how does a guitar work

7/30/2019 How Does a Guitar Work

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How does a guitar work?

Contents

Something about sound The strings The body The air inside More detail and other links

First, something about sound

If you put your finger gently on a loudspeaker you will feel it vibrate - if it is playing a low note

loudly you can see it moving. When it moves forwards, it compresses the air next to it, which raises

its pressure. Some of this air flows outwards, compressing the next layer of air. The disturbance inthe air spreads out as a travelling sound wave. Ultimately this sound wave causes a very tiny

vibration in your eardrum - but that's another story.

At any point in the air near the source of sound, the molecules are moving backwards andforwards, and the air pressure varies up and down by very small amounts. The number of

vibrations per second is called the frequency which is measured in cycles per second orHertz (Hz). The pitch of a note is almost entirely determined by the frequency: high

frequency for high pitch and low for low. For example, 110 vibrations per second (110

Hz) is the frequency of vibration of the A string on a guitar. The A above that (second freton the G string) is 220 Hz. The next A (5th fret on the high E string) is 440 Hz, which is

the orchestral tuning A. (The guitar A string plays the A normally written at the bottom of

the bass clef. In guitar music, however, it is normally written an octave higher.) We can

hear sounds from about 15 Hz to 20 kHz (1 kHz = 1000 Hz). The lowest note on thestandard guitar is E at about 83 Hz, but a bass guitar can play down to 41 Hz. The

orginary guitar can play notes with fundamental frequencies above 1 kHz. Human earsare most sensitive to sounds between 1 and 4 kHz - about two to four octaves abovemiddle C. Although the fundamental frequency of the guitar notes do not usually go up

into this range, the instrument does output acoustic power in this range, in the higher

harmonics of the most of its notes. (For an introduction to harmonics, see Strings andstanding waves. To relate notes to frequencies, seeNotes and frequencies. )

The strings
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The pitch of a vibrating string depends on four things.The mass of the string:

more massive strings vibrate more slowly. On steel string guitars, the strings get

thicker from high to low. On classical guitars, the size change is complicated by achange in density: the low density nylon strings get thicker from the E to B to G; then

the higher density wire-wound nylon strings get thicker from D to A to E.

The frequency can also be changed by changing the tension in the string using thetuning pegs: tighter gives higher pitch. This is what what you do when you tune up. The frequency also depends on the length of the string that is free to vibrate. In

playing, you change this by holding the string firmly against the fingerboard with afinger of the left hand. Shortening the string (stopping it on a higher fret) gives higher

pitch. Finally there is the mode of vibration, which is a whole interesting topic on its

own. For more about strings and harmonics, see Strings and standing waves.The strings themselves make hardly any noise: they are thin and slip easily through the

air without making much of disturbance - and a sound wave is a disturbance of the air. An

electric guitar played without an amplifier makes little noise, and an acoustic guitar

would be much quieter without the vibrations of its bridge and body. In an acoustic guitar,the vibration of the string is transferred via the bridge and saddle to the top plate body of

the guitar.

The body

The body serves to transmit the vibration of the bridge into vibration of the air around it.

For this it needs a relatively large surface area so that it can push a reasonable amount of

air backwards and forwards. The top plate is made so that it can vibrate up and downrelatively easily. It is usually made of spruce or another light, springy wood, about 2.5

mm thick. On the inside of the plate is a series of braces. These strengthen the plate. Animportant function is to keep the plate flat, despite the action of the strings which tends to

make the saddle rotate. The braces also affect the way in which the top plate vibrates. Formore information about vibrations in the top plate and in the body, see the links below.

The back plate is much less important acoustically for most frequencies, partly because it

is held against the player's body. The sides of the guitar do not vibrate much in thedirection perpendicular to their surface, and so do not radiate much sound.It is worth

making it clear that the body doesn't amplify the sound in the technical sense of amplify.

An electronic amplifier takes a signal with small power and, using electrical power fromthe mains, turns it into a more powerful signal. In an acoustic guitar, all of the sound

energy that is produced by the body originally comes from energy put into the string by

the guitarists finger. The purpose of the body is to make that conversion process more

efficient. In an electric guitar, very little of the energy of the plucked string is convertedto sound.

