A sonometer wire has a length of 114 cm between two fixed ends, where should two bridges be placed to divide the wire into three segments whole fundamental frequencies are in the ratio $1:3:4$?

$$\begin{gathered} In case of a given wire under cons\tan t tension \\ Fundamental frequency of vibration \\ f \propto \frac{1}{l} \\ \therefore l_1:l_2:l_3=\frac{1}{1}:\frac{1}{3}:\frac{1}{4}=12:4:3 \\ {l}_1=\frac{12}{19}\times 114\Rightarrow l_1=72cm \\ {l}_2=24cm \\ {l}_3=18cm \\ \therefore First bridge is to be placed 72 cm from one end. \\ Second bridge is to be placed 72+24=96\text{\hspace{0.17em}}cm from one end \end{gathered}$$