Calculating the tension required for vibrating wire to get frequency? Watch

OJ Emporium
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"A piano repairer replaces the wire that produces the highest note on a piano. The wire has a vibrating length of 0.050 m. He uses a wire with the following properties.
diameter = 3.5e-4 metres
density = 7.8e+3 kilogram per metres cubed
breaking stress = 3e+9 Newton per metres squared

Calculate the tension required for the vibrating wire to produce its correct frequency of 4.1 kHz."

What I did:
Got the equation for the frequency being  f = \frac{1}{2l} \sqrt\frac{{T}}{{\mu}}
Last edited by OJ Emporium; 3 days ago
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Teenie2
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The volume of the string is πr2 ℓ. where r = radius of the wire (half the diameter), and ℓ = length of the wire.
Then the mass per unit length, µ = ρV/ℓ . From there, you can plug your values into your equation and should get a value for T.
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