Loudness fools you. A sound with ten times the energy sounds only a little louder, not ten times — your ear compresses an enormous range into a comfortable one by hearing the LOGARITHM of intensity. That’s the decibel: every doubling of energy adds a mere 3, every tenfold adds 10. Slide the energy and watch the number crawl.
Sound level in decibels is L = 10·log₁₀(I / I₀), a ratio to a reference intensity. Because it is logarithmic, MULTIPLYING the intensity ADDS to the level: ×2 gives +3.01 dB, ×10 gives exactly +10 dB, ×100 gives +20. So the ~120 dB from a whisper to a jet engine spans a TRILLION-fold range of actual energy. A fail-loud self-check throws unless doubling the intensity adds 3.01 dB and a tenfold increase adds exactly 10 dB.
dB is a pure intensity ratio; perceived LOUDNESS (phons/sones) also depends on frequency (the equal-loudness contours) and duration. The 10·log₁₀ arithmetic and the +3/+10 steps are exact.