Answer
The tension should be reduced by 7.8%
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 tension:
$\frac{v}{\lambda} = f$
$\frac{\sqrt{\frac{F~L}{m}}}{2L} = f$
$\sqrt{\frac{F~L}{m}} = 2L~f$
$\frac{F~L}{m} = (2L~f)^2$
$F = 4~m~L~f^2$
We can find the required tension $F'$ to decrease the fundamental frequency by 4.0%:
$F' = 4~m~L~(0.96~f)^2$
$F' = 0.96^2 \times 4~m~L~f^2$
$F' = 0.96^2 \times F$
$F' = 0.922 \times F$
The tension should be reduced by 7.8%
