perceived loudness

Meaning: Perceived loudness is the listener's subjective sense of how strong a sound is. It rises with intensity (power per unit area), which is proportional to amplitude squared. Hearing is roughly logarithmic, so loudness is described on the decibel scale. Frequency also matters: the ear is most sensitive at roughly 2000 to 5000 Hz, so equal intensities at different pitches need not sound equally loud.

Equation: β = 10 log(I/I₀), where β is sound level in dB (dimensionless), I is intensity in W/m², and I₀ = 10⁻¹² W/m² is the reference intensity near the threshold of hearing. For a point source, I = P/(4πr²), where P is power in W and r is distance in m.

On the MCAT: Expect questions on how the dB level changes when intensity changes: ×10 gives +10 dB, ×100 gives +20 dB, and ×2 gives about +3 dB. Doubling the distance from a point source cuts intensity to one-fourth, about −6 dB. You may also be given a dB value and asked for I, or asked what level several identical sources produce together.

Common confusion: Students treat decibels as linear and think 80 dB is twice as intense as 40 dB. It is 10⁴ times as intense, because each 10 dB is a factor of 10. Also, the dB level is a physical measure of intensity, while perceived loudness follows it only approximately.