Understanding Velocity in Waves

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Homework Statement

I was told that a string on a guitar vibrates at a frequency of 110 Hz. The length of the string is .648 m and the tension is 100 N. I was told to find the mass per unit length, μ, of the string. Although I got the correct answer, I was wondering why my initial attempt was incorrect (shown below).

Homework Equations

$f_{n}$ = $\frac{n}{2L}v$

$v$ = $\sqrt{\frac{T}{μ}}$

The Attempt at a Solution

(Sorry for the formatting, I don't type in latex really quickly).

In this case, if it's a guitar, why is the velocity of the wave not equivalent to 345 m/s (343.2 m/s)? Why is it so much lower (142.56 m/s)?

Thank you.

 

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Oh, is the velocity referring to the velocity of the vibrating string?

I think I understand now.