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**1. The problem statement, all variables, and given/known data**

So I'm doing an IB extended essay on the relationship between frequency and tension of a violin string. As you apply more tension to the string (using weights and pulley), the frequency will be higher, as shown below. There's not too much problem with collecting data, but I'm worried about the simplicity of the topic.

## Homework Equations

v=wavespeed

T= tension force

u= linear density

k= spring constant

x=change length of string

f=frequency

L=lenght of string

v=sqrt (T/u)

f=sqrt (T/u)/2L

T=kx

## The Attempt at a Solution

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What I want to do to better the depth of the investigation is to use the fact that linear density changes with tension, though minimally, so the equation below may not be entirely accurate.

So linear density would increase:

u=m/(L+x)= m/(L+T/k)

which means the frequency would change:

f= sqrt [T*(L+T/k)/m] /2L

meaning tension will increase slightly more than what we predict with the initial linear density.

Is this correct? and is there a way to further explore my topic in more depth? like any more limitations of the mersenne's law and such.. Thank you!