Distinguish between particle-velocity and wave-velocity.

How is the velocity of sound in gaseous medium affected by pressure and temperature of the gas ?

Show that for constant temperature, $\frac{v_1}{v_2}=\sqrt{\frac{M_2}{M_1}}$  where $v_1$ is the speed of sound in a gas of molecular weight $M_1$ and $v_2$ that of the gas having molecular weight $M_2$.

Why is Laplace's correction necessary in Newton's formula for the velocity of sound waves in air ? What is this correction ?

Show that if the source moves away with the velocity of sound from an observer, who is at rest, the frequency of vibration is halved.