Question about the physics behind a guitar string

[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?

 

[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.

 

[MeJennifer]

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?

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

 

[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.

 

[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.

 

[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.

 

[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.

 

[Danger]

Some stringed instruments have sympathetic strings which are not plucked, but add structure to the sound.

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

 

[wysard]

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

 

[nuby]

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

 

[Andy Resnick]

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

There's quite a few:

http://en.wikipedia.org/wiki/Sympathetic_string

Plus, there's some oddball lutheiers out there that make kooky things:

http://www.beyondthetrees.com/oractext.html

 

[leftyguitarjo]

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

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

 

[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.

 

[lbasist]

Thanks for the help guys and cool sites

 

[Andy Resnick]

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.

Do you play anything?

 

[Danger]

Do you play anything?

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.

 

[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".

 

[Kurdt]

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.

 

[rbj]

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?

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"

 

[_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_

 

[leftyguitarjo]

Do you play anything?

you could say its a hobby...

 

[Danger]

I must admit that the chords chart surprised me. When I first saw it there, I fully expected to to be a periodic table.

 

[Kurdt]

ooh left handed guitars. I strung a right handed one upside down so I could look like a clever sod. I have a Jaguar that was in the background of a picture I posted here once.

https://www.physicsforums.com/attachment.php?attachmentid=7289&d=1152364427

 

[Andy Resnick]

you could say its a hobby...

Nice.

I like the chord chart in the background also. You may like these links:

http://philomel.com/musical_illusions/
Tritone paradox (and some other illusions)

http://www.terryblackburn.us/music/temperament/index.html
Alternate tunings

http://www.phys.unsw.edu.au/jw/soprane.html
Relationship between pitch and forming recogniziable words (in the context of Opera)

 

[billiards]

Anyone want to have a go at explaining to me how feedback works on an electric guitar?

 

[_Mayday_]

Hey Billiards!

I think wikipedia answers your question very well:

"Audio feedback is a special kind of feedback which occurs when a sound loop exists between an audio input (for example, a microphone or guitar pickup) and an audio output (for example, a loudspeaker)."

It goes on further to give an example:

"...A signal received by the microphone is amplified and passed out of the loudspeaker. The sound from the loudspeaker can then be received by the microphone again, amplified further, and then passed out through the loudspeaker again..."

Note that a microphone is given in this example but it would be the same for a guitar.

Hope this helped!

_Mayday_

 

[billiards]

But the guitar pickup is not a microphone. Nevertheless I believe the same principle applies to the electric guitar whereby the guitar string is excited by its own amplified sound. Although to get good feedback in practice you need to use some kind of distortion (which I believe is a boosting of the high frequencies, treble), lots of amplification, and often the guitarist will need to put energy into the string with their fretting hand, using vibrato techniques to coax the guitar to a sweet spot for feedback. I've heard of guitarists physically positioning their guitars in specific positions in the room (relative to the amp) to get specific pitches of feedback, I guess this must have something to do with the wavelength (in air) of the pitch they are trying to achieve and the acoustics of the room.

 

[Danger]

But the guitar pickup is not a microphone.

I'm not sure, but I think that it actually is. As far as I understand it, a microphone is a transducer that converts vibrations (air or string) into electrical signals.

 

[_Mayday_]

But the guitar pickup is not a microphone. Nevertheless I believe the same principle applies to the electric guitar whereby the guitar string is excited by its own amplified sound. Although to get good feedback in practice you need to use some kind of distortion (which I believe is a boosting of the high frequencies, treble), lots of amplification, and often the guitarist will need to put energy into the string with their fretting hand, using vibrato techniques to coax the guitar to a sweet spot for feedback. I've heard of guitarists physically positioning their guitars in specific positions in the room (relative to the amp) to get specific pitches of feedback, I guess this must have something to do with the wavelength (in air) of the pitch they are trying to achieve and the acoustics of the room.

Please read my post again. Both the microphone and the guitar pickup are audio inputs! The pickup acts as a microphone.

