How to derive Mersenne's fundamental frequency formula?

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SUMMARY

The discussion centers on deriving Marin Mersenne's formula for fundamental frequency, specifically equation 22. Key variables include L (length), F (force), μ (mass per unit length), and f (frequency). Participants seek clarity on the derivation process and the foundational principles required to understand the formula. The conversation highlights the importance of specifying the source material for accurate derivation.

PREREQUISITES
  • Understanding of basic physics concepts, particularly wave mechanics.
  • Familiarity with Mersenne's laws related to vibrating strings.
  • Knowledge of mathematical derivation techniques.
  • Proficiency in manipulating equations involving force, mass, and frequency.
NEXT STEPS
  • Research Mersenne's laws and their applications in acoustics.
  • Study the relationship between tension, mass per unit length, and frequency in vibrating strings.
  • Explore mathematical techniques for deriving formulas in physics.
  • Examine examples of fundamental frequency calculations in musical instruments.
USEFUL FOR

Students of physics, music theorists, and anyone interested in the mathematical foundations of sound and vibration will benefit from this discussion.

Mars Yeung
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I'm talking about equation 22,

0b75c5b7c37b54308041f081ba61edd5.png


Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it.

L would be the length, F would be force, and μ would be mass per unit length.
f is the frequency

Thanks
 
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I don't know your source. Can you specify what is given to derive it from?
 

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