If decibels are a ratio of the actual level to the starting level, what does a ratio less than 1 imply?

• A. The decibel value is zero
• B. The decibel value is positive
• C. The decibel value is undefined
• D. The decibel value is negative

Answer: (D)

Decibels quantify a ratio on a logarithmic scale, so they reflect how a level changes relative to a reference. If the actual level is lower than the starting (reference) level, the ratio is less than 1. The logarithm of a number between 0 and 1 is negative, and since decibels are computed as 10 log10(P2/P1) for power or 20 log10(V2/V1) for amplitude, that negative logarithm carries through as a negative decibel value. Zero dB occurs when the ratio is exactly 1 (no change), and a ratio of zero would be undefined because you can’t take the log of zero. So a ratio less than 1 implies a negative decibel value.