The air inside

The air inside the body is quite important, especially for the low range on the instrument.
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It can vibrate a little like the air in a bottle when you blow across the top. In fact if you

sing a note somewhere between F#2 and A2 (it depends on the guitar) while holding your

ear close to the sound hole, you will hear the air in the body resonating. This is called theHelmholtz resonance and is introduced below. Another way to hear the effect of this

resonance is to play the open A string and, while it is sounding, move a piece of

cardboard or paper back and forth across the soundhole. This stops the resonance (orshifts it to a lower frequency) and you will notice the loss of bass response when you

close up the hole. The air inside is also coupled effectively to the lowest resonance of the

top plate. Together they give a strong resonance at about an octave above the main airresonance. The air also couples the motion of the top and back plates to some extent.The

Helmholtz resonance of a guitar is due to the air at the soundhole oscillating, driven by

the springiness of the air inside the body. I expect that everyone has blown across the top

of a bottle and enjoyed the surprisingly low pitched note that results. This lowest guitarresonance is similar. Air is springy: when you compress it, its pressure increases.

Consider a 'lump' of air at the soundhole. If this moves into the body a small distance, it

compresses the internal air. That pressure now drives the 'lump' of air out but, when it

gets to its original position, its momentum takes it on outside the body a small distance.This rarifies the air inside the body, which then sucks the 'lump' of air back in. It can thus

vibrate like a mass on a spring. In practice, it is not just the compression of the air in thebody, but also the distension of the body itself which generates the higher pressure. This

is analysed quantitatively in Helmholtz Resonance.

More detail and other links

Anatomy of a Steel-String Acoustic GuitarThere are presently three basic types of guitar:

The nylon acoustic (Classical and Flamenco), the steel-string acoustic (folk) and theelectric.

The raw acoustics of the electric guitar aren't quite as interesting as the acoustic guitars(although you may be interested in Dan Russell's work); the body is essentially a good-

looking hunk of wood to counterbalance the weight of the neck and to keep the strings

vibrating a longer time. (Although excellent for rock 'n' roll, lead playing, or burningand inserting into your amplifier.)

Acoustic guitars produce sound due to a rather complicated interaction (or

"coupling") between the various components of the instrument. (See

Resonant Guitar Modes.) From here on, the word 'guitar' will exclusively refer tothe acoustic guitars only.

Anatomy of a Steel-String Acoustic Guitar

(Image reproduced courtesy of

Gilet Guitars)

Note that guitar terminology isby no means fixed or
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completely standardised---The soundboard is often called the 'top-plate', and the sides

are often called the 'ribs', for instance.

Nylon guitars usually have rather rounded bodies and the neck joins the body at half

the effective string length (12th fret). The finger board is relatively wide (about 60mm

at the body) and the top three strings (highest pitch) are made of nylon and the lowerthree are generally composite (silver-plated copper wire wrapped around a silk fibre

core).

The steel-string guitar family tends to have a little more geometric variation than the

nylon guitars. Most models have the neck join the body at the 14th fret, to increase the

fingerboard's effective length. The strings are usually either steel alloy or bronze.

An example of a classical. An example of a OOO ("Triple-O") steel-string.

Examples of: a Dreadnaught. The OO ("Double-O"), or the Jumbo.

Acoustically Important Construction FeaturesThree main features:

1 Coupling

2 Material Composition

3 Plate Bracing4 Coupling

'Coupling' simply refers to an interaction between two or more vibrating elements.

First of all, on a guitar, the string is excited (plucked or picked) by your fingers,vibrating the bridge, which then goes on to vibrate the soundboard and the

internal air cavity, then the back and sides and so on. If these these elements

interact well, the whole system is said to be strongly coupled.The body of the guitar acts so that the high pressure vibrations at the bridge are

turned into low pressure vibrations of the surrounding air. This is a form of

"impedance matching", in much the same way an electrical transformer raises orlowers a potential difference and is the main principle behind speaker cone design.

