- #1

Sethius

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## Homework Statement

A particular guitar string is supposed to vibrate at 217 Hz, but it is measured to actually vibrate at 222 Hz. By what percentage should the tension in the string be changed to get the frequency to the correct value? Do not enter units.

## Homework Equations

f=[itex]\frac{1}{2L}[/itex][itex]\sqrt{\frac{T}{\mu}}[/itex]

L=string length

T=Tension

[itex]\mu[/itex]=Linear Density

## The Attempt at a Solution

I know that frequency is proportional to the square root of tension given that all other factors remain constant. I solved two frequency equations for [itex]\frac{1}{2L}[/itex] and set them equal to each other with my T[itex]_{2}[/itex]being multiplied by a variable "k" being the conversion factor. my equation looked like this:

[itex]\frac{f_{1}}{\sqrt{T_{1}}}[/itex]=[itex]\frac{f_{2}}{\sqrt{kT_{2}}}[/itex]

I then canceled the [itex]\sqrt{T}[/itex]'s and ended up with [itex]\frac{f_{1}}{f_{2}}[/itex]=[itex]\frac{1}{\sqrt{k}}[/itex]. Solving for k I get 1.0466 which would equal a 4.66% increase in tension however this answer isn't correct. Thank you for any help