How does changing length and mass affect the frequency of a vibrating string?

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SUMMARY

The frequency of a vibrating string is directly influenced by its length and mass. Specifically, changing the length of the string results in a direct proportionality to the frequency, while altering the mass of the string inversely affects the frequency. This relationship is governed by the fundamental frequency formula for vibrating strings, which can be explored further through resources like the Wikipedia page on vibrating strings.

PREREQUISITES
  • Understanding of basic physics concepts, particularly wave mechanics.
  • Familiarity with the formula for the frequency of a vibrating string.
  • Knowledge of tension and its effects on string vibration.
  • Basic mathematical skills to manipulate formulas.
NEXT STEPS
  • Research the formula for the frequency of a vibrating string, specifically the equation f = (1/2L)√(T/μ).
  • Explore the impact of tension on string frequency and its relationship to mass and length.
  • Investigate practical applications of vibrating strings in musical instruments.
  • Learn about wave properties and how they relate to string vibrations in different mediums.
USEFUL FOR

Physics students, music educators, string instrument makers, and anyone interested in the principles of wave mechanics and vibration theory.

Syzygy271
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I found that if you have a stretched wire under tension that if you

a) change the length the change in frequency is directly proportional to the change in length.

b) change the mass the change in frequency is inversely proportional to the change in mass.

Does anyone know how to back this up with relevant physics? Any useful links?

Thanks.
 
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