How do you find the mass of a vibrating metal wire on a piano?

AI Thread Summary
To find the mass of a vibrating metal wire on a piano, the relevant equation is m = FL / v^2, where F is tension, L is length, and v is the velocity of the wave. The tension is given as 300.0 N and the length of the wire is 3.0 m. The fundamental frequency of 27.4 Hz can be used to find the wave velocity using the relationship v = fλ, where λ is the wavelength. After determining the wave velocity, the mass can be calculated. The discussion concludes with the user successfully finding the equation and the answer.
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Homework Statement



The longest "string" (a thick metal wire) on a particular piano is 3.0 m long and has a tension of 300.0 N. It vibrates with a fundamental frequency of 27.4 Hz. What is the total mass of the wire? ( in kg)

Homework Equations



The only relevant equation I could find is v = square root of ( FL / m )
or the linear mass density equations

The Attempt at a Solution



I move m to one side leaving m = FL / v^2 and tried velocity of sound 343 m/s but no luck.

This seems to be the only viable equation to me and I either don't know how to convert 27.4 Hz to velocity or am completely lost.

Thanks for any help
 
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What equations do you have for the frequency of a string under tension?
 
Thanks found the equation and answer.
 

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