Vibrating Copper

Vibrating Copper
The piano strings that vibrate with the lowest frequency consist of steel ?

wire around which a thick coil of copper wire is wrapped. Only the inner steel wire is under tension. What is the purpose of the copper coil?

The purpose of the “copper coil” is to add mass to the vibrating string so that it will vibrate at a lower frequency than the core wire would produce alone. This is because the frequency of a vibrating string is dependent on three variables, string length, tension, and mass per unit length. The formula for the frequency of a vibrating string is F=1/2L*sqrt(T/u) where F is frequency T is tension L is string length and u is mass per unit length. If you examine the above equation you see that adding mass (making u larger) makes F smaller. Smaller number, lower frequency. You may notice that increasing L or making T smaller lowers the frequency too. These factors have limitations though such as the length of string that can be housed and the need for some tension in the string. Trying to reach the lowest pitches without the added mass of the outer wire wrap would cause the string to go slack.