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 string fixed at one end is vibrating in its second overtone. The length of the string is $10\ cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

A string $2.0\, m$ long and fixed at its end is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions $a, b, c$ and $d$ are indicated on the string. The elemental portion which has maximum potential energy is/are

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 kg$ is suspended from the wire. When this mass is replaced by a mass $M$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is ... $kg$

The fundamental frequency of a sonometre wire is $n.$ If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be