The temperature varies linearly from sea level to approximately \(11 \mathrm{~km}\) altitude in the standard atmosphere. Evaluate the lapse rate- the rate of decrease of temperature with altitude-in the standard atmosphere. Derive an expression for the rate of change of sonic speed with altitude in an ideal gas under standard atmospheric conditions. Evaluate and plot the sonic speed from sea level to \(10 \mathrm{~km}\) altitude.