Question

Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is 1 : 4 : 9 : 16, then the ratio of their fundamental frequencies are:

• A. 16 : 9 : 4 : 1
• B. 4 : 3 : 2 : 1
• C. 1 : 4 : 2 : 16
• D. 1 : 2 : 3 : 4

Answer 1

The correct option is D 1 : 2 : 3 : 4

$f=\frac{1}{2\pi }\sqrt{\frac{T}{\mu }}f\propto \sqrt{T}$
Ratio of fundamental frequency
$\sqrt{T_1}:\sqrt{T_2}:\sqrt{T_3}:\sqrt{T_4}\sqrt{1}:\sqrt{4}:\sqrt{9}:\sqrt{16}$
1:2:3:4