The Loudness is a subjective term related to highness or lowness of the sound, as we hear at our ear. How our ear senses it. Our ears sense the vibrations of diaphragm, the vibrations are dependent on the changes in air pressure at the diaphragm. As we know the sound wave is a pressure wave in air. So loudness is related to the intensity, level of sound, amplitude and frequency of sound wave.
Our ears are not sensitive for all frequencies in the same way. Equal loudness curves for various frequencies have to be considered when we want to use Loudness. So loudness may not be used directly in various calculations as compared to level of sound and intensity.
Amplitude and frequency are precisely defined physical quantities. Energy in the sound wave per unit volume too. Then power is also clearly defined and is used in every electronic device to mention the power of sound wave generated. Finally,
Intensity = power/unit square area in the direction of observer. The intensity values vary a lot and numbers are not easy to talk about. So Level of sound is defined to talk about the numerical values in a more convenient way.
Level of sound at 0 dB is just heard, at 120 dB is too loud - cannot bear it.
Now, a sound wave of 56 dB intensity and of frequency 1000 Hz and another sound of 56 dB but of frequency 8000 kHz are not heard with the same loudness at the ear. If we choose 1kHz as the reference frequency for loudness, then loudness at other frequencies are expressed in terms of loudness of 1 kHz. This reference is called phon. If the sound is as loud at our ear as a sound of 1kHz of 56 dB, then we say it is 56 phons.
There is approximate relation between loudness and level of sound or intensity. A simple and approximate rule is that when intensity and power become 10 times, then loudness in phons becomes twice.