
though the sources I have encountered indicate that the pressure
inside the bell is higher than the pressure outside the bell, as has
Keith.

I would count the mouthpiece as a relative high pressure point with
large, if not maximal variations in pressure.

>> Perhaps the pressure is highest when 8 cm corresponds to 1/4
>> wavelength of the note being played.
>
> If you were speaking about a generic point, I would also guess so. =A0But
> you are speaking about the source hence I guess that the pressure
> _variations_ do not depend on the frequency.

I guess pressure variations shouldn't depend on frequency because they
*are* the frequency.

This 8 cm correspondence to 1/4 wavelength probably does not work
because of the tapered portion of the mouthpiece does not act
cylindrically.

> Well, at least not very
> directly. =A0Indeed the player has a different feeling for different
> notes, hence she needs to adapt to the response of the instrument.
> Assuming that the player can provide the same power for two different
> purely sinusoidal waves, than their amplitudes must be equal. =A0But of
> course a real sound is the superposition of many waves, each with its
> own amplitude, hence I don't know the answer :-)

Hence, the player is providing the power for the sinusoidal wave of
the principle pitch and all the sinusoidal waves of the overtones,
which may be generated by the interference patterns within the
instrument.

>> I'll try to figure out what note the 8 cm would serve as a quarter
>> wavelength for. =A0The first conclusion I come to is that it is the note
>> played by the mouthpiece alone.
>
> Not at all. =A0You need at least to add the barrel, because it depends
> also on the pipe. =A0But it could be that the barrel is not long enough
> for this exercise. =A0Please try
>
>
>> why we open the right hand pinky d'#/G# key for the
>> altissimo notes?
>
> The mechanism is similar to what happens when opening the register hole.
> =A0You put a constraint on the modes which can resonate in the
> instrument. =A0Opening the correct hole destroys the correct lower
> harmonics, so that only the higher ones can survive. =A0What you play is
> the lowest possible harmonic compatible with all perturbations induced
> by the open holes.

Is this linked at all with resonance fingerings such as one for throat g:
oox|xxo

>> That there is a high pressure point at the reed is a bit
>> counterintuitive to me
>
> More than counterintuitive: it's wrong. =A0Tha maximum refers to the
> amplitude of the small perturbations dP of the pressure.

It should be a maximum amplitude of small perturbations superimposed
on top of a high pressure point (because there is movement of air,
there has to be some sort of pressure gradient). What I was thinking
of as counterintuitive is no longer so, because the space in the
mouthpiece should have a lower pressure than the mouth and a higher
pressure than the space further down the bore of the clarinet.

>> because when we blow into the clarinet, we are
>> expressing high pressure air from inside our mouths into the tube of
>> the clarinet.
>
> Yes and no. =A0What we feel is a constant pressure, i.e. a constant
> resistance from the tube. =A0But this is because we can't follow the
> oscillations.

Right, it is oscillations in pressure superimposed on a high pressure
in the vocal tract.

> What really happens is that we create an overpressure
> when the reed is open. =A0The sequence of pressure "bursts" is the source
> of the sound
>
>
>
>> I do not understand impedance.
>
> Me neither :-P
>
>> From what I learned in the past,
>> impedance is resistance for alternating current. =A0I see that acoustic
>> impedance is sound pressure divided by (particle velocity times
>> surface area) or acoustic pressure over acoustic volume flow (1, 2).
>> It is a measure of resistance to transmission of sound. =A0I see that it
>> dampens the frequency of the oscillations. =A0It determines which
>> note(s) can be played with a given fingering (3).
>
> There is a close parallelism between acoustics and circuits. =A0As for the
> oscillating circuits, you need to work on the complex plane and use the
> complex quantity "impedance", whose real part is the resistance which
> everybody knows. =A0But there is also the immaginary part there... =A0I'll
> let other people to proceed along this route and comment on the rest of
> your message :-)
>
>
>
> Peter Gentry wrote:
>>
>> One aspect not discussed here so far is the frequency response of the re=
ed.
>> We all know that hardness and therefore stiffness affects the quality of=
the
>> sound (from squeaks to buzzes) but not much the intonation.
>
> Correct. =A0The reed has also its own permitted spectrum of oscillations
> and cannot do miracles. =A0Likely, good reeds allow us to get a
> satisfactory timber out of the instrument, which means that we can get
> the desired distribution of power across all harmonics emitted by the ree=
d.
>
>
>> Does this mean
>> that the reed is simply a means of injecting energy via pressure
>> fluctuations into the body of the instrument.
>
> Yes. =A0But it act as a valve: the player is actually the source of the p=
ower.

The player provides the power by deforming such that the reed vibrates
when air is forced past it.

>> The dynamic result depending
>> on the shape of the cylinder and its venting.
>
> No. =A0Dynamics is about the total power of the sound. =A0Being related to
> the power, it is related to the source. =A0[Of course there is an
> interplay between the vibrating reed and the rest of the instrument (as
> with the player).]

What is a dynamic result; volume (e.g. forte, mezzoforte, pianissimo etc.)?

Or is the dynamic result the variation in pitch?

-Jennifer
_______________________________________________
Klarinet mailing list
Klarinet@-----.com
To do darn near anything to your subscription, go to:
http://klarinet-list.serve-music.com