Calculating Wave Velocity, Mass, and Wavelength of a Guitar String

[BuBbLeS01]

Homework Statement

A. A typical steel B-string in a guitar resonates in its fundamental frequency at 240 Hz. The length of the string is 0.680 m. What is the wave velocity in the string?

B. The tension in the above string is 86.8 N. Calculate the mass of a 2 m long piece of the steel string.

C. What is the wavelength of the third harmonic of the guitar string described above?

Homework Equations

f = v/2L
Wavelength = 2L/m

The Attempt at a Solution

A. 326.4
How do I calculate B and C??

 

[rl.bhat]

B. In stretched string velocity v = sqrt(T/m) where T is the tentsion and m is the mass per unit length of the wire.
CDuring the third harminc the number of loops in the string will be 3.

 

[BuBbLeS01]

I am sorry but I don't understand how to calculate B still.

 

[BuBbLeS01]

Does anyone know how to do these?

 

[BuBbLeS01]

Anyone? I need help :( I'm not figuring this out...

 

[rl.bhat]

v = sqrt(T/m)
326.4 = sqrt(86.8/m). Square both the sides
326.4^2 = 86.8/m
m= 86.8/326.4^2
Mass of 2 m wire = 2m
Now solve.

 

[BuBbLeS01]

Okay so I get 0.00163 kg...how about part C?

 

[BuBbLeS01]

I get 834.87 for part C using wavelength = 2L/m

 

[rl.bhat]

I get 834.87 for part C using wavelength = 2L/m

Wave length of third harmonic = 2L/3