Question

A sonometer wire is subjected to a certain tension. If the tension is increased four times and the length of wire is reduced to half the original value, how is frequency of vibrations altered?

Answer 1

Given: `T_2 = 4 T_1 , l_2 = l_1/2`

To find: n₁ : n₂ = ? 

∵ n = `1/21 sqrt(T/m)`

∴ `n_1/n_2 = l_2/l_1sqrt(T_1/T_2)` 

`n_1/n_2 = 1/2 sqrt(1/4)`

 = `1/2 xx 1/2`

=` 1/4`

∴  n₁ : n₂ = 1: 4