## College Physics (4th Edition)

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%