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.