Difference between Density and Thickness on Strings??

I am having a hard time wrapping my head around the difference between density and thickness on strings.

As described by Aquila on their Red Strings:

"when you have standard strings on your ukulele, the higher strings are thinner than the lower strings. The problem this causes is that thinner strings are more resonant and true-sounding. This is why with a standard uke, the top strings are more brilliant than the low strings. Aquila have got around this by making four strings that are very similar in guage, changing the notes they produce not by thickness, but by density. How do they vary density? They put different amounts of copper in each string."

I use this example because of their description but I am interested in learning the difference as it pertains in general. It is not the string I am interested in. Just the concept.

What does this mean? How can it be denser and not thicker? I seem to be dense and thick when it comes to understanding this.

Thanks in advance.

rappsy said:

How can it be denser and not thicker?

Click to expand...

Say you had a quarter, and a plastic guitar pick.
They're roughly similar size, but the quarter is heavier than the guitar pick.
That's because metal is heavier than plastic.

Now imagine you have 4 jars.
The first jar, is all coins, and no plastic.
The second jar, is 1/4 coins, and 3/4 plastic.
The third jar, is 1/2 coins, and 1/2 plastic.
The fourth jar, is 3/4 coins and 1/4 plastic.

They would all be the same size, but the ones with more coins will be heavier.

Density is how heavy something is compared to the volume.
Heavier strings of the same size and tension will be lower pitched.

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

I may be wrong, but I thought that the main factor of density was that something with higher density, actually had more molecules (or atoms) per unit (gram) than something that was less dense.

In the way that 1 gram of water is more dense than 1 gram of air composed of water vapor, and as such density is not a factor of weight per se, which is bound by gravity, but density is a factor of mass, which involves gravity, but exists without it.

Lets pretend a ping pong ball and a golf ball are the same diameter.

If you hold each in your hand, the golf ball 'weighs' more.

Is it because the guts are a composite of rubber vs the air that is inside a ping pong ball?

or,

is it because the guts (and there are more of them) are packed in real tight (molecules closer together), and therefore have more mass, than the floating air particles inside the ping pong ball (which is essentially 'empty')?

I REMEMBER in school that density and weight are not the same; density being a concentration of mass in a given volume, and weight being a measure of the force of gravity on earth at 1-atmosphere as it pulls said mass towards the earths core.

Not sure if/how this relates to strings, and hope I have not confused things worse.

In the past when this topic has come up, fellow UU brothers OneBadMonkey (who works for GHS strings), Dirk (from Southcoast) or Rick Turner always had meaningful explanations, until/unless one of them joins the thread and offers a comment, maybe it's worth trying to find those conversations?

There are also many engineers on UU, maybe one of them will see this thread and chime in as well.

Sorry I cant offer more help, but now I too would like to know the answer.

Density is mass per unit volume, measured in, say, pounds per cubic foot, or grams per cubic centimeter

Thickness is just a length -- in the case of thickness of a string, it's the length of the diameter of the string. It would be measured in something like inches, or millimeters.

It turns out that the frequency of a vibrating string is determined by its length, its tension, and the mass per unit length of the string, which would be measured in something like grams per cm. This is not the same thing as density.

Because all the strings on a given instrument are more-or-less the same length, all else being equal, the heavier of two strings will vibrate at a lower pitch.

There's lots of ways to make a string heavier. You can use a larger diameter of the same material. Since there's more of it, it will weigh more. You can use a denser material that has the same diameter. Or you can do both.

But it isn't really the density per se. It's just how much the part of the string that's vibrating weighs. ETA: To be more strictly correct, I should say how much mass the part of the string that's vibrating has. But I think most people think of this in terms of weight.

Booli said:

I may be wrong, but I thought that the main factor of density was that something with higher density, actually had more molecules (or atoms) per unit (gram) than something that was less dense.

Click to expand...

Not necessarily more, but heavier atoms.

I think the OP has got responses that should answer his/her question

Say you have 2 strings of the same diameter...one is made of lead and one is made of aluminum. Lead is much denser, therefore heavier than aluminum. So, when strummed, the lead will not vibrate as much as the much lighter aluminum string.

Booli said:

density was that something with higher density, actually had more molecules (or atoms) per unit (gram) than something that was less dense.

Click to expand...

Well.. almost but not quite. You're almost on the right track, but you have to think smaller than an atom.
It's not the number of atoms, but how many nuclear pieces the atom has that gives it mass.

