# The Naked Scientists Forum

### Author Topic: How does a guitar string know its length?  (Read 4913 times)

#### DoctorBeaver

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##### How does a guitar string know its length?
« on: 30/07/2008 22:36:21 »
I've been thinking about strings and vibrations. A string can only vibrate an integer number of times of its length. Now, in the case of a guitar, the string is bounded at 1 end by the bridge and at the other end by the nut.
Normally, when plucking the string, you do so a lot closer to the bridge than to the nut. That means the information that it has been plucked reaches the bridge before it reaches the nut.

The information would reach the bridge and start travelling back along the string before the information has reached the opposite end. Then the information reaches the nut and bounces back, colliding with the information that has bounced back from the bridge.

So how does it settle into its proper vibratory mode? How does it "know" its length and what vibratory modes are permissible?

#### lyner

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##### How does a guitar string know its length?
« Reply #1 on: 30/07/2008 23:36:37 »
The string doesn't have to know anything. Only waves which have the right wavelength will be in the right phase when they reach the ends and get reflected to form a standing wave.
The easiest way to analyse what goes on is to assume that you try to excite the string with a single tone, applied near one end. If you choose a suitable frequency the energy you feed in will add to the standing wave and it will build up in level over many cycles (resonance). If it's the wrong frequency then no wave will build up.

Plucking the string is not so obvious but the impulse you give it will travel up and down the string at the rate governed by the length and the velocity (mass and tension). It takes a few return journeys before all the other frequencies which the initial pulse consisted of to die down and the main note is established (the resonant frequency). This gives the attack characteristic and varies from instrument to instrument.
The actual note you get will have a number of overtones and the actual mix depends on where you pluck. Right in the middle gives a softer sounding note because it contains a bigger proportion of fundamental. Very near the bridge gives a tinny sound because of the high level of overtones. Holding your finger, lightly, on the string half way along will suppress the fundamental (and odd harmonics) and give you an octave note - called a harmonic but it is, strictly, an overtone. That means it may not be exactly twice the fundamental frequency. Again this affects the actual quality of note or 'timbre'.
I could go on and on . . .

#### LeeE

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##### How does a guitar string know its length?
« Reply #2 on: 30/07/2008 23:47:07 »
Try plucking the strings at the twelfth fret and compare the timbre with the strings being plucked in the more normal position, nearer the bridge.  Then try plucking the strings about half an inch away from the bridge.  Basically, the nearer the bridge that you pluck the strings, the higher the frequency of the harmonics you cause by plucking the string off-center.  You get the same effect if you pluck the strings near the nut.

Although a string can only sustain vibrations that are an integer number of times it's length, you can impart non-integer vibrations into the string, which will reflect up and down it, adding their bit to the overall timbre.  They'll lose energy more quickly though.

More or less what sophiecentaur said
« Last Edit: 30/07/2008 23:48:54 by LeeE »

#### DoctorBeaver

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##### How does a guitar string know its length?
« Reply #3 on: 30/07/2008 23:48:29 »
Quote
It takes a few return journeys before all the other frequencies which the initial pulse consisted of to die down and the main note is established (the resonant frequency).

Thank you Sophie, that's what I was after.

There are, of course, several ways to produce "harmonics" from a guitar string; including some rather strange harmonics too!

#### lyner

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##### How does a guitar string know its length?
« Reply #4 on: 31/07/2008 09:44:24 »
Harmonics

There are very few instruments which produce true harmonics. The effective end of a string or an air column or a vibrating bar will vary with frequency and this means that the natural resonances are not at whole multiples of the fundamental.

The shape of the flared open end of a trumpet helps to compensate for this (it also helps in 'matching', which increases sound output).
This departure from the ideal is one of the things that give interesting sounds, along with the levels of these overtones. With some 'old' instruments this is very obvious - the weird sound of the Roman Horn is a good example.
I think, for the opposite reason, the special sound of the Hammond Organ  could be due to the fact that the harmonics are true harmonics; the 'perfection' sounds like an 'imperfection'.

#### LeeE

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##### How does a guitar string know its length?
« Reply #5 on: 01/08/2008 00:00:29 »
Hammond organs were often used with Leslie rotary speaker cabs and a lot of the classic Hammond sound comes from that.  The original Hammonds used 'tone wheels' for the actual sound generators - these were basically cogs with the appropriate number of teeth for each note, revolving in the field of an electromagnetic pickup.  Finally, they would typically be amplified by thermionic valve (tube) amps, which tend to produce even order harmonic distortion and which is usually perceived as a more attractive sound than the odd order distortion produced by early transistor amps.

#### DoctorBeaver

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##### How does a guitar string know its length?
« Reply #6 on: 01/08/2008 07:47:09 »
I've had 2 Hammonds - an M100

and a C3.

#### RD

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##### How does a guitar string know its length?
« Reply #7 on: 01/08/2008 08:01:25 »
Dr Beaver cannot resist posting pictures of his big organ.

#### DoctorBeaver

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##### How does a guitar string know its length?
« Reply #8 on: 01/08/2008 08:16:33 »
If you've got it...  [^]

#### lyner

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##### How does a guitar string know its length?
« Reply #9 on: 01/08/2008 10:49:55 »

#### lyner

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##### How does a guitar string know its length?
« Reply #10 on: 01/08/2008 10:50:57 »
Scratch the surface - there's always a schoolboy in there.

#### syhprum

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##### How does a guitar string know its length?
« Reply #11 on: 01/08/2008 13:09:50 »
I have read that some of the Hammond type organs had their tone wheels belt driven to introduce a degree of phase drift between the fundentals and the harmonics.
Perhaps the Doc could confirm.

#### lyner

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##### How does a guitar string know its length?
« Reply #12 on: 01/08/2008 14:17:23 »
Where I used to work they had an old Compton cinema organ. There were wheels with a range of recorded instrument tones on them. They were drived by a selsyn motor. There were two, duplicate sets, kept in sync by the selsyns and, by unlocking the coupling between the selsyns and letting them drift a bit, you got a fair 'chorus effect'.
Not as nice to listen to as the Leslie effect. I don't know whether anyone has synthesised a really good Leslie sound without waving something around in space.
I did like to be beside the seaside.

#### DoctorBeaver

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##### How does a guitar string know its length?
« Reply #13 on: 01/08/2008 17:50:47 »
I have read that some of the Hammond type organs had their tone wheels belt driven to introduce a degree of phase drift between the fundentals and the harmonics.
Perhaps the Doc could confirm.

I'm not sure about that. Each tone wheel was in its own housing, so I don't know the drive mechanism. I just played the damned things.

#### The Naked Scientists Forum

##### How does a guitar string know its length?
« Reply #13 on: 01/08/2008 17:50:47 »