Answer to Question #99633 in Physics for Seth Mandel

Question

classical acoustic guitar string has an active length (the so-called “scale” length) of 66 cm.
a) By how much must the string be shortened in order to increase its pitch by a perfect fifth? (Equivalently, what must the string’s active length become

Answer 1

Frequency $\nu = \frac{v}{\lambda} = \frac{v}{2l}.$

If $\nu_1 = 1.2\nu$, then $l_1 = \frac{v}{2\nu_1} = \frac{l}{1.2}$ , therefore $\Delta l = l(1 - \frac{1}{1.2}) = 11 sm.$