Answer
The fundamental frequency increases by 0.50%
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 1.0%:
$f' = \frac{1}{2}~\sqrt{\frac{1.01~F}{m~L}}$
$f' = \sqrt{1.01}\times\frac{1}{2}~\sqrt{\frac{F}{m~L}}$
$f' = \sqrt{1.01}\times f$
$f' = 1.005\times f$
The fundamental frequency increases by 0.50%
