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

A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes

Velocity of sound waves in air is '$$\mathrm{V}$$' $$\mathrm{m} / \mathrm{s}$$. For a particular sound wave in air, path difference of 'x' $$\mathrm{cm}$$ is equivalent to phase difference $$n \pi$$. The frequency of this wave is

The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to