What is Mersenne's Law and its connection to Pythagoras?

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Mersenne's Law describes the relationship between the fundamental frequency of a vibrating string and its tension, length, and mass per unit length. It states that the frequency is proportional to the square root of the tension and inversely proportional to both the length and the square root of the mass. The discussion also touches on Mersenne primes, highlighting the connection to the mathematician Marin Mersenne. Additionally, there is a reference to Pythagoras, suggesting he expressed similar concepts regarding frequency and vibration. Understanding these principles is essential for exploring the mathematical foundations of sound and music.
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Can someone please explain what Mersenne's Law is?
 
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mechanics) The fundamental frequency of a vibrating string is proportional to the square root of the tension and inversely proportional both to the length and the square root of the mass per unit length.
Above from a google search - you can get a lot more by doing it yourself.
 
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Interesting that Mersenne gets the credit for that. Pythagoras said something very similar if I recall.
 

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