What Is a Decibel? A Unit That Multiplies Instead of Adding
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Sixty decibels is not twice thirty. The scale is logarithmic, so each step of ten represents a tenfold change in power, and that choice was made because the range of sound intensities people deal with spans something like a factor of a trillion, which no ordinary linear scale could handle sensibly.
Why logarithms
The quietest sound a healthy young ear can detect and a sound loud enough to cause immediate damage differ in intensity by a factor of around a trillion. Writing those numbers out is unwieldy and comparing them intuitively is impossible, so the scale compresses them by taking the logarithm of the ratio between the measured quantity and a reference. A bel is the base-ten logarithm of a power ratio, which turns a factor of ten into one, a factor of a hundred into two and a factor of a trillion into twelve. Bels proved too coarse for practical use, so the working unit is a tenth of one, which is where the prefix comes from. That gives the familiar arithmetic: a tenfold increase in power is ten decibels, a hundredfold is twenty, and a thousandfold is thirty. The scale also matches perception better than a linear one would, since human response to intensity is compressive across most senses, so equal steps in decibels correspond more nearly to equal steps in perceived change than equal steps in raw intensity ever could.
The arithmetic that catches people out
Because the scale is logarithmic, ordinary addition does not apply and several results are counterintuitive:
- •Doubling the power adds about three decibels, not double anything, since the logarithm of two is roughly three tenths
- •Doubling the amplitude or the pressure adds about six decibels, because power goes with the square of pressure, which is why the same unit uses twenty times the logarithm for pressure and ten for power
- •Two identical uncorrelated sources together are three decibels louder than one, so a second motorway lane of identical traffic barely changes the number
- •Adding a sound ten decibels quieter than an existing one raises the total by less than half a decibel, which is why removing the loudest source matters far more than removing several quiet ones
- •A perceived doubling of loudness corresponds to roughly ten decibels, which is a tenfold increase in power, so intuition about loudness and physics about energy diverge sharply
- •Distance from a point source costs six decibels per doubling, since intensity falls with the square of distance, which is why stepping twice as far back helps much less than people expect
It is always a ratio to something
A decibel on its own is meaningless because it expresses a ratio, so every use carries an implied or stated reference. Sound pressure level in air uses a reference of twenty micropascals, chosen to approximate the threshold of hearing, which is why zero on that scale means barely audible rather than silent and why negative values are perfectly possible in an anechoic chamber. Underwater acoustics uses a different reference, one micropascal, which means underwater and airborne figures cannot be compared directly and differ by more than sixty decibels for the same physical intensity, a confusion that has produced misleading claims about the loudness of marine animals. Electronics uses references including one milliwatt and one volt, distinguished by suffixes. The general rule is that a number without a stated reference is ambiguous, and in acoustics that reference is usually assumed but should be stated. Weighting adds a further layer, since measurements are commonly filtered to approximate the ear's uneven frequency response, which is what the A-weighted figure quoted in noise regulations means.
Where the scale is used and misused
Occupational noise regulation is built on the arithmetic, with exposure limits defined as a level averaged over a working day and an exchange rate specifying how much the permitted duration halves for each increase, typically three decibels in Europe and five in some American standards, which is a substantial policy difference disguised as a technical parameter. Hearing damage depends on total energy received, so a short very loud exposure can equal hours of moderate noise, which is why a single gunshot or firework can cause permanent loss. Consumer figures are frequently unreliable, since manufacturers quote noise levels measured at unstated distances and with unstated weighting, and a quieter-sounding appliance may simply have been measured further away. Comparative charts circulating online routinely misstate values and confuse peak with average. The broader lesson is general to logarithmic scales, which include earthquake magnitude, stellar brightness and acidity, and in every case differences that look small are large and intuitions built on linear scales mislead.
The takeaway
Taking the logarithm of a ratio compresses a range spanning a factor of a trillion into a manageable scale, so ten units means ten times the power. Doubling power adds three and doubling pressure adds six, and two identical sources together are only three louder than one. Every figure is a ratio to a reference, and air and water use different references differing by over sixty units for the same intensity.