intensity

Meaning: Intensity is wave power spread over the area it crosses. For a given wave it is proportional to amplitude squared, so doubling the amplitude quadruples the intensity. A point source radiates over an expanding sphere, so intensity falls with the square of the distance.

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

On the MCAT: Passages ask for intensity at a new distance (I₁r₁² = I₂r₂²) or for a change in decibels. Each tenfold rise in intensity adds 10 dB, and doubling adds about 3 dB. In the photoelectric effect, raising the intensity at fixed frequency increases the number of photons and so the photocurrent (above threshold frequency). It does not change the maximum kinetic energy of ejected electrons, which depends on frequency.

Common confusion: Intensity is not the same as amplitude, loudness or pitch. Loudness is perceived and tracks decibel level, and pitch tracks frequency. Because decibels are logarithmic, 60 dB is 100 times the intensity of 40 dB, not 1.5 times.