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A Acústica do Violão


Julian J. Ludwig

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Recentimente estavamos discutindo o amadurecimento do violão e esses aspectos.

No outro fórum o Geraldo mandou um link muito interessante falando sobre a acustica do violão.

Legal ver o desenho das freqüências no tampo!

Acho que o Luthiers iriam gostar de ler, então estou mandando aqui.

Fonte: http://www.phys.unsw.edu.au/music/guitar/

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How does a guitar work?



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 in the 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.

travelling.gif

At any point in the air near the source of sound, the molecules are moving backwards and forwards, 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 or Hertz (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 fret on 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 the standard 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 ears are most sensitive to sounds between 1 and 4 kHz - about two to four octaves above middle 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 and standing waves. To relate notes to frequencies, see Notes and frequencies. )


The strings

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 a change 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 the tuning 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 a finger 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 down relatively 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. An important 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. For more 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 the direction 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 from the 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 converted to sound.

The air inside

The air inside the body is quite important, especially for the low range on the instrument. 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 the Helmholtz 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 (or shifts 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 air resonance. 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 guitar resonance 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 the body, 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
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Anatomy of a Steel-String Acoustic Guitar



There are presently three basic types of guitar:

The nylon acoustic (Classical and Flamenco), the steel-string acoustic (folk) and the electric. 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 burning and 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 to the acoustic guitars only.

Anatomy of a Steel-String Acoustic Guitar


guitar_anatomy.jpg
(Image reproduced courtesy of Gilet Guitars)
Note that guitar terminology is by no means fixed or 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 lower three 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.
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Acoustically Important Construction Features



  1. 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 or lowers a potential difference and is the main principle behind speaker cone design.

    The higher frequency (pitch) sounds are produced by string interaction with the bridge 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:

    guitarlowf.GIF
    (Low Frequencies)

    guitarhighf.GIF

    (High Frequencies)

    Schematic of Frequency-dependent Component Oscillations. Arrows show main direction 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 according to 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 of
    Chladni pattern diagnosis to check the main resonance symmetries of their 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 and binding (how the sides and top/back plates are connected), bridge type and placement, right down to what sort of adhesive was used during manufacture.

    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.)

  2. 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--- often rare 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 required acoustic properties. Much work has been done on testing the various acoustic properties of materials that comprise the guitar. Investigations have been carried out using synthesised materials such as fibreglass, carbon fibre and various polymers, in attempts to imitate/replace existing woods. The general rationale 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 with traditional timbers.
    Despite this, synthetic materials are used successfully in complementing traditional materials (such as carbon-fibre strut reinforcement on some soundboards), but it appears a pure synthetic that has a good sound and yet feels good to play is still some time away. It should also be mentioned that aesthetic 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!



  3. Plate Bracing

    Unlike many other stringed instruments (such as the violin family) the guitar has a braced sound board and back plate. This is primarily due to the central position of the bridge and saddle and the large surface area of the soundboard and back, combined with their relative thinness and having no soundpost.
    The guitar requires additional structural support. The modern, conventional, 'fan-bracing' was originally developed by the famous luthier Antonio de Torres Juan (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 Kasha has experimented with various asymmetric bracing geometries.The bracing is acoustically critical: varying bracing techniques will alter the stiffness-to-mass ratios and elastic moduli tremendously, thereby affecting how the guitar radiates sound.
    bracing1.jpgbracing2.jpgbracing3.jpgbracing4.jpgbracing5.jpg
    Some examples of guitar bracing geometries
    **

    Some of the designs above may seem a little archaic or bizarre, but they were generally 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 play the 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 the guitar. 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 in McIntyre, 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.

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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 the internal braces and to analyse the vibration of the structure of an acoustic guitar. The guitar modelled is the OOO model Gilet Guitars in Sydney, which is one of the laborotory's industrial supporters. produced by

wtp2small.jpgtp2small.jpg

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 that it can be seen and the maximum amplitudes are colour coded. All positions are given 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.)


Played guitars are not free--no-one has taken a guitar to the space station yet! Clamping the 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) mode
Back plate clamped, (0,1) mode


This is the work of Matthieu Maziere, Davy Laille, and David Vernet. They were all visiting students who did this work as a practicum project at UNSW.
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