A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$

Two wires are in unison. If the tension in one of the wires is increased by $2\%, 5$ beats are produced per second. The initial frequency of each wire is  .... $Hz$

A pipe $20$ $\mathrm{cm}$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $\mathrm{Hz}$ ?( sound velocity in air $= 330$ $\mathrm{m/s}$ ).

A light wave travels through three transparent materials of equal thickness. Rank in order, from the highest to lowest, the indices of refraction $n_1, n_2$ and $n_3$.

A transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement.

A wave on a string is travelling and the displacement of particles on it is given by $x = A\, sin\, (2t -0.1\, x)$. Then the wavelength of the wave is