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

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SUMMARY

The mass of a vibrating metal wire on a piano can be calculated using the equation m = FL / v², where F is the tension (300.0 N), L is the length of the wire (3.0 m), and v is the wave speed. The fundamental frequency of the wire is given as 27.4 Hz. To find the wave speed, the relationship between frequency and wave speed must be utilized, specifically v = fλ, where λ is the wavelength. The correct calculation yields the total mass of the wire.

PREREQUISITES
  • Understanding of wave mechanics and fundamental frequency
  • Familiarity with tension in strings and its effect on vibration
  • Knowledge of the relationship between frequency, wavelength, and wave speed
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the relationship between frequency and wave speed in vibrating strings
  • Learn about the linear mass density of strings and its calculation
  • Explore the concept of tension and its impact on the frequency of vibrating wires
  • Investigate the use of the wave equation in different mediums
USEFUL FOR

Physics students, music instrument technicians, and anyone interested in the acoustics of stringed instruments will benefit from this discussion.

bobby3280
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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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