The Dimensions of a Tuning Fork

January 30, 2009 12:09 PM

Would someone please give me the dimensions of a tuning fork, such as one used to tune a musical instrument? I'm an amateur machinist and I thought it might be fun to try making one this weekend for my granddaughter to play with.

I know the formula for calculating the dimensions and resulting frequency, but I still expect some trial and error and it may save me a lot of time and material if you could tell me four things:

1) The cross-sectional dimensions of a single tine
2) The length of the tines
3) The distance between the tines
4) The material it is made out of, if you know it. (I'm assuming that mild steel is commonly used, but I'm not sure).

Either metric or English units are fine. Thank you.

posted by 14580 to grab bag (13 comments total)

Violinists typically use an A440, which is about 3-4 inches long with round tines about 3/8th of an inch diameter and a half inch apart. The stem is about 3/4 of an incha long with a ball ont eh end. I haven't the slightest idea what the material is.
posted by mzurer at 12:17 PM on January 30

Your wikipedia link indicates they're usually made out of steel, but you could always make it out of something else. (Making a correctly calibrated tuning fork would appear to be a non-trivial problem.)
posted by zamboni at 12:27 PM on January 30

it will be most useful to him if somebody here happens to have both a tuning fork and calipers to measure them with. we machinists like to be precise.
posted by TrialByMedia at 12:42 PM on January 30

I've got an A440 tuning fork here which is this shape, but no way to measure it precisely I'm afraid. So I'll just give you the best measurements I can in the hopes they'll help.

The tines look slightly off-square to me, with the longer side face up if you lay the fork flat on the table.
Measuring it straight with a ruler, it looks like they are 4mm * 4.5mm (I don't have sub-mm marks on the ruler, but it looks closer to 4.5mm than to just four or five).
Wrapping a thread around a tine 14 times got me a length 236mm, so an average side of 4.2mm.

I can't really give you a good measurement for the lengths, as I can't decide on an obvious place to measure from at the base, and the tips I assume have been filed and adjusted, so they're not flat.
But the straight edge along the outside of each tine is 96mm long, and from the lowest dip of the centre hole to the tip is 91mm.

The tines are 7mm apart, as well as I can measure with this ruler.

I don't know what the material is exactly. But it appears to be steel, and has a bluish shine on the surfaces that haven't been corroded through use.

Hope that's of some use.
posted by lucidium at 1:16 PM on January 30

Using the formula on the Wikipedia page and the Wikipedia data for the Young's modulus and density of mild steel, I derived the following for a 440Hz mild steel tuning fork with cylindrical tines:

L² = 3.739R

Where L is the length of the tines in meters and R is the radius of the tines in meters. As you can see we have one equation and two unknowns, so simply set whichever variable you want and solve for the other. Using mzurer's estimate of .475cm for the radius, we get a length of 13.3cm, which is in the ballpark of mzurer and lucidium's figures but suggests that their forks were made out of something other than mild steel.

So, I think with that formula and lucidium's other measurements you should be able to make a decent one. Since it's much easier to adjust the length of the tines than the radius, I would make one with longer tines than necessary, use a computer to generate a reference tone, and then file the tines down until I got a good match.
posted by jedicus at 1:41 PM on January 30

You can make an adjustable tuning fork, which would likely have wider tolerances.
posted by rhizome at 1:52 PM on January 30

I think I've seen brass and aluminum ones...not sure. but pretty sure.

I worked in an instrument shop and we had a really nice one. It was large, I think it was aluminum (perhaps aluminum ones are larger for a given pitch)? It was maybe 6 inches long. It was attached to a wooden box. There was a rubber hammer to hit it with. It had a nice mellow ring that lasted for a while.
posted by sully75 at 1:58 PM on January 30

This pdf has some more dimensions. via here.
posted by zamboni at 2:02 PM on January 30

I happen to have a tuning fork and calipers. Who knew my piano tuning hobby and my B&E hobby might come in handy simultaneously some day? Here's hoping.

The tines have a rectangular (nearly square) cross section. They are .17 inches by .18 inches, with the longer dimension being the one that traverses from one tine to the next.
i.e. the longer direction is as (exaggerated) below:
XXXXX XXXXX
XXXXX XXXXX

The length of the tines is 3.3 inches measured on the inside, and 3.5 inches on the outside. These numbers are somewhat less reliable, since there are curves involved.

It's a 523.3 (key of C) fork made of "hardened and tempered blued steel".
posted by Humanzee at 4:16 PM on January 30 [1 favorite has favorites]

Why don't you just make it a little long and then carefully file it down until it's on pitch? You're never going to be able to make it exactly on pitch just by milling it to mimic the dimensions some dude gave you on the internets. (I'm not sure, but I think the filing method is how they make them for real). As for material: nice ones are made of steel of some kind; cheap ones from lightweight aluminum. If your granddaughter is going to be knocking it around, aluminum is probably adequate; you actually have to be kind of careful with steel forks because they chip easily and get out of tune.

Sounds like a good project. I've always wanted to make a set of forks but never quite found the time when I still had free access to a shop. *sigh*
posted by Commander Rachek at 8:37 PM on January 30

You can make an adjustable tuning fork, which would likely have wider tolerances.

Except they rarely work and they're nearly impossible to calibrate. Absolutely not a replacement for a real fork.
posted by Netzapper at 11:24 PM on January 30

Thank you for all the help. It has been awhile since I've had much practice converting units and plugging numbers into formulas and I wasn't sure of my calculations. I also didn't know how far apart the tines should be.
posted by 14580 at 8:02 PM on January 31

Though I have done no research, I suspect the distance between the tines plays an important role in the sound you hear and the pitch perceived. Additionally, if the tines are not identical, you may get weird interference and hear beats frequencies.
posted by kenbennedy at 12:22 PM on February 2