Answer
The fundamental frequency increases by 7.0%
Work Step by Step
We can write an expression for the wave speed along a string:
$v = \sqrt{\frac{F}{m/L}} = \sqrt{\frac{F~L}{m}}$
We can find an expression for the fundamental frequency:
$f = \frac{v}{\lambda}$
$f = \frac{\sqrt{\frac{F~L}{m}}}{2L}$
$f = \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
We can find the new fundamental frequency when the tension increases by 15%:
$f' = \frac{1}{2}~\sqrt{\frac{1.15~F}{m~L}}$
$f' = \sqrt{1.15}\times\frac{1}{2}~\sqrt{\frac{F}{m~L}}$
$f' = \sqrt{1.15}\times f$
$f' = 1.07\times f$
The fundamental frequency increases by 7.0%
