A sound wave is travelling with a frequency of $$50 \mathrm{~Hz}$$. The phase difference between the two points in the path of a wave is $$\frac{\pi}{3}$$. The distance between those two points is (Velocity of sound in air $$=330 \mathrm{~m} / \mathrm{s}$$ )

A transverse wave given by $$y=2 \sin (0.01 x+30 t)$$ moves on a stretched string from one end to another end in 0.5 second. If '$$x$$' and '$$y$$' are in $$\mathrm{cm}$$ and '$$\mathrm{t}$$' is in second, then the length of the string is

A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)

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