Physics - Wave on String Question with Solution | TestHub

According to question Length of wire $=L=100\mathrm{cm}$ And ratio of fundamental frequencies $$=1:3:5$$
$$\begin{array}{rl}{L}_1:L_2:L_3& =\frac{1}{1}:\frac{1}{3}:\frac{1}{5}\\ & =15:5:3\end{array}$$ Let $x=$ comman factor then $$\begin{array}{rl}& 15x+5x+3x=100\\ & \Rightarrow 2x=100\\ & \Rightarrow x=\frac{100}{23}\\ & \therefore L_1=15\times \frac{100}{23}\\ & =\frac{1500}{23}\mathrm{cm}\\ & \therefore L_2=5\times \frac{100}{23}\\ & =\frac{1500}{23}\mathrm{cm}\\ & \end{array}$$ $$\begin{array}{rl}\therefore L_3& =3\times \frac{100}{23}\\ & =\frac{300}{23}\mathrm{cm}\end{array}$$ This shows that bridge should be placed from $A$ at $\frac{1500}{23}\mathrm{cm}$ and $\frac{2000}{23}\mathrm{cm}$ respectively