How Much Does a Guitar String Stretch Under Tension?

[Jaklynn429]

Homework Statement

A 76 cm long, 1.0 mm diameter steel guitar string must be tightened to a tension of 2200 N by turning the tuning screws. By how much is the string stretched?

Homework Equations

F=kx
K=YA/L

The Attempt at a Solution

I don't know how to approach this problem because I feel like I don't have everything i need! I know that F=2200N. but How do i get K to find delta x?

 

[CompuChip]

What is Y? What does it depend on?

 

[Jaklynn429]

Y is Young's Modulus, which in my notes is just referred to as a measure of the substances inherent stiffness, and i don't know where to get this...

 

[LowlyPion]

Y is Young's Modulus, which in my notes is just referred to as a measure of the substances inherent stiffness, and i don't know where to get this...

Youngs modulus is a little more than that.
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html#c2

 

[Jaklynn429]

I understand that, but how is this going to help me in my problem? I'm sorry if I sound stupid...

 

[LowlyPion]

I understand that, but how is this going to help me in my problem? I'm sorry if I sound stupid...

Look at the formula for Young's modulus

Y = \frac{Stress}{Strain} = \frac{F/A}{\Delta L/L}

 

[Jaklynn429]

Would the stress be 2200 then?

 

[LowlyPion]

Would the stress be 2200 then?

No. But the Force 2200 N divided by the cross sectional area of a 1 mm diameter string would be though.

 

[HallsofIvy]

This website, http://en.wikipedia.org/wiki/Young's_modulus, gives Young's modulus for a variety of materials, including steel.

 

[Jaklynn429]

Okay. So now i have y=200. yay! So now i need area A which is [im assuming?] l*w? So .76*.001=A?

 

[LowlyPion]

Okay. So now i have y=200. yay! So now i need area A which is [im assuming?] l*w? So .76*.001=A?

A is cross section = π*R² = π*(.5*10^-3)²

.76m is your L

 

[LowlyPion]

Okay. So now i have y=200. yay! So now i need area A which is [im assuming?] l*w? So .76*.001=A?

By the way Y is 200 * 10⁹N/m²

 

[Jaklynn429]

I got my final answer to be .0106. Is this in meters, then? Do I need to convert to centimeters?

 

[Jaklynn429]

I figured it out, converted to CM and got my final answer as 1.06 cm, and it was right! Thank you so much for all your help!

 

[LowlyPion]

I figured it out, converted to CM and got my final answer as 1.06 cm, and it was right! Thank you so much for all your help!

Hope you didn't get too stressed or that it was too much of a strain.

Cheers

 

[CompuChip]

* grins at Pions puns *

Jaklynn, try to keep the units throughout your calculation, you can just consider them as ordinary variables. For example, if you try to do (0.76 m) * (0.001 m^2) you will get 0.00076 m^3. But m^3 is a unit of volume, not of area.
Similarly, if you forget converting something, you will end up with something like: cm * m, instead of m * m = m^2. This makes it easier to spot your errors beforehand.