What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 n? the wire is 0.600 m long and has a mass of 5.60 g?

The fundamental frequency of vibration of a string is given by

where
L is the length of the string
T is the tension
is the linear mass density, where m is the mass of the string

Let's start by calculating the mass density of the piano wire in the problem. Its mass is

and its length is L=0.600 m, so its mass density is


Therefore now we have everything to calculate the fundamental frequency of the piano wire. Using T=440 N and the first equation, we find: