decibel scale

Meaning: The decibel scale is a base-10 logarithmic scale for sound intensity level, which compresses the huge range of audible intensities into small numbers. A sound at the reference intensity, the threshold of hearing, is 0 dB. Every 10 dB increase multiplies intensity by 10, and 3 dB roughly doubles it.

Equation: β = 10 log(I/I₀), where β is the intensity level in dB (a dimensionless ratio), I is the sound intensity in W/m², and I₀ = 10⁻¹² W/m² is the reference intensity.

On the MCAT: Convert between dB and intensity using powers of 10: 60 dB means I = 10⁶ I₀ = 10⁻⁶ W/m². Combine with the inverse-square law for a point source in open space: intensity ∝ 1/r², so a tenfold increase in distance lowers the level by 20 dB. N identical sources raise the level by 10 log N dB, so two sources add about 3 dB.

Common confusion: Decibels are not linear. 80 dB is 10⁴ times, not twice, as intense as 40 dB. Also, do not add dB values from separate sources; add the intensities, then convert. Two 50 dB sources give about 53 dB, not 100 dB.