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[Waves] Standing waves problem (possibly...)

by hiuting
Tags: optics, standing waves, waves
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Sep16-10, 09:14 PM
P: 23
1. The problem statement, all variables and given/known data
The A-string (440Hz) on a piano is 38.9cm long and is clamped tightly at both ends. If the string is under 667-N tension, what is its mass?

2. Relevant equations
[tex]\lambda[/tex] = vT
[tex]\mu[/tex] = mass/length
v = [tex]\sqrt{F/\mu}[/tex]

3. The attempt at a solution
I don't really know which equations to use

I don't know if it's right
For fundamental harmonics, L = [tex]\lambda[/tex]/2
so 0.389m = [tex]\lambda[/tex]/2
[tex]\lambda[/tex] = 0.778m
[tex]\lambda[/tex] = vT
0.778 = [tex]\sqrt{F/\mu}[/tex] (1/440Hz)
0.778 = [tex]\sqrt{667/\mu}[/tex] (1/440Hz)
[tex]\mu[/tex] = 0.00569 = mass / 0.389m
mass = 0.0022kg
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Sep16-10, 09:45 PM
HW Helper
PF Gold
kuruman's Avatar
P: 3,440
Your third equation is incorrect. The square root of F/μ is the speed of propagation v, not the wavelength.
Sep16-10, 09:58 PM
P: 23
oh right. correction!

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