If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms speed of the gas molecules is

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of 108 kmph is (speed of sound in air $=330 \mathrm{~ms}^{-1}$ )

If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and heard per second respectively are

A small angled prism is made of a material of refractive index $\frac{3}{2}$. The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index $\frac{4}{3}$ is