If the temperature of a gas is increased from $127^{\circ} \mathrm{C}$ to $527^{\circ} \mathrm{C}$, then the rms speed of the gas molecules

An air column in a tube of length 50 cm , closed at one end is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at 42 cm from the open end is

A metal rod of length 125 cm is clamped at its midpoint. If the speed of the sound in the metal is $5000 \mathrm{~ms}^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is

If the distances of the object and its real image from the principal focus of a concave mirror are 16 cm and 9 cm respectively, then the focal length of the mirror is