A simple question: you have an acoustic guitar with a 20 inch scale and tune it to say E. Now transfer the string to a 25 inch scale and retune it to E. By what percentage would the tension increase?
The square of the frequency of a vibrating string is directly proportional to the tension, and inversely proportional to the square of the length of the string. So, for two strings of identical composition vibrating at the same frequency:
T2 = (L22 / L12) * T1.
For L1 = 20in and L2 = 25in, we have L2 = 1.25 * L1, or L22 = 1.5625 * L12. This means that:
T2 = 1.5625 * T1 = (1 + 0.5625) * T1.
The tension in the 25 inch string is 56.25% higher than the tension in the 20 inch string. Hmmm, in retrospect, you probably should have asked this over at the SE Physics site.