For a particle performing linear S.H.M. of amplitude 'r', the potential energy is '$\lambda$' times its total energy. The displacement of particle is

In a sonometer experiment, the fundamental frequency of vibration of wire is '$n_1$' when wire is stretched by hanging a metal bob. If the bob is completely immersed in water, the frequency of vibration of wire becomes '$n_2$'. The relative density of the metal of the bob is

The beats are produced when there is a superposition of two sound waves which will have

In a pipe closed at one end, air column is vibrating in the fourth overtone so the vibrating air column has '$x$' nodes and '$y$' antinodes. The values of $x$ and $y$ are respectively