b
\(f=\frac{V}{2 L} \Rightarrow f \propto \frac{1}{L}\)

\(f_1: f_2: f_3=1: 2: 3\)

\(\Rightarrow \frac{1}{L_1}: \frac{1}{L_2}: \frac{1}{L_3}=1: 2: 3\)

\(\Rightarrow L_1: L_2: L_3=\frac{1}{1}: \frac{1}{2}: \frac{1}{3}\)

\(\Rightarrow L_1: L_2: L_3=6: 3: 2\)

Let \(L_1=6 x, L_2=3 x, L_3=2 x\)

Total length of sonometer wire \(=110 cm\)

\(L_1+L_2+L_3=110\)

\(6 x+3 x+2 x=110\) \(x=10\)

\(\therefore L _1=60 cm , L _2=30 cm , L _3=20 cm\)

Hence, bridges should be placed at distance of \(60 cm\) and \(90 cm\) from \(A\).