Change guitar string tension and vibration

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SUMMARY

The discussion centers on calculating the percentage change in tension required to adjust a guitar string's vibration frequency from 225 Hz to the desired 220 Hz. The formula used is f = (1/2L)√(T/μ), leading to the derived equation f1/f2 = 1/√k. The user calculated k as 0.956049, indicating a necessary tension change of approximately 4.395%. However, the user is uncertain about the accuracy of this result and seeks clarification on potential errors in their calculations.

PREREQUISITES
  • Understanding of guitar string physics and vibration frequency
  • Familiarity with the formula f = (1/2L)√(T/μ)
  • Basic algebra for manipulating equations
  • Knowledge of percentage calculations
NEXT STEPS
  • Review the derivation of the frequency-tension relationship in string instruments
  • Explore the impact of string length and mass per unit length on frequency
  • Investigate the effects of tension changes on guitar string performance
  • Learn about the significance of precision in frequency measurements
USEFUL FOR

Musicians, guitar technicians, and physics students interested in the mechanics of string instruments and frequency adjustments.

Becca93
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Change in guitar string tension - Please help?

Homework Statement



A particular guitar string is supposed to vibrate at 220 Hz, but it is measured to actually vibrate at 225 Hz. By what percentage should the tension in the string be changed to get the frequency to the correct value? Do not enter units.


Homework Equations



f= (1/2L)√(T/μ)

I solved for 1/2L and got
f1/(√T1) = f2/(√T2)
f1/(√T) = f2/(√kT)

Cancel the √T's, and you're left with
f1/f2 = 1/√k


The Attempt at a Solution



I took
f1 = 225 Hz
f2 = 220 Hz

k = (f2/f1)^2
k = (220/225)^2
k = 0.956049

1-k = 0.04395
Meaning you'd have to change the string by 4.395%

But this is not the right answer.

So far, I've tried the following and none of them have been correct.
4.40
4.60
4.80
4.39

Can anyone please instruct me on what I'm doing wrong?
 
Last edited:
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Did you try it with a negative sign?
 

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