A rectangular block of mass '$$\mathrm{m}$$' and crosssectional area A, floats on a liquid of density '$$\rho$$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency '$$n$$' equal to ( $$g=$$ acceleration due to gravity)

A sound of frequency $$480 \mathrm{~Hz}$$ is emitted from the stringed instrument. The velocity of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$. After completing 180 vibrations, the distance covered by a wave is

A sonometer wire '$$A$$' of diameter '$$\mathrm{d}$$' under tension '$$T$$' having density '$$\rho_1$$' vibrates with fundamental frequency '$$n$$'. If we use another wire '$$B$$' which vibrates with same frequency under tension '$$2 \mathrm{~T}$$' and diameter '$$2 \mathrm{D}$$' then density '$$\rho_2$$' of wire '$$B$$' will be

The path difference between two waves, represented by $$\mathrm{y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right)$$ and $$y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$$ is