sound level

Meaning: Sound level, β, expresses sound intensity on a logarithmic scale relative to a reference intensity, the threshold of hearing. A log scale is used because audible intensities span many orders of magnitude. A sound at the threshold has β = 0 dB. Each factor of 10 in intensity adds 10 dB, and a factor of 2 adds about 3 dB.

Equation: β = 10 log₁₀(I/I₀), where β is the sound level in decibels (dB, dimensionless), I is the intensity in W/m², and I₀ = 1.0 × 10⁻¹² W/m² is the threshold of hearing. For a change between two sounds, Δβ = 10 log₁₀(I₂/I₁).

On the MCAT: A passage gives intensities or dB values, and you predict the change when a source is added or the listener moves. For a point source in open space, I = P/(4πr²), where P is power in W and r is distance in m. Doubling the distance cuts intensity to one quarter, which lowers the level by about 6 dB. Questions often ask you to convert between dB and intensity using powers of 10.

Common confusion: Decibel values do not add directly. When two sources combine, their intensities add. Two 60 dB sources give about 63 dB, not 120 dB. Also, sound level is a physical measure, while loudness is perceived and depends on frequency as well.