[Waves] Standing waves problem (possibly )

AI Thread Summary
The problem involves calculating the mass of a piano string under tension. Given the string's length of 38.9 cm and tension of 667 N, the fundamental frequency is 440 Hz. The relationship between wavelength, tension, and mass per unit length is crucial for the solution. The incorrect use of equations was noted, specifically confusing the speed of propagation with wavelength. The corrected mass of the string is determined to be approximately 0.0022 kg.
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Homework Statement


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?

Homework Equations


\lambda = vT
\mu = mass/length
v = \sqrt{F/\mu}

The Attempt at a Solution


I don't really know which equations to useI don't know if it's right
For fundamental harmonics, L = \lambda/2
so 0.389m = \lambda/2
\lambda = 0.778m
\lambda = vT
0.778 = \sqrt{F/\mu} (1/440Hz)
0.778 = \sqrt{667/\mu} (1/440Hz)
\mu = 0.00569 = mass / 0.389m
mass = 0.0022kg
 
Last edited:
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Your third equation is incorrect. The square root of F/μ is the speed of propagation v, not the wavelength.
 
oh right. correction!
 
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