Effect of temperature on vibrational frequency of a violin string

[ean514]

Homework Statement

How does temperature affect the vibrational frequency/pitch of a violin string?
What would be the methodology to determine this experimentally?

I'm planning on doing my physics IA (internal assessment-- basically a high-school level independent investigation) on the relationship between temperature and the frequency of a violin string. I'm wondering if my methodology would work in determining this, and possible ways to extend my investigation as it is pretty simple at the moment.

Relevant Equations

T=kx

Variables:
Dependent: Vibrational frequency of violin string (Measured using mobile tuning app)
Independent: Temperature in which string is plucked (Measured using infrared thermometer)
Controlled: Violin String, Tension of violin string, Length of violin string, Method of plucking violin string, Insulation of system

Methodology:

• Apparatus: The two ends of the violin string will be fixed with a constant tension in a styrofoam box. The violin string will be marked in the middle (at the antinode), as to ensure the string is plucked at the same place each trial.
• Method: The apparatus will be put in different temperatures; I plan on obtaining data across temperatures of -20 degrees celsius ~ +40 degrees celsius. Colder temperatures will be obtained by placing the apparatus outside/in the snow, whereas warmer temperatures will be obtained using a heater/blow-dryer. The temperatures inside the apparatus will be measured using an infrared thermometer. The string will then be plucked at the marked point, and the resulting frequency will be measured using a mobile sound app.

I am concerned about the simplicity of my investigation, and that I do not have many calculations/numerical data processing given my current methodology.

My teacher has suggested that I could potentially link my investigation to the speed of sound, but I am a bit lost as to how to go about in doing this.

Would there be any way to explore my topic in greater depth? (ie. speed of sound, altering method, etc.)

 

[Chestermiller]

https://www.physicsforums.com/threa...th-change-in-temperature.833185/#post-5232551

 

[Steve4Physics]

Controlled: Violin String, Tension of violin string, Length of violin string, Method of plucking violin string, Insulation of system

Hi @ean514.

Some things to consider...

If the string’s length and tension are both somehow kept accurately constant, why do you think the frequency should change?

Is it possible to keep the string’s tension and length accurately constant if the temperature changes? Remember, the string will expand/contract as temperature changes (and so will the apparatus holding it).

And a practical problem - how will you measure the temperature of the string given that an infrared thermometer will also pick up infrared radiation from the surroundings as well as from the string?

 

[ean514]

Hi @ean514.

Some things to consider...

If the string’s length and tension are both somehow kept accurately constant, why do you think the frequency should change?

Is it possible to keep the string’s tension and length accurately constant if the temperature changes? Remember, the string will expand/contract as temperature changes (and so will the apparatus holding it).

And a practical problem - how will you measure the temperature of the string given that an infrared thermometer will also pick up infrared radiation from the surroundings as well as from the string?

Thank you for the pointers.

I was planning on using the same string across all my trials/temperatures, hence the "constant" initial length.
The string/apparatus would expand/contract as a result of change in temperature, and hence the frequency would change.

This investigation was prompted by my observations of changes in pitch when playing my violin outdoors versus indoors-- as there are much more variables to consider when using an actual violin in the experiment, I attempted to simulate it using just the string and a styrofoam box/some sort of container to isolate the system to an extent. Would there be a better way to set up the experiment?

 

[kuruman]

As @Steve4Physics remarked

If the string’s length and tension are both somehow kept accurately constant, why do you think the frequency should change?

As a concert-goer, my question to you is why do the orchestra musicians tune their instruments after they enter the concert hall? Why not do it backstage and then start playing as soon as they come on stage?
Yes, the temperature of the air in the concert hall is expected to be higher than backstage (each attendee put out the heat of about a 100 W light bulb) and more humid with said attendees breathing which affects the speed of sound in the hall. Nevertheless, a string that vibrates at 440 Hz in cool and dry air will vibrate at the same frequency in warm and humid air unless $~\dots~$ back to @Steve4Physics's remark.

Why do you think a styrofoam box is a good model for a violin and why the need for isolation? You are confusing physical modeling with mathematical modeling. Prior to a concert, the orchestra musicians tune their instruments to the first violin not to the first styrofoam box. I recommend that you use your actual violin to take measurements and then model the violin mathematically as a string stretched between two points on a piece of spruce. Do some calculations to guide your thinking about the size of the effect to expect and whether you have what you need to measure it.

 

[Steve4Physics]

Thank you for the pointers.

I was planning on using the same string across all my trials/temperatures, hence the "constant" initial length.
The string/apparatus would expand/contract as a result of change in temperature, and hence the frequency would change.

This investigation was prompted by my observations of changes in pitch when playing my violin outdoors versus indoors-- as there are much more variables to consider when using an actual violin in the experiment, I attempted to simulate it using just the string and a styrofoam box/some sort of container to isolate the system to an extent. Would there be a better way to set up the experiment?

Have you done any preliminary trials/measurements to check that you can get some sensible results? What happened?

I notethat this is ‘high school’ level, but it’s not clear how much of the relevant background physics you are familiar with.

There are 3 key factors that determine the frequency of a vibrating string. Can you say what they are? Each of these factors is affected by temperature. Their combined effect would be quite difficult to analyse but an attempt it might be possible if your physics and maths are good.