Question: A wire under tension vibrates with a frequency of 450 per second. What would be the fundamental freq...

Question

A wire under tension vibrates with a frequency of 450 per second. What would be the fundamental frequency if the wire were half as long, twice as thick and under one-fourth tension?

Answer 1

Solution

n = $\frac{1}{2\mathcal{l}}\sqrt{\frac{T}{\pi r^{2}\rho}}$ = 450

n' = $\frac{1}{2\left( \frac{\mathcal{l}}{2} \right)}\sqrt{\frac{T/4}{\pi 4r^{2}\rho}}$ = $\frac{n}{2}$ = $\frac{450}{2}$ = 225 Hz