Loudness grows as a power law of intensity, not linearly.

Evidence

For levels above about 30 dB SPL, the function also looks like a straight line, so we might be tempted to conclude that there is a proportional, linear relationship between loudness and sound level in dB SPL. However, notice that the y-axis is plotted on a logarithmic scale, and a 10-dB change in dB SPL is associated with a doubling of loudness. As a result, Stevens (1956) noted that loudness and intensity (in W/m2) have a power law relationship at moderate to high stimulus intensities. — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 714

Categorization

• DEFINE: Introduces Stevens’ power law relationship between loudness and intensity.