The higher frequency (pitch) sounds are produced by string interaction with thebridge and then the sound board, whereas the lower frequencies are essentially

driven by the internal air cavity/sound hole and ribs/back coupling effects:The interaction looks roughly like this:

(Low Frequencies)
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(High Frequencies)

Schematic of Frequency-dependent Component Oscillations.Arrows show maindirection of vibratory interaction. Note that some of these influences act in both

directions as mechanical feedback, eg. Bridge vibration affects the string's motion

as a secondary influence.Coupling between parts depends on geometry, sound frequency and the materials

used.

Interaction strengths between various components need to be optimised accordingto taste; a certain amount is needed to radiate the sound transferred from the

string's vibration, but too much coupling produces some harsh and very ugly

tones*.Coupling can be, and is to an extent, controlled during construction; luthiers often

make use ofChladni patterndiagnosis to check the main resonance symmetries oftheir instrument and make any necessary changes.Apart from being sensitively dependent on materials and bracing (see below)

various other factors also influence coupling strengths, such as purfling andbinding (how the sides and top/back plates are connected), bridge type and

placement, right down to what sort of adhesive was used during manufacture.

5 The soundhole is designed so that the body acts as a Helmholtz resonator,(tuned roughly to A2 (55.0 Hz) for steel-strings, G#2 (103.8 Hz) for classical

and between F#2 and G2 (92.5-98.0 Hz) for Flamenco guitars.)

6 Material Composition

The materials from which a guitar is constructed have very direct consequences

on its acoustic qualities. Because the traditional material used is wood--- oftenrare hardwoods and cut from as close to the centre as possible---there are

certain economic and conservation issues that would be partly addressed if a

more readily obtained and controllable medium were to have the requiredacoustic properties. Much work has been done on testing the various acoustic

properties of materials that comprise the guitar. Investigations have beencarried out using synthesised materials such as fibreglass, carbon fibre and

various polymers, in attempts to imitate/replace existing woods. The generalrationale was to produce materials with much less variation and at less cost

than traditional woods, but so far the results have not been promising:

1 The attempts studied tended to have as much acoustic variation as

traditional woods; and

2 Still didn't have the stiffness-to-mass ratio, elastic moduli, damping,

or longitudinal to lateral grain properties required to compete withtraditional timbers.

7 Despite this, synthetic materials are used successfully in complementing

traditional materials (such as carbon-fibre strut reinforcement on somesoundboards), but it appears a pure synthetic that has a good sound and yet
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feels good to play is still some time away. It should also be mentioned thataesthetic considerations also play a large part in purchasing a guitar---even if

an instrument sounds good, it won't be very popular if it looks like a politician!

8 Plate Bracing

Unlike many other

stringed

instruments (suchas the violin family)

the guitar has abraced sound board

and back plate.This is primarily

due to the central

position of thebridge and saddle

and the largesurface area of the

soundboard andback, combined

with their relativethinness and

having no soundpost.The guitar requires additional structural support. The modern, conventional,

'fan-bracing' was originally developed by the famous luthier Antonio de TorresJuan (1817-1892). A recent major development in soundboard bracing was

made by Australian luthier, Greg Smallman. The structure utilises a 'criss-cross'lattice bracing composed of carbon fibre/epoxy and balsa braces, tapering in

height radially outwards from underneath the bridge saddle. Dr Michael Kashahas experimented with various asymmetric bracing geometries.The bracing is

acoustically critical: varying bracing techniques will alter the stiffness-to-massratios and elastic moduli tremendously, thereby affecting how the guitar

radiates sound.

Some examples of guitar bracing geometries**

Some of the designs above may seem a little archaic or bizarre, but they weregenerally devised with a specific purpose. One problem encountered with

guitars is that, with a symmetric bracing pattern, at a certain frequency, a node(position where vibration is a minimum) may be produced right on the point

where the string that created the note is positioned, meaning that you can playthe particular note on that string really quite hard, yet the sound created will

have a fairly low intensity---this can often occur in the 'tripole' mode of theguitar. To counteract this effect, bracing patterns may be offset, so that the

resonance modes are slightly asymmetric.

