Fundamental frequency and tension

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SUMMARY

The discussion centers on calculating the required tension for a guitar string to achieve a fundamental frequency of 388 Hz, given its initial tension of 259 N at a frequency of 429 Hz. The relevant equations include the wave speed equation, v = sqrt(T/u), and the fundamental frequency equation, f1 = v/2L. By substituting the equations and manipulating the ratios of frequencies, the solution can be derived without needing to know the linear mass density or length of the string. The participant successfully resolved their confusion regarding the cancellation of unknowns to find the required tension.

PREREQUISITES
  • Understanding of wave mechanics and fundamental frequency
  • Familiarity with tension and linear mass density concepts
  • Knowledge of algebraic manipulation and substitution methods
  • Basic principles of string instruments and their physics
NEXT STEPS
  • Study the relationship between tension and frequency in stringed instruments
  • Learn about the effects of linear mass density on wave speed
  • Explore the derivation of wave equations in different mediums
  • Investigate practical applications of these principles in instrument tuning
USEFUL FOR

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

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Homework Statement



A guitar string has a fundamental frequency of 429 Hz when its tension is 259 N.
The string is being tuned to a fundamental frequency of 388 Hz. What is the required tension?

Homework Equations



v = sqrt(T/u): where v is the speed, T is the tension and u is the linear mass density
f1 = v/2L: where f1 is the fundamental frequency, v is the speed again and L the length of the string

The Attempt at a Solution



sqrt(T/u) = f1(2L)
sqrt(259/u) = 858L

I tried to use the speed equations to find u or L, which would allow me to calculate the v after and then get the frequency, but I'm still left with 2 unknowns. Am I using the wrong equations to solve this?
 
Physics news on Phys.org
You have two equations, one for f1=429Hz and one for f2=259Hz
Write each one as f=v/2L and substitute for v in terms of T and u
Then do f2/f1=
 
Oh I get it now. It should have been obvious but I was just having trouble with cancelling out the unknown terms. Thanks I managed to get the answer.
 

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