So take Hydrogen, and Helium because they're the most basic.
If you look at a periodic table of elements. Hydrogen is 1, and helium is 2.
So, a hydrogen atom has one proton, one neutron, and 1 electron.
A Helium atom has 2 protons, 2 neutrons, and 2 electrons, so it has twice the mass of hydrogen.

So.. you're almost right in that it's the number of building blocks in a unit that makes something more mass than another, but the blocks to look at are smaller than atoms when you're looking at mass.

spookelele said:

Well.. almost but not quite. You're almost on the right track, but you have to think smaller than an atom.
It's not the number of atoms, but how many nuclear pieces the atom has that gives it mass.

So take Hydrogen, and Helium because they're the most basic.
If you look at a periodic table of elements. Hydrogen is 1, and helium is 2.
So, a hydrogen atom has one proton, one neutron, and 1 electron.
A Helium atom has 2 protons, 2 neutrons, and 2 electrons, so it has twice the mass of hydrogen.

So.. you're almost right in that it's the number of building blocks in a unit that makes something more mass than another, but the blocks to look at are smaller than atoms when you're looking at mass.

Click to expand...

Thanks for clearing that up. Makes perfect sense now.

I used to love this physics/chemistry stuff in school (joules, moles, etc) but forgot most of the finer points. I am really enjoying this discussion thus far.

However, does this mean that fluorocarbon (FC) trings have more sub-atomic particles per linear centimeter than say, 'nylon' strings (as in Dupont/Segovia)?

Laymans observation seems to bear this out, in that a given set of strings that are FC, are thinner gauge than a typical set of nylon for the same scale length, so to achieve the same pitch frequencies at a relative tension, the THINNER FC strings would have to have more mass, density, more sub-atomic particles in order to achieve this.

Please correct/redirect me if I am wrong.

That's a much harder question to answer.

So.. a FC is carbon chain with Florine branches, while nylon is a carbon/nitrogen chain with oxygen and hydrogen branches.
C=6, N=7, O=8, F=9

A Nylon segment is 6+7+8+1 roughly... = 22
FC segment is 6+6+9+9 roughly...= 30

The difficulty comes because plastic molecules are not straight. They're like.. tangled wads of string, some of which is more accordian'ed than others. Nylon is always nylon. But fluorocarbon refers to the type of molecule segments, not how they're all bonded together. Like.. Teflon is a fluorocarbon polymer, in the sense we use the word for strings, but there are others, and I'm not sure which the strings are made of.

Nylon is 1.15g/cm^3
Teflon is 2.2g/cm^3

There's a lot of great information already mentioned about the density of strings, so I'm not going to rehash it.

In terms of thickness, or the gauge, of strings however, it really is nothing more than the final diameter of the string. Period. There is no intrinsic value in terms of how much tension a string will have when tuned up, or whether it's a stiff or loose feeling string.

The only time you can use the thickness of a string for something other than simple measurement is if you're using a .032 black nylon for a C string and want to know if going to a .035 black nylon would give you more tension. At that point, since you're comparing two strings, made of the same material, you can make a decent guess.

Otherwise, thickness is not a reliable source to calculate the tension of a string.

Where would the world of ukes be without "Nerds".....

:rotfl:

One Bad Monkey said:

Otherwise, thickness is not a reliable source to calculate the tension of a string.

Click to expand...

I think physicists disagree with you.

If you have the density of the material (1.15g/cm^3), and the diameter of the string, you can calculate the linear density(u).
By using a known tension (T), you can calculate propagation velocity (v)



Once you have (v) for the material, you can calcuate the rest of the variations.



We know the frequency/pitch(f) because it's the note.
We calculated (v) above for the material.
We know (L) from the scale length.
We can calculate the new (u) because we know the density of nylon, and the volume based on the diameter.
So, we can solve for T.

spookelele said:

I think physicists disagree with you.

Click to expand...

Okay.

spookelele said:

I think physicists disagree with you.

If you have the density of the material (1.15g/cm^3), and the diameter of the string, you can calculate the linear density(u).
By using a known tension (T), you can calculate propagation velocity (v)

View attachment 75616

Once you have (v) for the material, you can calcuate the rest of the variations.

View attachment 75618

We know the frequency/pitch(f) because it's the note.
We calculated (v) above for the material.
We know (L) from the scale length.
We can calculate the new (u) because we know the density of nylon, and the volume based on the diameter.
So, we can solve for T.

Click to expand...

This is awesome info, but my brain hurts when I look at math on the computer screen. I will try to do some figuring with these formulae myself and see what I can come up with.

I wish there was an online, browser-based string tension 'calculator', where you can just put in these values and it gives you the result you want.

