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myrek
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Homework Statement
A guitarist has a problem that the E-string (330Hz) often breaks when tuning it. The string is made of Copper and it has a diameter of 0.3mm. After some quick calculations based on the length of the guitar neck we can determine that the wave velocity is 530m/s
It is known that string on musical instruments often break if the tension exceeds 2% what advice would you give the guitarist to avoid breaking the strings?
Homework Equations
I'm not sure what to calculate using youngs modulus.
The Attempt at a Solution
I have been battling this problem for some time and I'm not sure exactly what the "answer" should be. I have approached it the following way.
first I calculated the wave length
λ=v/f, λ=530/330, λ=1.6m
I then know that the length of the string is
L=λ/2, L=0.8m
since I know the length and diameter of the wire i looked up the density and calculated the mass of the string according to the following calculation
m=A*L*ρ
m= (∏*0.00015*0.00015)*0.8*8900
m=5.03E-4 kg
I then calculated the linear mass density according to formula μ= 5.03E-4 /0.8
μ=6.29E-4 kg/m
finally I can calculate the string tension
F=v2*μ
F=530*530*6.29E-4 = 177N
So now I know that the string tension is 177N. I'm not sure exactly what to do with it.
my prof gave me the tip to use youngs modulus.
I looked up youngs modulus for Cu to be 120GPa.
The equation looks like Y = (F/A)/(ΔL/L)
but I'm not sure exactly what answer he is looking for. I think ΔL/L = 1.02 because of the maximum tension allowed is 2%
Should I rearrange the equation to see which stress is required to extend the wire 2%?
Any help appreciated.