Mass of a Wire?

Question

The longest "string" (a thick metal wire) on a particular piano is 2.0m long and has a tension of 300.0N. it vibrates with a fundamental freqency of 27.5 Hz.

what is the total mass of the wire?

Answer 1

I get 49.6 grams, which is the mass of ten nickels.

I'll leave the physics and differential equations
to the textbooks and start with f = sqrt(T/mu) / 2L
where f is the frequency 27.5 hertz,
T is the tension 300 newtons,
L is the length 2 meters,
and mu is the greek letter usually used for
mass per unit length of the wire, in kg/m.
This is the usual formulation for vibrating strings.
We'll stay in mks units.

You can do the algebra and solve for mu (easier on
scratch paper than on a keyboard) and should get
mu = T / (f-squared x 4 x L-squared)
= 300 / (27.5 x 27.5 x 4 x 2 x 2) = 300/12100
= 0.0248 kilograms per meter

Times 2 meters equals a total mass of 0.0496 kg.

Answer 2

wn = 2pi*f

where f = 27.5 hz

wn ^ 2 = k/m

where k = the spring constant.

A wire is essentially a cylinder. The spring constant for a cylinder is k = EA/L

Hence, m = EA/[wn^2*L]

You can determine EA from the value of the force

Answer 3

ur name is Trevor too!!