intensity of sound

Meaning: Intensity is the power carried by a sound wave through a unit area perpendicular to its direction of travel. It depends on amplitude: doubling the pressure amplitude quadruples the intensity. A point source radiates equally in all directions, so its power spreads over a sphere whose area grows as r². Intensity therefore falls as 1/r² with distance, and doubling the distance cuts intensity to one quarter.

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

On the MCAT: Expect ratio problems. If distance doubles, intensity drops by a factor of 4 (about 6 dB lower). If intensity rises 100-fold, β rises by 20 dB. Passages may give two sources and ask you to add intensities, not decibel values, or ask how β changes when the number of identical sources increases.

Common confusion: Intensity is not pitch or loudness. Pitch follows frequency, while loudness is the perceived effect of intensity. The decibel scale is logarithmic, so 60 dB is not twice as intense as 30 dB. It is 1000 times as intense.