A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $$9 \mathrm{~kg}$$ is suspended from the wire. When this mass is replaced by a mass $$\mathrm{M}$$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of '$$M$$' is

Equation of two simple harmonic waves are given by $${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m$$ and $${Y_2} = 4\sin 8\pi \left( {{t \over {0.16}} - {x \over {1.6}}} \right)m$$ then both waves have

A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its $$2^{\text {nd }}$$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $$50 \mathrm{~N}$$ and the speed of sound is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4 \sin (3 x+60 t) ~m}$$. The mass per unit length of the string is