*Such as the 'wolf' note in the cello. A great explanation for this can be found inMcIntyre, M. E. & Woodhouse, J., "The Acoustics of Stringed Musical Instruments",

Interdisciplinary Science Reviews, 3 pp.157-173, 1978 J.W. Arrowsmith, Ltd.

**after Fletcher, N. and Rossing, T. "The Physics of Musical Instruments" (2nd ed.)1998, Springer-Verlag New York Inc.

Acoustic Concepts/Measurement Technique"Pythagoras was first guided to the notion that mathematics held a key to understanding
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nature by observations of the relation between musical intervals and natural numbers"*

1 Acoustic Radiation Patterns

2 Spectral Responses3 Time Domain/Envelope

A very large range of acoustical concepts can be derived that have the same form as those

in electronics or general mechanics, such as impedance (and resistance), conductivity,capacitance and radiation.

We can construct acoustic mechanical models (eg. using simple springs as acoustic

resonators) and acoustical 'circuits' (eg. using resistors to represent acoustic impedance,

AC power sources for an applied oscillatory sound ('tone').)

For example, here are equivalent mechanical and electrical schemes for a binary

oscillator model of top-plate/air cavity coupling for the guitar (assuming a rigid back andsides):

Sketch of mechanically and electrically equivalent systems. Left: Two-Mass Analogue.

Right: Electrical Circuit Analogue.**

The science of acoustics may not be able to answer all of the musical questions asked, butit certainly plays a vital role in objectifying quantities such as frequency, sound intensity,

gain, sustain etc., as they are produced by various instruments and techniques of playing.

For the guitar specifically, we can examine three acoustical qualities:4 Acoustic Radiation Patterns

Acoustic radiation patterns are formed due to the way the guitar vibrates in its various

resonant modes. The patterns are just a map of how the sound intensity varies withthe angle and distance from the instrument.

The total sound intensity at your ear at is not only dependent upon the frequency(pitch) the guitar is played at, but at what distance and angle your ear is to theinstrument.

Guitar radiation patterns tend to be anisotropic - how loud the instrument is depends

on what angle your ear is to the instrument. For example, an "A3" note (110 Hz,typically close to a steel-string's monopole air resonance) may not sound much louder

at various angles from the guitar (keeping the same distance!), but a "B4" (247 Hz,

close to a standard steel-string's top-plate dipole resonance) you may find that you
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hear a noticeably different sound intensity at various angles. Try it out!

{Sketch of angular dependence on intensity}

Sketch of angular dependence of sound intensity, guitar in dipole mode

The complicated patterns formed in space due to the various modes of the guitar is

one of the reasons it is so hard to capture that 'live' sound on recordings. A lot of

people like listening to 'live' music because of the complex change in sounds as youmove around.

Spectral Response

A sound spectrum is a plot of how the intensity of a particular sound varies with

frequency. A useful way of looking at a sound produced by an instrument is to examine

its spectral response.

A typical way to measure an instrument's spectral response is to excite the instrumentwith some sort of mechano-acoustic oscillator, such as:

o A speaker attached directly; oro A solenoid (electromagnet) magnetically influencing a rare-earth magnet

attached to the instrument.

Diagram of various apparatus used to measure spectral response. Left: Speaker-drivensystem. Right: Solenoid-driven system.

The oscillator is connected to a function generator (usually connected to a computer)which 'scans' over a frequency range. A transducer such as a microphone converts the

resulting output signal into an electrical one, at a fixed point; a spectrum can then be

plotted.The spectral response can tell a lot about a particular instrument, showing

characteristics, including the main resonances and how sharp they are.A flat response represents an equal intensity of sound produced at every frequency, yet a

guitar generally has a series of peaks and valleys:
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5

Comparison of two spectral responses. Left: Flat response (even weight over the tonal

range). Right: Typical response from musical instrument.

It actually turns out that most people seem to prefer a varied, rather than flat,

response. The interesting shapes in a response curve are sometimes called features

and our mind is very good at recognising features - perhaps most people's minds

prefer the complexity of spectral features inherent to most traditional instruments,rather than the simpler 'pure' tones characterised by a flat response.

6 Intermediate Timescale Phenomena

Intermediate timescale phenomena refer to acoustic events noticeable on a moremoderate timescale (of the order of 10ms or less). In a way, this really applies mostly

to envelope effects.