 

[cepheid]

I'm not sure, but I think that it actually is. As far as I understand it, a microphone is a transducer that converts vibrations (air or string) into electrical signals.

Heh, we had a small battle of the bands here at UBC one time -- Engineering Physics students vs. Engineers Without Borders* volunteers (also students). One of my friends had a guitar pickup. I hadn't really seen one before, so I asked him how it worked. He looked at me, and I looked at him, and we both blurted out something about it being an "acoustic to electric transducer". Then we started laughing, because we were both in engineering physics*, so you'd think at least one of us would know more details than that, but we couldn't do much more than state the obvious. (Using the word "transducer" allowed us to be about as vague as possible). Meh, you had to be there.

*Incidentally we were both also EWB members, so we had to pick sides.

Just wanted to say thanks for this thread guys, it's pretty cool. I only play piano, but I enjoyed all the links regarding sympathetic strings. I've often wondered about how the sitar can produce both the steady background "drone" and the short-duration strumming sounds.

 

[billiards]

Ha Ha Ha, this thread rocks! Especially if you can't be bothered to take it seriously (jeezus christ, bless our sacred souls). I was reckoning that the microphone is the same as a guitar pickup, but then I was trying to recompensate for the obvious discrepancy that a microphone doesn't require a vibrating string to stimulate a current (whereas the pickup does); in the end I (think I) realized that actually the microphone does(!), but this "string" isn't the obvious string one would associate with a guitar, perhaps it's some kind of coil? Perhaps not, I dunno, all I know is they are pressure sensors, scalar fields are below my understanding :-).

 

[phlegmy]

IDEALLY the tension should NOT CHANGE when you fret the fretboard.

the frets are spaced out very carfully to shorten the string only.
obvioulsy because you you press the string onto the fretboard your stretching it every so every so slightly which will increase the tension.

i notice that when i play guitar with very light gauge strings that it sometimes sounds out of tune when fretted. this is becasue I'm pressing tooo hard on the fretboard, stretching the string behind the fret.

also to increase the pitch you can bend the string upwards (or downwards!) the change in pitch in this circumstance is due to change in tension [yes there is a fractional very very very small change in length but that's not important!]

 

[leftyguitarjo]

I want to know how a natural harmonic on a guitar works.

 

[phlegmy]

when you pluck an open guitar string the two ends remain stationary [this may sound obvious!] while the rest of the string vibrates or oscisllates up and down.
this oscillation is made up of a number of modes of vibration



http://cnx.org/content/m11118/latest/
the above page showns a diagram of the modes of vibration of a string
have a look at the second set of illustrations on this page,
to play a "harmonic" on a guitar you can lightly touch halfway along the string [above the 12th fret].
by holding the string halfway you are only allowing the 2nd 4th 6th 8th 10th etc modes of vibration because in theese modes, the point you are holding does not vibrate, so you're not affecting them [much]
the others don't sound because where you are lightly pressing the string is where the fundamental, 3rd 5th 7th etc modes want to vibrate, so you're effictivly damping them out.

 

[rcgldr]

IDEALLY the tension should NOT CHANGE when you fret the fretboard.

Or simply placing the frets so that the change in tension is accounted for and the desired note is a combination of the (slightly less) shortened distance and increase in tension. Taking the bridge height, fret board, and targeted gauge of strings into account would allow fior more accurate placement.

I want to know how a natural harmonic on a guitar works.

Part of this depends on where you pluck the string. Pluck the strings near the middle and you get mostly the primary (lowest) harmonic. Pluck a string near the bridge and you get a more treble sound due to a higher ratio of higher harmonics. You can also place your fingers lightly on a string at key points to generate near pure harmonics: over the 12th fret will double the frequency, over the 7th fret will triple the frequency and over the 5th fret will quadruple the frequency. A table from Wiki:

http://en.wikipedia.org/wiki/Guitar_harmonics

Note that the strings don't generate sound directly on an acoustic guitar, instead they just vibrate the bridge which in turn vibrates the main body of the guitar which generates the sound. Stringed instruments require a sound board or the equivalent in order to produce significant sound.