# [Waves] Standing waves problem (possibly )

1. Sep 16, 2010

### hiuting

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

Last edited: Sep 16, 2010
2. Sep 16, 2010

### kuruman

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

3. Sep 16, 2010

### hiuting

oh right. correction!