Loudness, or volume, is the way that the human ear perceives sound. At its simplest, when the amplitude is increased, sound gets louder, and when it is decreased, sound gets quieter.
There are two things that contribute to our perception of sound. The first is the amplitude of the sound and the second is the frequency of the sound. Both of these things are precise measurements of sound rather than a perception.
This change in loudness brought on by an increase in amplitude is not proportionate. It all comes down to waveforms and how they vibrate. It is these vibrations that make sound. Amplitude affects the size of the vibration, while the frequency affects the speed of the vibration. This is what gives sound its pitch.
So, a sound with the same level of amplitude but a different frequency will have a different loudness to the human ear. For example, a bass sound will sound quieter than a mid-range sound even when both have the same amplitude. But if the amplitude of the bass sound is increased, its volume will increase and it will become louder.
Finally, the amount of increased volume that is achieved by an increase in amplitude is also affected by the frequency. So, turning the amplitude level in the mid-range sound from the previous example will not have the same proportional effect on loudness as the bass sound.