In a sonometer wire, a tuning fork forms a standing wave with five antinodes. It changes the number of antinodes from five to three when the suspended mass changes from 9 kg to M kg. The value of M is

The formation of standing waves in the two situations is depicted as following:

Also, we know that the velocity of wave pulse on a stretched taut string is given by:

$v=\sqrt{\frac{T}{\mu }}$

Frequency in the two situations is related as $f=\frac{5v_1}{2l}=\frac{3v_2}{2l}$ where $v_1\text{ and }{v}_2$ are the respective speeds in the two situations.

Now equating these two equations by putting the values of v₁ and v₂, we get

$\begin{array}{l}5\sqrt{\frac{9g}{\mu }}=3\sqrt{\frac{Mg}{\mu }}\\ \Rightarrow M=25\mathrm{kg}\end{array}$