I'm using Audacity to edit some audio (I'm a novice). The sound amplitude is displayed from -1.0 to 1.0. What are the units of amplitude? Are they decibels (dB)?

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They are not decibels. In essence, the amplitude is relative and has no unit. The [-1 1] range for digital audio signals is convention. The range is discrete and the number of steps in it depends on the bit resolution of the signal. For different bit resolutions, the minimum and maximum are still -1 and 1.

Also, when describing basic unscaled periodic signals like sine or cosine, their output is in the [-1 1] range (cos(0) = 1, sin(π/2) = 1, cos(π) = -1, sin(π * 3/2) = -1).

Scaling a digital signal to the [-1 1] range is called 'normalizing' and maximizes the signal's RMS while preventing clipping and leaving it linearly scaled (disregarding quantization error).

To calculate the dB FS (Decibels relative to Full Scale) of a digital signal, you use

dB FS = 20*log10(abs(A))

where A is the amplitude of the signal. If you substitute A for 1 (or -1) you will notice that the equation outputs 0 dB FS. This is the upper limit of the digital volume scale and means that all available bits are used to represent that amplitude. Note however that this only calculates the momentary or peak volume of a signal which is not representative of the felt volume (loudness).

In DAWs like Audacity and others, typically either the signal's peak volume or RMS (or sometimes both) is displayed in dB FS with the decibel meter.

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