Fundamental frequency of a guitar string

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SUMMARY

The fundamental frequency of a guitar string can be calculated using the formula f = sqrt(T/(m/L)) * 1/(2L). In this discussion, a guitar string measuring 78 cm in length and weighing 3.6 g is under a tension of 505 N. The effective length used for the calculation is 60 cm, leading to an adjusted mass of 2.769 g. After correcting for mass, the frequency is determined to be 465 Hz, indicating the importance of using the correct parameters in the formula.

PREREQUISITES
  • Understanding of wave mechanics and frequency calculations
  • Familiarity with the tension formula in string physics
  • Basic knowledge of mass and length relationships in physics
  • Proficiency in using square root and division operations
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  • Study the derivation of the wave equation for vibrating strings
  • Learn about the effects of tension and mass on frequency in string instruments
  • Explore the concept of harmonics and overtones in string theory
  • Investigate the impact of string length on pitch and sound quality
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Musicians, physics students, and guitar makers interested in understanding the acoustics of string instruments and the calculations involved in determining fundamental frequencies.

raw_rock7
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1. The problem is: A guitar string is 78 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 60 cm, and the string is under a tension of 505 N. What is the frequency of the fundamental?
I don't get why it gives me two distances. Which one is L?



2. The equations I've been using haven't been working, so this is pretty much my problem.



3. When I plugged values into the equation f= sqrt(T/(m/L)) * 1/(2L), I got the answer of 241.762 Hz
 
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I don't know much about this, but I wonder if there is a little trick in the mass.
It looks like you are only using 60 cm of a 78 cm string with mass 3.6g. So the mass you want to use in the formula would be 60/78*3.6 g.

I get 465 Hz with that small adjustment, which makes me think you made an error in your calculator work - or I did!
 

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