Why does the decibel scale use logarithms rather than equal steps of sound pressure?

The decibel scale uses logarithms rather than equal steps of sound pressure because the human ear possesses an enormous dynamic range, responding to sound intensities that span 12 orders of magnitude between the threshold of hearing and the threshold of pain. To remain sensitive to both extremely quiet and very loud sounds, the ear’s response is inherently nonlinear, focusing on ratios rather than absolute changes in pressure or intensity.12

A logarithmic scale is used because it mirrors this biological function more accurately than a linear scale. By using logarithms, each unit of increase on the decibel scale corresponds to a constant multiplicative factor in absolute intensity. This approach aligns with the observation that the human ear perceives changes in sound based on ratios; for instance, the smallest detectable change in intensity—the "just noticeable difference"—is approximately one decibel. Consequently, the decibel scale provides a practical, manageable way to quantify acoustics that aligns with human perception and Weber’s law, which states that the just noticeable change in a stimulus is a constant ratio of the original stimulus.2134