To raise the fundamental frequency by a perfect fifth, the tension must increase by a factor of 25.
Fundamental frequency
Since the fundamental frequency of a spring is;
fo= 1/2l√T/M
fo = fundamental frequency
l = length
T = tension
M = mass in kilograms
The fifth overtone frequency = 5fo
So, the fundamental frequency is proportional to the square root of the tension. Hence, to raise the fundamental frequency by a perfect fifth, the tension must increase by a factor of 25.
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