Two waves are represented by the equation, $$\mathrm{y}_1=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx}+0.57) \mathrm{m}$$ and $$\mathrm{y}_2=\mathrm{A} \cos (\omega \mathrm{t}+\mathrm{kx}) \mathrm{m}$$, where $$\mathrm{x}$$ is in metre and $$\mathrm{t}$$ is in second. What is the phase difference between them?

The fundamental frequency of an air column in pipe 'A' closed at one end coincides with second overtone of pipe 'B' open at both ends. The ratio of length of pipe 'A' to that of pipe 'B' is

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