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
Your third equation is incorrect. The square root of F/μ is the speed of propagation v, not the wavelength.