# Thermal Expansion of piano wire

• Ambulatourer
In summary, the conversation discusses setting up an Excel spreadsheet to demonstrate the expected change in string frequency due to temperature changes on a piano. The main focus is on the length and diameter of the strings, their thermal coefficient of expansion, and the tension and speed of sound on the wire. The goal is to accurately predict the pitch change for each note on the piano under different temperature conditions. Additional physics knowledge may be needed to fully understand and accurately calculate these changes.
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!

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:

## 1. What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature. This occurs because as the temperature increases, the particles within a material begin to vibrate more, causing the material to expand. When the temperature decreases, the particles vibrate less and the material contracts.

## 2. How does thermal expansion affect piano wire?

Piano wire is made of steel, which is known to have a relatively high coefficient of thermal expansion. This means that it expands and contracts significantly with changes in temperature. As the temperature increases, piano wire will expand and become longer, and as the temperature decreases, it will contract and become shorter.

## 3. What factors can affect the thermal expansion of piano wire?

The amount of thermal expansion in piano wire is affected by several factors, including the composition and structure of the wire, the temperature range it is exposed to, and the length and diameter of the wire. It can also be influenced by external factors such as tension and stress placed on the wire.

## 4. How does thermal expansion impact the tuning of a piano?

The thermal expansion of piano wire can cause changes in the tension of the strings, which in turn can affect the tuning of a piano. As the temperature changes, the strings may tighten or loosen, causing the pitch of the notes to change. This is why pianos need to be regularly tuned, especially in environments with significant temperature fluctuations.

## 5. Can thermal expansion cause damage to piano wire?

Yes, thermal expansion can cause damage to piano wire if the temperature changes are too extreme or sudden. This can lead to the wire becoming overstretched or breaking. To prevent this, pianos are typically kept in climate-controlled environments to minimize temperature fluctuations and protect the delicate piano wire.

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