Answer
The fundamental frequency increases by a factor of 1.20 which is an increase of 20%
Work Step by Step
Since we can assume that the tension and mass density of the string do not change, the wave speed also does not change.
We can find an expression for the fundamental frequency:
$f = \frac{v}{\lambda}$
$f = \frac{v}{2L}$
We can find the new fundamental frequency when the length of the vibrating part of the string is $\frac{5L}{6}$:
$f' = \frac{v}{2(\frac{5L}{6})}$
$f' = \frac{6v}{2(5L)}$
$f' = \frac{6}{5}\times \frac{v}{2L}$
$f' = 1.20\times f$
The fundamental frequency increases by a factor of 1.20 which is an increase of 20%
