Newton assumed that sound propagation in a gas takes place under which condition?

Match Column - $A$ with Column - $B$.

Column - $A$	Column - $B$
$(a)$ Speed of longitudinal waves in gas and liquid.	$(i)$ $v = \sqrt{\frac{B}{\rho}}$
$(b)$ Speed of longitudinal waves in solid rod.	$(ii)$ $v = \sqrt{\frac{Y}{\rho}}$
$(c)$ Speed of sound in air according to Newton.	$(iii)$ $v = \sqrt{\frac{P}{\rho}}$
$(d)$ Speed of sound in air according to Laplace.	$(iv)$ $v = \sqrt{\frac{\gamma P}{\rho}}$

During the propagation of a longitudinal wave,in the region of compressions and rarefactions,

$A$ man sets his watch by a whistle that is $2\, km$ away. How much will his watch be in error? (Speed of sound in air = $330\, m/s$)

Obtain the equation for the speed of a sound wave in air and identify the error in this equation.

Use the formula $v=\sqrt{\frac{\gamma P}{\rho}}$ to explain why the speed of sound in air:
$(a)$ is independent of pressure,
$(b)$ increases with temperature,
$(c)$ increases with humidity.