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

by hiuting
Tags: optics, standing waves, waves
 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 $$\lambda$$ = vT $$\mu$$ = mass/length v = $$\sqrt{F/\mu}$$ 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 = $$\lambda$$/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
 PF Patron HW Helper P: 3,440 Your third equation is incorrect. The square root of F/μ is the speed of propagation v, not the wavelength.
 P: 23 oh right. correction!

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