*"The Acoustics of Stringed Musical Instruments", M.E. McIntyre & J. Woodhouse.Interdisciplinary Science Reviews, 3, pp.157-173 (1978)

**from Fletcher, N. and Rossing, T. "The Physics of Musical Instruments" (2nd ed.)

1998, Springer-Verlag New York Inc.*** "Comparison between Experimental and Predicted Radiation of a Guitar", A. LePichon, S. Berge & A. Chaigne. Acta Acustica 84, pp.136-145 (1998)

***"Radiation from the Lower Guitar Modes" G. Caldersmith. American Lutherie, 2,

pp.20-24 (1985)

The Virtual Guitar

The Virtual Guitar is a finite element model, created using the software system CATIA

V5. This modelling tool is used to describe the geometry and the distribution of theinternal braces and to analyse the vibration of the structure of an acoustic guitar. The

guitar modelled is the OOO modelproduced by Gilet Guitars in Sydney, which is one of

the laborotory's industrial supporters.
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In the left image, the top plate has been rendered transparent to show the internal

bracing, and in the right image the bottom plate has been rendered transparent.

Vibration Analysis

This image shows the (0,0) mode for a free guitar. The amplitude is exaggerated so thatit can be seen and the maximum amplitudes are colour coded. All positions are given
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with respect to the resting positions of the strings, which is why the strings seem to

remain stationary in the image. The strings are modelled with their measured stiffness,

the wood is modelled using measured values of the elastic moduli.In the images below, several approximations are made, so these should be considered

as qualitative behaviour only. (For more information about the naming of modes, see

Chladni patterns.)Free guitar, (0,0) mode

Free guitar, (0,1) mode

Played guitars are not free--no-one has taken a guitar to the space station yet! Clampingthe back plate is an approximation of what happens when the instrument is held against

the player's body.

Back plate clamped, (0,0) mode

Back plate clamped, (1,0) modeBack plate clamped, (0,1) mode

This is the work ofMatthieu Maziere, Davy Laille, andDavid Vernet. They were all

visiting students who did this work as a practicum project at UNSW.

Back to Guitar Acoustics

Chladni patterns for guitar plates

Chladni patterns show the geometry of the different types of vibration of the guitar top plate. This

site has an introductory explanation of modes of vibration and a library of photographs of the

Chladni patterns of a guitar top plate and an intact guitar.

The results reported on this site are part of a practicum project by Thomas Erndl a visiting student

from Fachhochschule Regensburg, Germany.

Modes of vibration

(See also the explanations ofthe guitar, and Strings, harmonics and standing waves.) A modeof vibration is just a way of vibration. Think what happens when you strike a xylophone bar in the

middle and set it vibrating. The bar is supported at two points towards the ends. The simplest mode

of vibration is this: when the middle of the bar goes up (as shown by the solid lines in the figure)

the ends of the bar go down. When the middle goes down (dashed lines), the ends go up. The two

points that do not move are called nodes and are marked N in the diagram. (If "modes" and "nodes"

sound confusing, remember that the node has no motion.)

Sketch of a simple mode of

vibration.

This first mode of the xylophone

bar is rather similar to a mode of vibration of a simple rectangular plate which is called the (0,2)

mode (the naming convention is explained below.)

Photographs of the Chladni pattern of:

mode (0,2) of a uniform rectangular aluminium plate.
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In this pictures, the lines are formed

from sand that has collected at the

nodes, but has been shaken off the

moving regions. The top plate of a

guitar is more complicated in shape,

and so the nodes also have a morecomplicated shape. White sand was

used for the black-painted aluminium

plate, and black sand for the guitar top

plate.

Why are there nodes?

The supports of the xylophone bar do not cause the nodes, rather they are placed at the positions

which are nodes so as to facilitate this vibration. In an object which is not firmly clampled, a

vibration cannot easily move the centre of mass of the object. It follows that, if some part is going

up, another part is going down. In the simple motion at resonance, the point(s) that divide(s) these

regions are nodes. When a violin or an isolated part is vibrating, the centre of mass doesn't move

much, so once again it can be divided into parts that are going up and others that are going down. In

these simple modes of vibration, the motion of different parts is either exactly in phase or exactly

out of phase, and the two regions are separated by nodes. The nodes are points for a quasi one-

dimensional object like a string, or lines for a quasi two-dimensional object like a plate. (There is

more explanation inStrings, harmonics and standing waves.)

