" :(Aside: it might be a good idea to register) You are correct on two main issues: (a) reference to power in the definition of decibel is misleading (restrictive); (b) the decibel is simply a mapping from a logarithmic to a linear scale. However, your calculations are incorrect since the logarithm is defined only for dimensionless quantities, so 'log(y Watts)' is meaningless. :Here is the problem with explaining the decibel satisfactorily: any definition of the decibel based on its historical roots (instead of mathematical ""good practice"") will remain troublesome. A cleanup yields the following. :: (a) Define B (bel) as a function such that x B = for any positive number x. Define d (deci) for any x by x d
" :(Aside: it might be a good idea to register) You are correct on two main issues: (a) reference to power in the definition of decibel is misleading (restrictive); (b) the decibel is simply a mapping from a logarithmic to a linear scale. However, your calculations are incorrect since the logarithm is defined only for dimensionless quantities, so 'log(y Watts)' is meaningless. :Here is the problem with explaining the decibel satisfactorily: any definition of the decibel based on its historical roots (instead of mathematical ""good practice"") will remain troublesome. A cleanup yields the following. :: (a) Define B (bel) as a function such that x B = for any positive number x. Define d (deci) for any x by x d =