Question

ect : JEE 2020
A sonometer consists of two wires of same length, same material whose radši are in the ratio 2:3. The
ratio of tension in two wire if their fundamental frequencies are equal is
1) 1:4
21 2:3 31 9:4 41 4:9
Answer: 0 1
2.
03
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Answer 1

Given:

Two wires of the same length.

Of the same material.

Radius is in the ratio 2:3.

Their fundamental frequencies are equal.

To find:

The ratio of tension in two wires.

Solution:

r₁/r₂ = 2/3

Fundamental frequency (ν)

$\nu = \frac{1}{2l} \sqrt{\frac{T}{m} }$

ρ = m/v

m = ρv

$\nu = \frac{1}{2l} \sqrt{\frac{T}{\rho.\pi r^{2}l} }\\\\\nu = \frac{1}{2lr} \sqrt{\frac{T}{\rho \pi l} }$

ν ∝ √T/r

$\frac{\nu _1}{\nu _2} = \frac{\frac{\sqrt{T_1}}{\sqrt{T_2} } }{\frac{r_1}{r_2} } \\\\(\frac{r_1}{r_2} )^{2} = \frac{T_1}{T_2}\\\\\frac{T_1}{T_2} = (\frac{2}{3} )^{2}\\\\\frac{T_1}{T_2} = \frac{4}{9}$

Therefore, the ratio of tension in two wires is 4:9.