Modes of guitar plates

One of the modes is comparable with

a mode of vibration of a rectangular

plate. In this mode the nodal lines

separate the plate in three parts, so it

can be compared with the (0,2) mode

of the rectangular plate, with the

middle part moving 180 out-of-phase

with the ends.

The modes for the guitar plate are

complicated by the presence of the

sound hole and the bracing.

More guitar Chladni patterns.

How are Chladni patterns formed?

There are at least three different methods. The plate can be made to resonate by a powerful sound wave which is tuned to the

frequency of the desired mode.

The plate can be bowed with a violin bow. This is easiest if one choses a point that is a

node for most of the modes that one doesn't want, but not for the desired node.

The plate can be excited mechanically or electromechanically at the frequency of the

desired mode.
http://www.phys.unsw.edu.au/jw/strings.htmlhttp://www.phys.unsw.edu.au/music/guitar/patterns.htmlhttp://www.phys.unsw.edu.au/jw/strings.htmlhttp://www.phys.unsw.edu.au/music/guitar/patterns.html


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For the photographs on this site, a small (4g) magnet was fixed to the bridge. An oscillating

magnetic field (provided by a coil connected to an audio amplifier and a signal generator) was used

to provide an oscillating force whose frequency is tuned to the resonance of the mode. Experiments

using different masses showed that the mass of the magnets caused us to underestimate the

frequency by about 10 Hertz in some cases. But there were also patterns obtained with a magnet

which could not be obtained without a magnet (e.g. by a speaker). That means, that the vibrating

system has changed qualitatively by adding the magnet to the plate.In all cases, some finely divided material is placed on the plate. The material used here is fine sand.

When the plate resonates, the motion becomes large over most of the surface and this causes the

sand to bounce and to move about. Only at or near the node is the sand stationary. Thus the sand is

either bounced off the plate or else collects at the nodes, as shown in the photographs.

Why are Chladni patterns useful?

The adjustment of the top plate is important to the properties of the final instrument. The most

important adjustments are thinning the wood towards the edge of the plate, and thinning the braces.

Chladni patterns provide some feedback to the maker during the process of adjusting the plate to its

final shape. Symmetrical plates give symmetrical patterns; asymmetrical ones in general do not.

It is very difficult to relate the frequencies of the modes of the isolated top plate to those of the

modes of a finished guitar. Fortunately, adjustments can be made to an intact instrument: thinning

the top plate close to the edge, and adjusting the bracing by reaching through the soundhole with

specially shaped tools. The "tuning" of plate resonances is less formalised in guitar making than in

violin making. Over the centuries, violin makers have discovered empirical relations between the

modes of free plates and the properties of the finished instrument. Many scientists have been

interested in the acoustics of violins, and many violin makers have been interested in science, so a

lot has been written about the acoustical properties of violins and their parts. See:

"Research Papers in Violin Acoustics", CM Hutchings and V Benade, eds, Ac.Soc.Am.

1996

"The acoustics of violin plates" by Hutchins, C.M. Scientific American, Oct.1981, 170-176.

"Experiments with free violin plates" by Jansson, E.V., Moral, J.A. and Niewczyk, J. J.

CAS Journal Vol 1 No 4 (Series II) 1988.

"The Physics of Musical Instruments" by Fletcher, N.H. & Rossing,T.D. Springer-Verlag,

New York, 1991.

Mode Tuning for the Violin Makerby Carleen M. Hutchins and Duane Voskuil CASJournal Vol. 2, No. 4 (Series II), Nov. 1993, pp. 5 - 9

The Catgut Acoustical Society home page
http://www.marymt.edu/~cas/research/articles/modetune/http://www.marymt.edu/~cas/http://www.marymt.edu/~cas/research/articles/modetune/http://www.marymt.edu/~cas/

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