How tightening a string affects frequency?

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SUMMARY

Tightening a string increases its tension, which directly affects the frequency of the note produced. According to the physics of standing waves, the fundamental frequency (f) is inversely proportional to the length (L) of the string and directly proportional to the square root of the tension (T). The formula f = (1/2L)√(T/μ) illustrates this relationship, where μ is the linear mass density of the string. Therefore, tightening a string decreases its wavelength while increasing its frequency, contrary to the initial assumption presented in the discussion.

PREREQUISITES
  • Understanding of fundamental frequency in wave mechanics
  • Knowledge of standing wave principles
  • Familiarity with the formula f = (1/2L)√(T/μ)
  • Basic concepts of tension and linear mass density in strings
NEXT STEPS
  • Research the relationship between tension and frequency in string instruments
  • Explore the effects of string length on pitch in musical acoustics
  • Study the concept of linear mass density and its impact on wave speed
  • Learn about harmonic frequencies and their applications in stringed instruments
USEFUL FOR

Musicians, physics students, and educators interested in the acoustics of string instruments and the mathematical relationships governing sound production.

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Homework Statement


How does tightening or loosening a string affect the frequency of the note? make specific references to the relationship between fundamental frequency and the standing wave in the string.

Use mathematical arguments from physics to demonstrate the relationships between the variables that you include in your answer.

Homework Equations



None as far as I know

The Attempt at a Solution



I figure that tightening the string increases wavelength, but decreases frequency. I don't know how to incorporate fundamental frequency and standing waves.
 
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Have you ever played the guitar, by any chance? If so, think about how you tune it!

As for the mathematical / physical argument: do you happen to know of any formulas that relate length to frequency? (Or something else to frequency, with a standing wave)?
 

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