Decibels cannot be summed directly because they are logarithmic power ratios

Evidence

How does the addition of sources affect the sound pressure level (SPL), the sound power level (SWL) and the sound intensity level (SIL)? For the SWL and SIL, because we are adding powers, the results will be the same whether the sources are correlated or not. However, for SPL, there will be a difference between the correlated and uncorrelated results. The main difficulty that arises when these measures are used to calculate the effect of combining sound sources is confusion over the correct use of decibels during the calculation. … Decibels are power ratios expressed on a logarithmic scale, and this means that adding decibels together is not the same as adding the sources’ amplitudes together. This is because adding logarithms together is equivalent to the logarithm of the product of the quantities. Clearly this is not the same as a simple summation! … When decibel values are to be added together, it is important to convert them back to their original ratios before carrying out the addition. If a decibel result of the summation is required, then the sum must be converted back to decibels after the summation has taken place. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 275

Decibels are power ratios expressed on a logarithmic scale, and this means that adding decibels together is not the same as adding the sources’ amplitudes together. This is because adding logarithms together is equivalent to the logarithm of the product of the quantities. Clearly this is not the same as a simple summation! … When decibel values are to be added together, it is important to convert them back to their original ratios before carrying out the addition. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 276

Categorization

• DEFINE: Clarifies the fundamental operational rule of decibel arithmetic — convert to linear ratios, sum, convert back — essential foundation for any psychoacoustics reading.
• XREF: Connects directly to a common practical confusion when mixing tracks and setting levels in audio work. — connects to: A decibel value is meaningless without an attached reference level — Almo Farina, Soundscape Ecology: Principles,…, 1943
• corroborated: 3 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 275; David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 276