Which characteristic of sound is logarithmic and cannot be added directly?

The characteristic of sound that is logarithmic and cannot be added directly is decibels. This is because decibels (dB) represent a logarithmic measure of sound intensity or sound pressure level. When working with sound levels in decibels, they reflect the logarithmic nature of human perception of sound; for instance, an increase of 10 dB is perceived as roughly twice as loud, even though it represents a tenfold increase in actual sound intensity.

To combine sound levels expressed in decibels, one cannot simply add them arithmetically due to their logarithmic nature. Instead, one must convert the decibel levels back to their linear intensity values (power or pressure), perform the addition, and then convert the result back into decibels. This principle underscores the unique behavior of decibels compared to other sound characteristics like amplitude, frequency, and wavelength, which can be added or manipulated using simpler arithmetic.