Thread: Stringbed frequency to monitor string tension

1. Good news re CarlTune, the developers listened to our complaints and the latest most recent update today has restored sensitivity to previous level.

2. Originally Posted by visor
Good news re CarlTune, the developers listened to our complaints and the latest most recent update today has restored sensitivity to previous level.
great stuff, I like how it leaves the reading on screen so I'll get that update.

3. ZM62 mx60 1260hz. manual drop weight and freshly strung so cannot count it, but that frequency is very high for 21/23lbs!

4. Originally Posted by DuckFeet
ZM62 mx60 1260hz. manual drop weight and freshly strung so cannot count it, but that frequency is very high for 21/23lbs!
just wait, it'll stabilize lower after a few days of play to around 1100-1130 Hz

5. freshly strung zm62 at 23x24 lbs, 1210 Hz
after overnight, 1190 Hz
after 2 hrs play, 1170 Hz

compared to 22x23 lbs, which has now stabilized around 1130 Hz after several weeks of play

6. @kwun @Mark A @blableblibloblu

So, I had some free time yesterday and while explaining stringbed frequency to stringtehcno, I discovered an interesting relationship between 2 different tensions of the same string.

From http://en.wikipedia.org/wiki/Vibrating_string , we kmow that there are only 3 variables that affect stringbed frequency :

Where:
is the tension,
is the linear density (that is, the mass per unit length) ie. string thickness
is the length of the vibrating part of the string.

Therefore:
- the shorter the string, the higher the frequency
- the higher the tension, the higher the frequency
- the lighter (ie thinner) the string, the higher the frequency

There's also an interesting relationship between frequency and tension in that formula. If one is comparing the same string at two different tensions, then is constant and can also be considered constant (since the few cms in length difference at various tensions are negligible relative to the total length of string), then we can see that we can relate the two frequencies by

f1 / f2 = √(T1/T2)

or

f1 = f2 x √(T1/T2)

Hence, two tensions are also then related by

T1 / T2 = (f1 / f2)²

or

T1 = T2 x (f1 / f2)²

So, now we can easily calculate or predict what the tension or frequency is or should be at any given frequency or tension for any particular string.

7. Originally Posted by visor
@kwun @Mark A @blableblibloblu

So, I had some free time yesterday and while explaining stringbed frequency to stringtehcno, I discovered an interesting relationship between 2 different tensions of the same string.

From http://en.wikipedia.org/wiki/Vibrating_string , we kmow that there are only 3 variables that affect stringbed frequency :

Where:
is the tension,
is the linear density (that is, the mass per unit length) ie. string thickness
is the length of the vibrating part of the string.

Therefore:
- the shorter the string, the higher the frequency
- the higher the tension, the higher the frequency
- the lighter (ie thinner) the string, the higher the frequency

There's also an interesting relationship between frequency and tension in that formula. If one is comparing the same string at two different tensions, then is constant and can also be considered constant (since the few cms in length difference at various tensions are negligible relative to the total length of string), then we can see that we can relate the two frequencies by

f1 / f2 = √(T1/T2)

or

f1 = f2 x √(T1/T2)

Hence, two tensions are also then related by

T1 / T2 = (f1 / f2)²

or

T1 = T2 x (f1 / f2)²

So, now we can easily calculate or predict what the tension or frequency is or should be at any given frequency or tension for any particular string.
Ahh - formulas (ae?).

It'll be interesting to see how this maps to real life (and we've got to dial in some way to account for "up-time", too).

8. ^ But the interesting thing is that if you know one tension measures a particular frequency, then if you measured a lower frequency a few weeks later, then you can calculate exactly what that lower tension is.

So take one of my readings for zm62 for example. 1210 Hz out of the machine at 23x24 lbs, ends up 1130 Hz after 3 wks of playing. That means it has become 20.9 lbs.

Or if we allow it to rest and stabilize after stringing, after 1 day with no playing it measured 1180 Hz and take that as 24 lbs, then 1130 Hz after 3 wks of playing becomes 22.0 lbs.

Formulas (ae? ) don't lie.

9. will have to put those formulas to the test!

The string stiffness thread is also interesting.

I'm still shocked by the stiffness results from that other thread (microlegend being so stiff)

10. 0.70 done a couple of weeks ago ringing at 1100Hz. I know it's a hard string depending on who you ask, if this is even relevant, but I still think this is too high for 24x26 progressive on Victor 80 hole. Old Victor pattern I think.

Thoughts? I bought a scale which seems accurate to +/-5g or so to test. Even if that is half a pound out it's a rough guide.

My 26lb squash attempt 'felt like 32'

11. I thought I might add something to this discussion I don't know if this paper has been mentioned here, but you can calculate the actual string tension on any racket. It's very accurate but also very sensitive to the variables so it can be hard to get measurements. If you do it right though you know the true tension accross different rackets.

