# What happens when you pluck a guitar string?

1. Jul 23, 2011

### physickkksss

Hi guys, I know the basics of waves and standing waves, but I am trying to understand what exactly happens when you pluck a guitar string...

So, due to standing waves, a string that is clamped down on both ends needs to vibrate in one of its resonant frequencies:

f = (harmonic number)* v/2L

But I've read that when you pluck a guitar string, the sound produced is a combination of ALL of the fundamental frequencies.

That does not make sense to me. When you pluck ONE string, can't it only vibrate at ONE frequency, and thus produce a pitch of that frequency?

2. Jul 23, 2011

### olivermsun

Think this one may have been discussed in the past, but basically think of the disturbance you make when you pluck the string. Instead of a sinusoid, it's more of a kink, right? So, it contains lots of sinusoidal components; the ones which survive are the fundamental wavelength of the string and integer multiples which also "fit" on the string, thereby producing the harmonics.

3. Jul 23, 2011

### physickkksss

Ok I understand this part...one actually imparts many different frequencies on the string, but it can only vibrate at its fundamental harmonic (or a multiple)

This is the part I dont get. Cant ONE string only vibrate at ONE frequency?

So shouldn't the string settle at one of its harmonic frequencies and then produce a pitch at that frequency? How can it produce all of them at once?

4. Jul 23, 2011

### bp_psy

A string on a guitar can be considered as a series of damped oscillators. Each of these oscillators has a natural frequency. If you want to make a oscillator vibrate continuously at a frequency other than its natural frequency you must supply it with with energy ,this is called driven oscillator.If you stop the driving force the oscillator it will eventually damp the driving frequency and vibrate at its natural frequency and its harmonics until it completely stops .For an oscillator the natural frequency is given by its constant physical properties like spring constant and mass, inductance and capacitance.When you pluck a string you make all parts of the guitar vibrate at multiple frequencies but since the pluck originates from a string that is composed from a series of oscillators that have the same natural frequency, most of the frequencies will be damped quickly.What will have the most energy when the vibration will final propagate trough the whole guitar is the note you plucked and its harmonics. This is pretty much what makes a musical instrument possible.
You could make a string vibrate at just some frequency but just by driving it with some single frequency driving force. With a pluck of a string this can't be achieved because what you do is make the string vibrate at multiple frequencies but it chooses at what frequencies to vibrate .
For the question "How can it produce all of them at once?" i recommend you play with this :

5. Jul 23, 2011

### I like Serena

I believe you can get a string to vibrate at (almost) exactly one frequency if you enforce it by for instance connecting the string to an electronic sinusoidal wave generator.

As for how multiple harmonics can be in a string at once, look for instance at this picture:
http://www.coe.drexel.edu/ret/personalsites/2007/Dirnbach/curriculum_files//harmonics.png

The various waves are superimposed on each other.

6. Jul 24, 2011

### physickkksss

cool, those replies helped a lot

Thanks :)

7. Jul 24, 2011

### rcgldr

It might help to visualize a string with a combination of fundamental and double frequency. The double frequency on it's own would have a staionary node at the mid point of the string, but combined with the fundamental frequency, that node oscillates at the fundemental frequency. A guitar player can place his finger lightly on the mid point of the string to prevent node movement and pluck it at about 1/4 the way down the string to get a mostly double frequency sound.

Although the overall output of a guitar string is a composite waveform, the entire string movement does not follow that composite waveform. Instead the actual string movement at any point on the string is affected by the nearness of the nodes and peaks related to the frequencies produced by the string. From a 2d side view at any moment in time, you would see peaks and valleys along the length of the string due to the combined frequencies.

The soundboard of the guitar that actually produces the sound, also has pockets of peaks and valleys related to the frequency being produce.

Link to a video someone made of guitar string movement, the first one is affected by the rotating shutter, so the second one is a better example.

http://createdigitalmusic.com/2011/...l-guitar-string-movement-and-iphone-shutters/

Last edited: Jul 24, 2011
8. Jul 24, 2011

### I like Serena

9. Jul 24, 2011

### physickkksss

I understand that the string itself does not move a lot of air, so you cannot hear it
It transfers its vibrations to the soundboard, which moves much more air
This leaves the sound hole, and we get an amplified sound

My question is that wouldn't the wood need to have the same harmonic frequencies as the string? (ie. a tuning fork can only transfer its sound by resonance to a tuning fork with the same natural frequency).

If the wood is indeed selected to have the same natural frequency of the string, then how does it resonate with all of the different strings on the guitar?

10. Jul 24, 2011

### I like Serena

A string is designed to have a specific resonance frequency determined by its length.

