Loudness is dependent on amplitud,e which in turn is dependent on number of molecules. The more the number, more the amplitude.
But isn't amplitude just a measure of how displaced can the particle be from mean position?
Why does number of particles affect that?
Loudness doesn't depend on the number of molecules, at least not directly. The loudness depends on the amplitude of the acoustic pressure, not the total pressure. The total pressure depends on the number of molecules (and temperature, etc.), but the acoustic pressure is the difference between the total pressure and the ambient pressure. The acoustic pressure amplitude has everything to do with the source of the disturbance and relatively little to do with the propagation medium. You can have arbitrarily small acoustic pressure regardless of the medium.
The main way that the number of molecules (and other properties of the propagation medium) affect sound is through the sound speed and the mass density. Changes in these properties can lead to reflection-transmission problems in which not all of the energy passes through the interface. From this perspective, the number of molecules in air versus the number and type of molecules in your ear organs actually affect how much of the sound energy gets in to your ear to be detected. So, from this perspective the number of air molecules do affect the loudness.
