What are the nodal points on a guitar string when plucked?

[sameeralord]

Hello guys,

I just have few questions about this.

[PLAIN]http://www.acousticguitarelectricguitarlessons.com/images/guitar/Electric-Guitar-Parts.jpg

Now I understand how a standing wave is formed. However I'm unsure what the nodal points are if I pluck an open string. Is it the headstock and the bridge?

1. If each guitar string has harmonics, how does this occur. I read that it can vibrate at many natural frequencies but I don't understand how a string could vibrate at many natural frequencies at once to create harmony? Does this occur at once or is it like one type vibration, and then another type of vibration.
2. Do you need resonance to create standing waves. I'm thinking not because all you need is to pluck the string to create a standing wave.
3. When I hold the string at a particular note, let's say a string in second fret, then where are the nodal points? Is it between the headstock and where I placed the finger or is it between the bridge and the place where I placed the finger?

Thanks a lot for any help in advance

 

[Stonebridge]

The nut and the bridge define the (open) length of the string for the purpose of the frequency of the note you get when you pluck the string.
When you fret a note, the vibrating length of the string is shortened such that the fret next to your finger, the one the string is pressing down on, defines the new length. (The length to the bridge)
The 12th fret produces a string vibrating length that is half the distance between the nut and the bridge. This produces a note an octave higher than the open string.
When you pluck a string it resonates at a number of frequencies simultaneously. These frequencies form a so called harmonic series. The lowest frequency, called the fundamental, is the one you hear as the note the string plays.
For the bottom E string, for example, this frequency is about 82Hz
http://en.wikipedia.org/wiki/Guitar_tunings#Standard_tuning
The other (higher) frequencies that the string vibrates with have much less energy associated with them, and are heard not as separate notes, but as the colouring (or timbre) of the string.
You can hear the the sound of the first of these higher frequencies if you pluck a string and then just touch with your finger gently at the 12th fret. You will hear a note an octave higher than the open string, because you have artificially created at node at that point and forced the string to effectively vibrate in two halves. The note has a frequency that is double that of the open string. (Fudamental)

 

[sameeralord]

Thanks a lot for your great response

I have just one question left. When you say that each string has many natural frequencies, how does this occur? Does one part of the string vibrate at a different frequency to other parts of the string? I don't understand how a string could vibrate at many frequencies at the same time? One after another I can understand.

 

[billiards]

The string vibrates in a very complicated way. The point is, you can break down that complex vibration down into simple modes of vibration -- so the complex vibration can be thought of as a superposition of lots of simpler modes. That's not an easy thing to just digest like that, you will probably have to think about that for a while before it sits comfortably.

Actually one of the cool things about the guitar is that you can control which modes of vibration you excite, simply by where you hit the string. If you hit the string dead in the middle (12th fret) you'll mainly excite the fundamental frequency and your tone will be dominated by that frequency and you will get a dull tone, if you hit the strings near the bridge you will excite higher frequencies and you will hear a brighter tone.

 

[Stonebridge]

There's a really good Java applet that shows this in action right here
http://www.falstad.com/loadedstring/
you can choose the harmonics you want and see the final waveform.

 

[sameeralord]

Thanks for the response but I don't understand the 12th fret analogy. When I hold the finger at 12th fret are there 2 vibrations in the 2 parts of the string separated by the finger. I thought only the area from the bridge to the 12th fret vibrates.

 

[billiards]

Yes. If you put your finger there, right at the middle of the string, then you create a standing wave with a node where your finger is.

What I was saying was even simpler: now instead of putting your finger in the middle, pluck the string in the middle, if you do it very precisely you get a standing wave with nodes at the end points of the string, you are exciting the fundamental mode. Now what would happen if you hit the string somewhere not in the middle? Then the string would deform in some more complicated manner, that is to say, you would have excited more modes of vibration, and you would hear that as a brighter tone.

 

[Stonebridge]

Thanks for the response but I don't understand the 12th fret analogy. When I hold the finger at 12th fret are there 2 vibrations in the 2 parts of the string separated by the finger. I thought only the area from the bridge to the 12th fret vibrates.

If you fret the string at the 12th fret (ie. press your finger on the fretboard and hold it there) and then pluck the string in the usual way, the string vibrates between the fret and the bridge. The vibrating length is exactly half the open length of the string. This is the normal way to play a guitar.

In order to produce a harmonic, you just touch the string for an instant just over the 12th fret metal. This causes the string to vibrate in its so called 1st harmonic. That is, in two halves. The note you get is the same in both cases.
If you know someone who plays, get them to demo it. It's far better than anything I can say here in words.