Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
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for pure sine waves

and
Equation 4.10 Relationship between and for pure sine waves
Of course most of the sounds we hear are not simple waveforms like those shown; natural
and musical sounds contain many frequency components that vary over time. In any case, the
RMS amplitude is a better model for our perception of the loudness of complex sounds than is
peak amplitude.
Sound processing programs often give amplitude statistics as either peak or RMS
amplitude or both. Notice that RMS amplitude has to be defined over a particular window of
samples, labeled as Window Width in Figure 4.6. This is because the sound wave changes over
time. In the figure, the window width is 1000 ms.
Figure 4.6 Amplitude statistics window from Adobe Audition
You need to be careful will some usages of the term "peak amplitude." For example, VU
meters, which measure signal levels in audio equipment, use the word “peak” in their displays,
where RMS amplitude would be more accurate. Knowing this is important when you’re setting
levels for a live performance, as the actual peak amplitude is higher than RMS. Transients like
sudden percussive noises should be kept well below what is marked as “peak” on a VU meter. If
you allow the level to go too high, the signal will be clipped.
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