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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

[tex]\lambda[/tex] = vT

[tex]\mu[/tex] = mass/length

v = [tex]\sqrt{F/\mu}[/tex]

## 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

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