Physics - Wave on String Question with Solution | TestHub

The fundamental frequency of a string is given by Given: $l=l_1+l_2+l_3$... (i) $\mathrm{n}=\frac{1}{2l}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}}$ $\Rightarrow \mathrm{n}\propto \frac{1}{l}$ or $\mathrm{n}l=\mathrm{k}$ $\therefore l_1=\frac{\mathrm{k}}{{\mathrm{n}}_1},l_2=\frac{\mathrm{k}}{{\mathrm{n}}_2}$ and $l_3=\frac{\mathrm{k}}{\mathrm{n}3}$... (ii) $\therefore$ Original length $l=\frac{\mathrm{k}}{\mathrm{n}}$... (iii) Putting eq (ii) and (iii) into eq (i) $\frac{\mathrm{k}}{\mathrm{n}}=\frac{\mathrm{k}}{{\mathrm{n}}_1}+\frac{\mathrm{k}}{{\mathrm{n}}_2}+\frac{\mathrm{k}}{{\mathrm{n}}_3}$ $\therefore \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$