b
Total length of sonometer wire, \(l=110 \mathrm{cm}\) \(=1.1 \mathrm{m}\)

Length of wire is in ratio,\(6: 3: 2\) i.e \(60 \mathrm{cm}\), \(30 \mathrm{cm}, 20 \mathrm{cm}\)

Tension in the wire, \(T=400 \mathrm{N}\) 

Mass per unit length, \(\mathrm{m}=0.01 \mathrm{kg}\) 

Minimum common frequency \(=?\)

As we know,

Frequency, \(v=\frac{1}{21} \sqrt{\frac{T}{m}}=\frac{1000}{11}-H z\)

Similarly, \(v_{1}=\frac{1000}{6} \mathrm{Hz}\)

\(v_{2}=\frac{1000}{3} \mathrm{Hz}\)

\(v_{3}=\frac{1000}{2} \mathrm{Hz}\)

Hence common frequency \(=1000 \mathrm{Hz}\)