A sonometer wire resonates with a given tuning fork forming a standing wave with five antinodes between the two bridges when a mass of `9 kg` is suspended from the wire. When this mass is replaced by a mass 'M' kg, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. Find the value of `M`.

Explanation

In the first case, five antinodes are formed between the two bridges. It corresponds to fifth harmonic.
Number of loops, `p=5`
`therefore` frequency `upsilon=(3)/(2L)sqrt((Mg)/(m))`
`therefore (5)/(2L)sqrt((9g)/(m))=(3)/(2L)sqrt((Mg)/(m))or5sqrt(9)=3sqrt(M)`
or `25xx9=9MorM=25kg`.