In the appendix what the paper shows is that a string bed can be modelled as an elastic membrane. Such a membrane's vibrational frequency depends on its mass and surface area while shape has very little effect (useful for us). If you take a square membrane, it vibrates at the same frequency as the average of many independant strings layed out in the same shape, which is much simpler to model. They verified this was also the case with an eliptical membrane, within 1%. So you can take advantage of that and turn it into:

All SI units, so f being frequency in hz, T being string tension in Newtons, μ being string mass per unit length in kg/m and L being string length in m, which in this case is (closely) approximated by:

A being the area of the racket head.

So there are three things you need to measure at least reasonably accurately.

- Frequency
- The area of the racket head (close to the outside edge)
- Mass of that type of string

That's all you need but I've found it hard to hunt down string mass. Frequency we can all do given this thread Area of a racket is bit fidley with isometric heads but at least you can pull out a tape measure and get something close. String mass is really important and I've tried finding manufacturer specs to no avail. I suppose those of you who are stringers can just weight a piece.

Anyway, let's do an example. I just got a VT7 (yeah, I'm no pro) and specified to string with BG80 @ 23 lbs. The frequency is close to 1050 hz. A casual measurement of the racket seems to give an area of about 392 cm^2 or 0.0392 m^2, which makes L = 0.198 m. I don't have an accurate value for string mass because I'm not about to cut the string off I can at least approximate for illustrative purposes though. I read that stringing a racket adds somewhere around 4-6 g to the racket and by my estimate it's around 9 m of string or so. That gives a string mass of roughly 0.55 grams per meter or 0.00055 kg/m. Here's a rearrangement:

So,

Giving us a force of 95.1 N of tension. 95.1 N / 9.8 N/kg = 9.7 kg equivalent down here on earth Or 21.34 lbs. The only problem is the huge error on my area/string numbers. It's probably 21.34 +/- at least 20%. Gotta get some good measurements. Any volunteers?

There's another paper floating around that has excellent data on tension loss over time but I can't seem to find it right now. I hope someone found this interesting

12. @Lieu201

Wow, tks! Very interesting indeed!

I'm not accessible to do the recalculation at the moment, but BG80 is 3.5g and length is approx 9.1m on the racket. We'll need a stringer to help us nail down accurately on the length.

How the fundamental frequency of a vibrating string depends on the string's length, tension, and mass per unit length is described by three laws:
1. The fundamental frequency of a vibrating string is inversely proportional to its length.
Reducing the length of a vibrating string by one-half will double its frequency, raising the pitch by one octave, if the tension remains the same.
2. The fundamental frequency of a vibrating string is directly proportional to the square root of the tension.
Increasing the tension of a vibrating string raises the frequency; if the tension is made four times as great, the frequency is doubled, and the pitch is raised by one octave.
3. The fundamental frequency of a vibrating string is inversely proportional to the square root of the mass per unit length.
This means that of two strings of the same material and with the same length and tension, the thicker string has the lower fundamental frequency. If the mass per unit length of one string is four times that of the other, the thicker string has a fundamental frequency one-half that of the thinner string and produces a tone one octave lower.

Source :
http://science.howstuffworks.com/sound-info4.htm

14. Frequency: ~1194Hz
Racket head area: 54 inch^2 (manufacturer data; TC700)
String mass NBG98: ? (two piece 22x22 instead of 22x23 as recommended)

= tension?

Just installed a few tuner apps on windows phone and very hard to get a reading. Across three or four of them this number roughly pops up (1192-1198 spotted along a host of nonsensical ones at ~max sensitivity). Accurate Tuner is supposed to be the best one and it (painstakingly) gives 1194-1195Hz.
Taken from a long lost/misplaced (back of the closet) racket that was strung 3 years ago (@ iirc 13x14KG) and has never been used apart from a few short serves and wall hits at home after it should have settled down a bit

15. Originally Posted by demolidor
Frequency: ~1194Hz
Racket head area: 54 inch^2 (manufacturer data; TC700)
String mass NBG98: ? (two piece 22x22 instead of 22x23 as recommended)

= tension?
Not sure about racquet head Area as I don't measure it but 24lbs?

16. i'm gonna guess 26 lbs if that frequency is right off the stringing machine

or 28 lbs initially if that frequency is on a racket that's strung more than 2 weeks ago

17. Originally Posted by DuckFeet
Not sure about racquet head Area as I don't measure it but 24lbs?
Mizuno had listed it as 54 inch^2 for this model and 56 for their (more) conventional isometric shaped models.

Originally Posted by visor
i'm gonna guess 26 lbs if that frequency is right off the stringing machine

or 28 lbs initially if that frequency is on a racket that's strung more than 2 weeks ago
"3 years ago" (strung at 13x14kg or 29x31lbs). Thought it might be of interest in the tension holding capacity but I will try to re-measure with the PC software Mark mentioned.
To press it still feels pretty tight, comparable to BG80 at 28 or 29lbs ... so 26 might be close. Kwun listed a NBG98 at 26 with around the same frequency I saw somewhere above (so 24x26 actually it was).

This is what I am working with atm (has to be set at max sensitivity to pick up the sound and as you can see this has certain consequences )

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