[Waves] Standing waves problem (possibly )

[hiuting]

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

 

[kuruman]

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

 

[hiuting]

oh right. correction!