In music, two notes are said to be an octave apart when one note is exactly twice

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In music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency f0. To increase the frequency by an octave, to 2f0, by what factor would you have to

(a) Increase the tension

(b) Decrease the length?

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