Question

A piano wire having a diameter of $0.60mm$ is replaced by another wire of same material but with a diameter of $0.62mm$. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is______$\%$.

Answer 1

Answer: -3.2

$v=\frac{1}{Dl}\sqrt{\frac{T}{\pi d}}$
$\Rightarrow v\propto \frac{1}{D}$
$\Rightarrow \frac{v^{\prime }}{v}=\frac{D}{D^{\prime }}$
$\Rightarrow \left(\frac{v^{\prime }}{v}-1\right)\times 100=\left(\frac{D}{D^{\prime }}-1\right)\times 100$
$=\left(\frac{0.60}{0.62}-1\right)\times 100$
$=-\frac{100}{31}=-3.2\%$