A tuning fork of frequency '$$n$$' is held near the open end of tube which is closed at the other end and the lengths are adjusted until resonance occurs. The first resonance occurs at length $$L_1$$ and immediate next resonance occurs at length $$L_2$$. The speed of sound in air is

A sound wave of frequency $$160 \mathrm{~Hz}$$ has a velocity of $$320 \mathrm{~m} / \mathrm{s}$$. When it travels through air, the particles having a phase difference of $$90^{\circ}$$, are separated by a distance of

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 $$320 \mathrm{~ms}^{-1}$$]

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