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by what factor would a string’s tension need to be changed to raise its fundamental frequency by a perfect fifth?

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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.

Learn more about fundamental frequency; https://brainly.com/question/25694821

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