Maybe I'll have to try and write one in Python or Javascript? If so, I'll publish it online for everyone to use. No promises though, since my time is spoken for right now. Also, I have no idea if anyone else would be interested in something like this.

Few string companies publish the linear density info, in fact the only info I've seen is available from the D'Addario web site as a PDF file.

I'd like to be able to plug in the diameter, scale length and linear density, and get tension, or put in tension, scale length and linear density and get diameter, for a given string material, whether it be nylon, fluorocarbon, nylgut, REDS, metal or any other strings, but not all the parameters to do the calculations are readily available it seems.

The problem goes further when you want to compare strings of different materials, from different makers, as it seems there is no scientific way for a layman to do an apples-to-apples comparison on paper before actually buying the strings. As such I have spent a small fortune to try out lots and lots of different strings over the past 18 months, and the only qualitative and quantitative results I can offer are my own subjective perceptions of 'sound' and 'feel', which is probably not going to help anyone else, unless they have the same or similar instrument with the strings in question, AND ALSO have a similar playing technique to mine.

So in the end, the only absolute conclusions that can be offered are 'Your Mileage May Vary', which is not really helpful.

Hey Rappsy has it been made clear to you now. If so please PM me with an explanation cause I am afaraid to ask.

Booli said:

I wish there was an online, browser-based string tension 'calculator', where you can just put in these values and it gives you the result you want.

Click to expand...

I usually put the formula in an excel spreadsheet, which works. But as you mentioned also, most of this information (specifically, the unit weight [or, linear density]) is not readily available because until recent, ukulele players haven't been this interested in the ins/outs of strings.

Booli said:

Few string companies publish the linear density info, in fact the only info I've seen is available from the D'Addario web site as a PDF file.

Click to expand...

I'm working on that right now. Lots of weighing.

Booli said:

I'd like to be able to plug in the diameter, scale length and linear density, and get tension, or put in tension, scale length and linear density and get diameter, for a given string material, whether it be nylon, fluorocarbon, nylgut, REDS, metal or any other strings, but not all the parameters to do the calculations are readily available it seems.

Click to expand...

All you really need is 1. frequency of pitch (easily found), 2. scale of instrument (easily found) and 3. linear density/unit weight (which you can actually find if you can weigh the string in question and then divide the weight by the length). The problem, as you've mentioned, is that finding No. 3 is the issue, mainly due to the fact that until recent, most ukulele players weren't as concerned with tension of string as say, guitarists or bassists are.

It's amazing and great that ukulele is starting to get this involved, however still remember that while charts and calculations and physics are all well and good, fingers and ears play instruments and at the end of the day, a set of strings that on paper looks very unbalanced may be exactly what you want.

One Bad Monkey said:

It's amazing and great that ukulele is starting to get this involved, however still remember that while charts and calculations and physics are all well and good, fingers and ears play instruments and at the end of the day, a set of strings that on paper looks very unbalanced may be exactly what you want.

Click to expand...

+1000.

Even if you calculate all the numbers, it doesn't tell you how it sounds, and really, thats what we're shopping for with strings right?

One Bad Monkey said:

It's amazing and great that ukulele is starting to get this involved, however still remember that while charts and calculations and physics are all well and good, fingers and ears play instruments and at the end of the day, a set of strings that on paper looks very unbalanced may be exactly what you want.

Click to expand...

spookelele said:

+1000.

Even if you calculate all the numbers, it doesn't tell you how it sounds, and really, thats what we're shopping for with strings right?

Click to expand...

I agree with both statements above, but it would be nice to have some kind of absolute reference point as per the math/physics.

And in the end as per what you both have said above, it brings me back to:

Booli said:

the only ... results I can offer are my own subjective perceptions of 'sound' and 'feel'...

Click to expand...

One Bad Monkey said:

(specifically, the unit weight [or, linear density])...I'm working on that right now. Lots of weighing.

Click to expand...

Thanks for taking the time to do this. Us 'string geeks' will certainly appreciate having access to the information.

One Bad Monkey said:

All you really need is ... 3. linear density/unit weight (which you can actually find if you can weigh the string in question and then divide the weight by the length).

Click to expand...

If I wanted to weigh strings from other makers, would a small postal scale have enough precision and accuracy for usable numbers?

Booli said:

If I wanted to weigh strings from other makers, would a small postal scale have enough precision and accuracy for usable numbers?

Click to expand...

That's actually what I use; a digital postal scale. However, I usually grab a couple dozen so I can then get a more accurate measurement.

But yes, as long as the scale is precise enough, you can weigh the string, and then divide the weight by the length of the string and that will get you the unit weight/linear density.