Steel Guitar String: Find First 5 Modes, Sketch Eigenfunctions

[scott_uca03]

Homework Statement

A steel guitar string with a diameter of .3 mm and 65 cm long has a tension of 100 N. Find the frequencies of the first five modes of vibration and sketch a graph of the associated eigenfunctions. The density of steel,7700 kg/m^3 is needed to find $$\mu$$.

Homework Equations

I know c^2=T/$$\mu$$. I also know that Fn=nc/2L. I also know the solution to the problem, but I am unsure how to find $$\mu$$ .

The Attempt at a Solution

 

[Brian_C]

Isn't that just the linear mass density of the string? You need to calculate the volume per unit length of the string, then convert it to a mass per unit length. This should be easy because the string is cylindrical.

 

[scott_uca03]

Yea, I've found the volume of the string. I'm unsure how to find the mass though. If I could find the mass I could find the density and that's what I'm looking for to finish the problem.

 

[HallsofIvy]

Use google to find what you don't know! Since you said this is a steel wire, I googled on "density of steel" and found that the density of steel, while it varies slightly with the type of steel, averages around 7.9 grams per cubic centimeter. Multiply by the cross-section area of the string to find the mass per centimeter.

 

[scott_uca03]

Thanks a lot. Put me on the write track and I figured it out.