Standing waves on a guitar

[scilearner]

Hello guys,

 

I just have few questions about this.

 

 

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

[swansont]

A single tone implies a sinusoidal wave. If you strike or pluck the string, the original displacement is not a sine, but is some other shape, which is made up of the Fourier components.

[scilearner]

Thanks for the response I have just one question left. When each string vibrates at 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.

[Cap'n Refsmmat]

Take a few sine waves of different frequencies and add them together, and see the sort of graph you get. (It looks rather goofy.) That's what the graph of the displacement of the string at one particular point would look like with several different frequencies playing at once.

[scilearner]

Thanks Captain now I know what happens but I still have a small question. So if all frequencies are played at the same time, does that mean some atoms in the string vibrate at different frequency to other. I just can't visualize an object vibrating at many frequencies. For example if I push a swing it would go up and down at a fixed rate right, it can't do many things at once.

[StringJunky]

This might make it a bit clearer:

 

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html

 

The Nodal Points are where the amplitude of the wave form is zero so the ends, be it your fretted finger and saddle or the nut and saddle are nodal points.

 

If you pluck and touch a vibrating string just right at the halfway point you 'kill' the Fundamental and are left with two vibrating portions of string of equal length that vibrate at twice the frequency of the Fundamental (one octave higher). If you touch it at a quarter length you kill the Fundamental and First Overtone and get 4 vibrating portions between 5 nodes that vibrate at 4 times the frequency of the Fundamental (Two octaves higher).

 

All those nodes I mentioned are always there but you are eliminating the next lowest harmonic to hear each higher group by the technique of touching at the appropriate points...it should give you some insight into how all the frequencies are generated simultaneously.

[scilearner]

Thanks for the response 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.

 

This is my misunderstanding

 

1. When I hold a string does the whole string vibrate or the area up to my finger. Also when I play the 12th fret are harmonics still created in the string?

2.When you hold the string somewhere does the fundamental frequency change to something else? Is that how you get different notes.

[StringJunky]

Thanks for the response 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.

 

This is my misunderstanding

 

1. When I hold a string does the whole string vibrate or the area up to my finger. Also when I play the 12th fret are harmonics still created in the string?

2.When you hold the string somewhere does the fundamental frequency change to something else? Is that how you get different notes.

 

1. When you lightly and briefly touch exactly above the 12th fret position to bring out the harmonic you kill the natural note and set up two independent sections of vibrating string each with a frequency twice what it was before...so, yes, both sides vibrate either side of the 12th fret when you pluck and touch it there. If you touch it a quarter of the length you set up 4 sections...3 one side of the point you touched and one the other side!

 

When you finger the twelfth fret properly the harmonics are still there.

 

2. When you finger down on a fret normally, only that part between the fingered /fretted note position and the saddle vibrates.

 

Be aware, my first method is for bringing out the harmonic...the second one is the fundamental. If you change the string length by firmly fretting at different positions on the neck you change the lowest frequency (fundamental) that string can produce and hence its musical note . The smallest step in western music is a half step or half note (1 fret difference either side of any position = 1/2 step).

Edited April 19, 2010 by StringJunky