A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency $$500 \mathrm{~Hz}$$ is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$]

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)