Physics - Wave on String Question with Solution | TestHub

Total length of the wire, $\mathrm{L}=114\mathrm{cm}$ ${\mathrm{n}}_1:{\mathrm{n}}_2:{\mathrm{n}}_3=1:3:4$ Let ${\mathrm{L}}_1,{\mathrm{L}}_2$ and ${\mathrm{L}}_3$ be the lengths of the three parts As $\mathrm{n}\propto \frac{1}{\mathrm{L}}$ $$\begin{array}{rl}& \therefore {\mathrm{L}}_1:{\mathrm{L}}_2:{\mathrm{L}}_3=\frac{1}{1}:\frac{1}{3}:\frac{1}{4}=12:4:3\\ & \therefore {\mathrm{L}}_1=72\mathrm{cm}\left(\frac{12}{12+4+3}\times 114\right)\\ & {\mathrm{L}}_2=24\mathrm{cm}\left(\frac{4}{19}\times 114\right)\\ & \text{ and }{\mathrm{L}}_3=18\mathrm{cm}\left(\frac{3}{19}\times 114\right)\end{array}$$ Hence the bridges should be placed at $72\mathrm{cm}$ and $72+24=96\mathrm{cm}$ from one end.