Thermal Expansion of piano wire

[Ambulatourer]

I'd like to setup an Excel spreadsheet to demonstrate the expected change in string frequency due to small changes in temperature. How should I go about doing this?

This is the data from the piano that I can gather:
-string length
-string diameter
-string area
-string/partial frequency

How do I put this information together to show how, for example, a 1 degree increase in temperature will effect a pitch change in cents across the entire piano? There are other parts like the wood and the iron frame that also expand, but I'm not so concerned with those aspects at the moment. I would like to be able to compare what the strings should do in isolation, with what I can observe directly from the piano under different conditions.

At the piano, I normally observe a 0.2-0.3 cent decrease for a 1 degree increase in temperature around A4. I would like to be able to predict exactly what it should be for each note.

Any help would be greatly appreciated!

 

[Simon Bridge]

The important factor will be the length - since the string is very long compared to it's diameter.
You will also need the thermal coefficient of length expansion for the wire... most wires are under tension, changing the "length" will not change the length of the wire on the frame, but will change how tightly it fits over the frame. So you need youngs modulus, and how that turns the wire into a spring - though you can get the spring constant by measuring.

The tension affects the speed of sound on the wire, the frame fixes the wavelength, so you get the frequency from ##v=f\lambda##.

i.e. you need more physics than you are considering.

Also see:
https://www.physicsforums.com/threads/calculate-a-thermal-expansion-pitch-change.250590/