sound intensity

Meaning: Sound intensity is the average power a sound wave carries through a unit area perpendicular to its travel. For a given medium and frequency, it is proportional to the square of the amplitude, so doubling the amplitude quadruples the intensity. A point source spreads its power over a sphere, so intensity falls as 1/r².

Equation: I = P/A = P/(4πr²) for a point source, where I is intensity (W/m²), P is power (W), A is area (m²), and r is distance from the source (m).

On the MCAT: Ratio questions are common: doubling the distance cuts intensity to one-fourth, and tripling it gives one-ninth. Sound level is β = 10 log(I/I₀), in decibels (dB), with I₀ = 10⁻¹² W/m² as the threshold of hearing. Each tenfold rise in intensity adds 10 dB, and doubling the intensity adds about 3 dB. Passages may give a graph of dB against distance or ask how many identical sources produce a given level.

Common confusion: Intensity is not the decibel level. Intensity (W/m²) adds directly for independent sources, while decibels are logarithmic. Two 60 dB sounds together give about 63 dB, not 120 dB.