Decibel Scale is Logarithmic, Like the Richter Scale
In fact, a physics colleague, Mark Srednicki of U.C. Santa Barbara, brought to my attention a much greater gaffe in one episode, in which sound waves are used as a weapon against an orbiting ship. As if that weren't bad enough, the sound waves are said to reach “18 to the 12th power decibels.” What makes this particularly grate on the ear of a physicist is that the decibel scale is a logarithmic scale, like the Richter scale. This means that the number of decibels already represents a power of 10, and they are normalized so that 20 decibels is 10 times louder than 10 decibels, and 30 decibels is 10 times louder again. Thus, 18 to the 12th power decibels would be 10 (18)^12 , or 1 followed by 11,568,313,814,300 zeroes times louder than a jet plane!
Notes:
Krauss describing a particularly egregious science-blunder in an episode of Star Trek.
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The Physics of Star Trek