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

A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced per second will be