the amplitude of a wave is the height of the wave and the higher the amplitude the more energy it takes to move that wave. this means that waves with higher amplitudes have less energy
The word loudness belongs to psycho acoustics and tells how we feel this sound, that is not measuring the sound like we do with a sound pressure meter.
Listening to music means motion to the ear...
the greater the amplitude the greater the energy of the wave. When the energy is greater it will have a louder sound because the wave is more energetic.