Physics - Wave on String Question with Solution | TestHub

Let$\mathit{\text{l}}$be the length of the string.

The fundamental frequency is given by

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

$\text{or}\mathrm{\nu }\propto \frac{1}{l}$($\because \mathrm{T}$and$\mathrm{\mu }$are constant )

$\text{or}\mathrm{\nu }\propto \frac{\mathrm{k}}{l}$( where$\mathrm{k}$is a constant )

Here,$l_1=\frac{\mathrm{k}}{{\mathrm{\nu }}_1}$,$l_2=\frac{\mathrm{k}}{{\mathrm{\nu }}_2}$,$l_3=\frac{\mathrm{k}}{{\mathrm{\nu }}_3}$and$l=\frac{\mathrm{k}}{\mathrm{\nu }}$

But$\mathit{\text{l}}={\mathit{\text{l}}}_1+{\mathit{\text{l}}}_2+{\mathit{\text{l}}}_3$

$\therefore \frac{1}{\mathrm{\nu }}=\frac{1}{{\mathrm{\nu }}_1}+\frac{1}{{\mathrm{\nu }}_2}+\frac{1}{{\mathrm{\nu }}_3}$