loudness

Meaning: Loudness is the perceived strength of a sound. It depends mainly on intensity, the power per unit area carried by the wave, which is proportional to the square of the amplitude. Because hearing spans a huge range, intensity is compared on a logarithmic decibel scale. The ear is not equally sensitive at all frequencies, so equal intensities at different frequencies need not sound equally loud.

Equation: β = 10 log(I/I₀), where β is the intensity level in decibels (dB), I is the intensity in W/m², and I₀ = 10⁻¹² W/m² is the threshold of hearing.

On the MCAT: Questions ask how β changes. A tenfold rise in I adds 10 dB, and doubling I adds about 3 dB. Moving away from a small source, intensity falls as 1/r² (r is the distance in m), so doubling the distance lowers β by about 6 dB. Identical independent sources add their intensities, not their decibel levels, so two sources raise β by about 3 dB.

Common confusion: Loudness is not pitch. Pitch follows frequency, while loudness follows amplitude and intensity. Decibels are logarithmic, so 60 dB is not twice as intense as 30 dB. It is 1000 times the intensity, because a 30 dB difference is three factors of ten.