Proportionality relationships in Mersenne's Law

[Gdurr]

Hello.
Is anyone able to explain the 3 proportionality relationships present in Mersenne's Law, specifically in a conceptual sense? Mathematically they are easier to understand however it is difficult to understand them conceptually relating to strings. Any help would be appreciated.
:)

 

[gtoguy97]

Mersenne's Law states that the length of a vibrating string is inversely proportional to the square root of the tension, and directly proportional to the square root of the linear mass density. This means that if the tension is doubled, the length will be cut in half, and if the linear mass density is doubled, the length will double. The three proportionality relationships present in Mersenne's Law are as follows: 1. Length is inversely proportional to the square root of the tension. This means that as the tension increases, the length of the string decreases in an inverse proportion. 2. Length is directly proportional to the square root of the linear mass density. This means that as the linear mass density increases, the length of the string increases in direct proportion. 3. Length is inversely proportional to the square root of the frequency. This means that as the frequency increases, the length of the string decreases in inverse proportion. These proportionality relationships are important for understanding how different factors affect the length of a vibrating string. By understanding these relationships, musicians can adjust the tension, mass density, and frequency of the strings to create the desired sound.