Four wires of identical lengths, diameters and of the same material are stretched on a sonometer wire. If…
Four wires of identical lengths, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tensions is $1 : 4 : 9 : 16$, then the ratio of their fundamental frequencies is
$16 : 9 : 4 : 1$
$4 : 3 : 2 : 1$
$1 : 4 : 2 : 16$
$1 : 2 : 3 : 4$
Solution
Fundamental frequency $= \frac{v}{2l} = \frac{\sqrt{T/\mu}}{2l} \Rightarrow f \propto \sqrt{T}$
So, the ratio of fundamental frequencies $= 1 : 2 : 3 : 4$.