Q: A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by mass M. the wire resonates with the same tuning fork forming three antinodes for the same position of the bridges. The value of M is

(a) 25 kg

(b) 5 kg

(c) 12.5 kg

(d) 1/25 kg

Ans: (a)

Sol:Let μ = Mass per unit length of the wire

$\large \frac{5}{2l}\sqrt{\frac{9 g}{\mu}} = \frac{3}{2l}\sqrt{\frac{M g}{\mu}}$

Squaring ,

25 × 9 = 9 × M

M = 25 kg