A soundboard is designed to not have a resonance frequency.
It will vibrate with any frequency.

Btw, the majority of the sound does not leave the soundboard by the sound hole.

11. Jul 24, 2011

### olivermsun

I don't know how a guitar works specifically, but I have seen analysis of the body of stringed instruments such as the violin, and actually there are many vibrating modes. Here the varying thicknesses of the wood, the shape of the body, and the cavity contained in the body, allow much more complicated resonances than the resonances in the string. So, I would guess that the guitar soundboard and body also have many distinct resonances rather than none.

12. Jul 24, 2011

### physickkksss

How does that fit with the statement:
all objects have a natural frequency or set of frequencies at which they vibrate when struck, plucked, strummed or somehow disturbed

Maybe its because normally objects quickly damp out frequencies other than its natural frequency, so the soundbox just does not damp out all those other frequencies too much?

13. Jul 25, 2011

### I like Serena

Yeah, well, if you knock on the soundboard it will indeed vibrate with a characteristic set of frequencies.
But it can also vibrate at other frequencies without really dampening out.

However, if you make a string vibrate with a frequency that does not match its length, it will dampen out immediately.

14. Jul 25, 2011

### physickkksss

Yeah so I guess that must be it....

The soundboard, like any other object, does have its own natural frequency that it is prone to vibrate at. However, it must have the quality of not quickly dampening out other frequences, as would most other objects. That would make it good at transferring the vibrational frequencies of all the guitar strings.

15. Jul 25, 2011

### chingel

I think the soundboard is just carrying the sound waves and vibrating along with it. Just like air can vibrate at all sorts of frequencies and carry all sorts of sound waves. The string is against the bridge, which is against the soundboard, the string gives it's vibrations to the soundboard, which carries them and vibrates along.

Why does a string dampen out immediately if I make it vibrate at a frequency that does not match it's length?

16. Jul 25, 2011

### sophiecentaur

Say you excite the string with a nearby loudspeaker. The energy from the loudspeaker, whatever frequency, will hit the string and make it vibrate and it will dissipate. However, if the frequency of sound from the LS happens to be at a suitable frequency, the vibrations, being in step, will add up (build up) and cause the string to vibrate with a high amplitude because some of the energy is being absorbed into the resonant system. Once enough energy has been absorbed onto the system, it will, as before, dissipate at the rate it is being supplied and the string will be vibrating at the maximum amplitude. The resonant system can only store energy at certain frequencies, which is why it only 'responds' to those frequencies. A string on a solid bodied guitar will have fewer losses than on an acoustic guitar so the resonance will be more 'frequency selective' and the note will sustain for longer when the excitation is removed and the energy gradually dissipates. (Hence the Brian May effect)

Last edited: Jul 25, 2011
17. Jul 25, 2011

### Pythagorean

See "harmonic series (music)" as opposed to the mathematical concept.

18. Jul 25, 2011

### sophiecentaur

Oh - you just opened another can of worms!!!
Yes; overtones from all musical instruments do not coincide exactly with harmonics of the fundamental. Nice to listen to but not nice to analyse.

19. Jul 25, 2011

### rcgldr

I'm not sure it does. The main difference in the case of a frequency that is not an integer multiple of the fundamental frequency is that the nodes travel back and forth along the string, as opposed to being fixed in place. The harmonic frequencies will sustain longer due to resonance, but non-harmonic frequencies will decay depending on how much the string retains energy. I'm not aware of any additional dampening factor for non-harmonic frequencies.

The soundboard is being driven by the strings, so it's harmonics aren't as much of an issue, as long as they don't over amplify a particular frequency A soundboard or a speaker can handle a range of frequencies, and similar to the string, non-harmonic frequencies result in the hills and valleys moving around a 2d plane, while harmonic frequencies result are mostly fixed in place.

20. Jul 25, 2011

### sophiecentaur

How would you make it do that in the first place? If you had a mechanical vibrator to drive the string, then it's hard to say what it would do if you suddenly removed the drive. I imagine that the string would start to vibrate at its fundamental frequency (plus harmonics) because it would be as if you had just plucked it. It would have no memory of how it got to the shape that it was displaced by the drive and impulses would move along the string, redistributing the energy (a bit of BS there, I'm afraid) as the waves settled down such that the remaining oscillations were just the natural ones - which would decay relatively slowly because of the energy stored in the resonance. The other components of the energy in the system would release in a 'snap'. which is also what you get when you first pluck a string.
So, unless you are quoting an actual experiment (?), I suggest that your thought experiment wouldn't go as you say. If you excited the string off-frequency with a weak coupling, then a resonance just wouldn't have built up in the first place.