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`.

Options

A. 25kg
B. 5kg
C. 12.5kg
D. 1/25kg

Answer

A

Explanation

`f=(5)/(2l)sqrt((9g)/(u))=(3)/(2l)sqrt((Mg)/(mu)) implies M=25kg`
f: frequency of the tuning fork
`mu`:Mass of per unit length of the wave
l: length of the wire, g:acceleration due to gravity