# Question about the physics behind a guitar string

1. Apr 16, 2008

### lbasist

Why does pressing different positions on your guitar string produce different pitches?

Obviously different pitches are caused by different frequencies, but is that change in frequency caused by the change in tension or the change in length or something else?

2. Apr 16, 2008

### Danger

Welcome to PF, Lbasist.
Pressing on the string at a certain point essentially shortens it. Vibrations are damped out at the point of contact. That's the best that I can offer, but there are others here who can elaborate upon the situation.

3. Apr 16, 2008

### MeJennifer

Both, but on a guitar mostly by the change in length.

4. Apr 16, 2008

### ks_physicist

Pressing it straight down doesn't change the tension too much, but it does change the length.

Bending a note (pushing the string laterally on the fretboard) changes the tension. So does using the whammy bar.

5. Apr 16, 2008

### linton

the pitch of a string is it's resonating frequency, which is dependent on the length, mass, and tension of the string, so changing anyone of these properties will change the strings resonating frequency... Obviously the quickest and easiest way to do this is to virtually change the length of the string, by pressing it onto the fretboard.

6. Apr 16, 2008

### leftyguitarjo

Man, this is a cool thread. I've been playing guitar for about 5 years now, and I think it would be neat to learn about the physics part of it.

7. Apr 16, 2008

### Andy Resnick

Yeah, the physics of musical instruments would be a great addition to any physics curriculum, even as an elective.

All the above relates to very general acoustic properties of the string, no matter what the string is made of, where it is plucked, the resonant properties of the body, characteristics of the neck, or location and type of electric pickup. Some stringed instruments have sympathetic strings which are not plucked, but add structure to the sound. Taking those into account leads to all kinds of new and strange effects, the most fun being feedback.

8. Apr 16, 2008

### Danger

I've never even heard of that before. Cool. What instruments?

9. Apr 16, 2008

### wysard

The only one I can think of off the top of my head is the Sitar, but there must be many more. Anyone?

10. Apr 16, 2008

### nuby

Here's a video that shows the movement of the guitar strings in slow motion.

Last edited by a moderator: Sep 25, 2014
11. Apr 16, 2008

### Andy Resnick

12. Apr 16, 2008

### leftyguitarjo

I'm sure you've heard of a sitar.

13. Apr 16, 2008

### Danger

Yeah, I've heard of sitars, but I've never seen one close-up and had no idea how they were played; they always seemed pretty much like guitars to me, except for sounding weird. Andy, you're right about that site. There are some spooky looking devices on it.

14. Apr 16, 2008

### lbasist

Thanks for the help guys and cool sites

15. Apr 17, 2008

### Andy Resnick

Do you play anything?

16. Apr 17, 2008

### Danger

I'm just now learning to play the radio. With persistence, and a lot of luck, I hope to master the tape deck by this time next year.

17. Apr 17, 2008

### Andy Resnick

Nice. Me, I've perfected the art of scaring elderly neighbors and small children by banging on wooden cylinders and metal disks. Sure, the cops have shown up a couple of times... It's art, dammit! It's not bad, it's "provocative".

18. Apr 17, 2008

### Kurdt

Staff Emeritus
As people have mentioned, the frequency of standing waves on strings depend on the length of the string, the mass per unit length and the tension. Here is a page that gives a brief description of the physics.

http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/string.html

With the guitar it is the changing of length of the strings that causes the change in frequency. As you probably know the 12th fret halves the length of the string and doubles the frequency. You might be interested in fretting calculations, as you will notice that frets do not have the same distance between them.

The mass per unit length is varied by having strings of different thickness, so they can all be set at approximately the same tension.

Last edited: Apr 17, 2008
19. Apr 17, 2008

### rbj

The physics is here:

http://en.wikipedia.org/wiki/Wave_equation
http://en.wikipedia.org/wiki/Standing_waves

If you do not understand how Partial Differential Equations work, the only other explanation i've ever seen (for a wave traveling in one direction) puts you in the inertial frame of the wave (so it looks like the string is sliding by in the opposite direction) and you can show that whatever the bump on the string looks like, it retains its shape, even as the string is pulled past you.

to answer your question more directly, there is a constant wave speed on a string that depends on the string weight (mass per unit length) and tension (newtons). also, where the string is terminated against a rigid structure (the bridge and nut or fret of the guitar) the wave is reflected back. the longer the string is, the more time it takes for a wave to make the round trip. the time for a round trip is the period of vibration which is the reciprocal of the fundamental frequency, f. the pitch of the note (measured in semitones) is 12 log2(f/f0)) where f0 is the reference frequency (like "A440" means the A immediately above Middle C is 440 Hz and pitch is the distance away from that A). so as you fret the string (and terminate it at a shorter length), the fundamental frequency (and all of the harmonics) gets higher. Note that when you fret it 12 frets up from the nut (one octave), the length of the string is nearly exactly 1/2 of the open string. (you can also find a nodal point there.) Thats because of the exponential relationship between frequency (which is inversely proportional to the length) and pitch. Go up one octave, double the frequency.

you might get some of this in college freshmen physics. and more in Diff Eq when you first learn about Partial Differential Equations.

The stuff that relates pitch to frequency is more about the science and math regarding music. Check out Gareth Loy's book: "Musimathics"

20. Apr 17, 2008

### _Mayday_

A higher pitch is due to a higher frequency. I think that it is mainly due to the change in length of the string, though tension may also play a role. You don't need to understand the equation below fully but it will show you how it all works, don't be put off by the equation!

$$f=\frac{1}{2l}\sqrt{\frac{T}{\mu}}$$

$$f = Frequency$$

$$l = Length$$ (This is what changes when you change fret)

$$T = Tension$$

$$\mu = Mass$$

OK, that is as complicated as I will go. Please note what I am doing is only to help in your understanding. Let's give $$\sqrt{\frac{T}{\mu}}$$ the value of 10. Now we have:
$$f=\frac{1}{2l}\times10$$

Now let us vary the length of the string!

If the length of string was 1 metre (Note, the bottom of the equation is 2 x Length)

$$f=\frac{1}{2}\times10 = 5Hz$$

Now let us increase the length to 2 metres

$$f=\frac{1}{4}\times10 = 2.5Hz$$

Conclusion

As you can see the shorter string has a higher frequency (5Hz) than that of the longer string (2.5Hz). So the shorter string will have a higher pitch, and the longer string a deeper pitch. This is why there is a change in pitch. Tension may play a role, though I do not think that much, though if it does please could someone inform me of this.

I hope this has helped somewhat.

_Mayday_