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 tuning fork vibrating with a sonometer having $20 cm$ wire produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 cm.$ the frequency of the tuning fork (in Hertz) must be

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \,m ,$ while the distance between one crest and one trough is $1.5 \,m$ The possible wavelengths (in $m$ ) of the waves 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 … $kg$