What is the relation between loudness and sound intensity?

Answer 1

Yes, but it's not easy to understand. There is a dependance of sound levels and corresponding factors: Subjectivly sensed loudness (volume), objectively measured sound pressure (voltage), and theoretically calculated sound intensity (acoustic power). Scroll down to related links and look at "Sound level change and the loudness factor".

Answer 2

Sound intensity is defined as the sound power per unit area. The usual context is the measurement of sound intensity in the air at a listener's location. The basic units are Watts/m2 or Watts/cm2 . Many sound intensity measurements are made relative to a standard threshold of hearing intensity.

Sound loudness is a subjective term describing the strength of the ear's perception of a sound. It is intimately related to sound intensity but can by no means be considered identical to intensity. The sound intensity must be factored by the ear's sensitivity to the particular frequencies contained in the sound. This is the kind of information contained in equal loudness curves for the human ear. It must also be considered that the ear's response to increasing sound intensity is a "power of ten" or logarithmic relationship. This is one of the motivations for using the decibel scale to measure sound intensity. A general "rule of thumb" for loudness is that the power must be increased by about a factor of ten to sound twice as loud. To more realistically assess sound loudness, the ear's sensitivity curves are factored in to produce a phon scale for loudness. The factor of ten rule of thumb can then be used to produce the sone scale of loudness. In practical sound level measurement, filter contours such as the A, B, and C contours are used to make the measuring instrument more nearly approximate the ear.