String Frequencies By Temperature.

[olive5]

I'm working on some physics problems involving sound frequencies with string and wind instruments, and the current problem has the temperature drop from 20deg Celsius, to -12.7deg Celsius. Too my knowledge this problem disregards any wood expanding/contracting done by the instrument by the environment, but only the strings themselves and what frequency they produce by the change in tune. I haven’t been able to find any information on how temperature affects string frequencies... only on how they affect wind instrument frequencies.

Could anybody shed some light onto this topic?

 

[pam]

You would need to find a table of the temperature coefficient of expansion for catgut,
and then a table for Young's modulus for catgut. Then a bit of a calculation would give the result. It is certainly much less of an effect for strings than air.
Actually it wouldn't affect a competent violinist at all. Don't you tune a violin by ear while adjusting the tension, or be beats with a tuning fork if you have a bad ear?

 

[astrokreng]

I can provide information on how temperature affects string frequencies. In general, the frequency of a string is determined by its length, tension, and mass per unit length. Temperature can affect all three of these factors, thus affecting the frequency of the string.

Firstly, temperature can affect the length of a string. As the temperature decreases, the string may contract slightly, resulting in a shorter length. This would lead to a higher frequency of the string. Conversely, as the temperature increases, the string may expand, resulting in a longer length and a lower frequency.

Secondly, temperature can affect the tension of a string. As the temperature decreases, the material of the string may become stiffer, resulting in a higher tension. This would lead to a higher frequency. On the other hand, as the temperature increases, the material may become more flexible, resulting in a lower tension and a lower frequency.

Lastly, temperature can also affect the mass per unit length of a string. As the temperature decreases, the density of the material may increase, resulting in a higher mass per unit length. This would lead to a lower frequency. As the temperature increases, the density may decrease, resulting in a lower mass per unit length and a higher frequency.

In summary, temperature can affect the frequency of a string through its effects on length, tension, and mass per unit length. It is important to consider these factors when studying sound frequencies in instruments, as they can have a significant impact on the resulting sound.