Chapter 11, Problem 19Q

Why do the strings used for the lowest-frequency notes on a piano normally have wire wrapped around them?

To determine

Why do the strings used for the lowest-frequency notes on a piano normally have wire wrapped around them?

Answer to Problem 19Q

Solution:

The mass of the string is greatly increased without changing the length or the tension of the string, which produces a low fundamental frequency on it.

Explanation of Solution

Considering two steel strings of equal length and subjected to the same tension, the string of higher mass will have a lower resonance frequency.

By wrapping the string with wire, we can get a great increase of the mass of the string without changing the length or the tension of the string, and thus the string has a low fundamental frequency.

We can explain this mathematically, using the equation of the fundamental frequency of oscillation for a string with both ends fixed and the formula of the speed of waves on the string, which are combined in order to get the new frequency.