I'm not talking about FFT, just the raw sound wave and the RMS of it.


  • $\begingroup$ Can you provide the defintion of RMS for a sound wave? The definition I know only applies to voltage and current. $\endgroup$
    – MBaz
    Sep 30 '19 at 16:04
  • 2
    $\begingroup$ @MBaz: RMS is defined for any signal: square, take the mean, take the root. Typically you would this is on the sound pressure but you can also do it on the particle velocity, at least in the far fied $\endgroup$
    – Hilmar
    Sep 30 '19 at 16:20
  • $\begingroup$ @Hilmar Thanks. What I was wondering about was, how to square a sound wave? Using specific measurements like sound pressure or velocity makes sense. $\endgroup$
    – MBaz
    Sep 30 '19 at 16:30


The sensitivity of human auditory is very dependent on frequency and without any type of frequency weighting, a raw RMS estimate will be pretty much useless.

There are some standard frequency weighting curves, most popular being the "A" weighting. See https://en.wikipedia.org/wiki/A-weighting. The sensitivity is also dependent on the absolute level and hence there are multiple weighting curves.

Sp frequency weighted RMS is a good starting points, but they typical ignore any sensitivity to time domain behavior like impulse, transient, masking, etc. There are good models to predict actual perceived loudness but they tend to be rather complicated.


As Hilmar pointed out, loudness, is a frequency dependent psychoacoustic metric (like most if not all of them). Taken directly from Pulkki's book:

Sounds between the threshold of hearing and threshold of pain are perceived with increasing ‘strength’ or ‘volume’. This subjective feature of sound is called loudness. The loudness level has been defined such that the sound pressure level of a 1-kHz pure tone in dB has the same loudness level in phon units

For more information you can have a look at either the aforementioned reference book or in Wikipedia or any other acoustics textbook (I could propose some if you intend to go through them).

Again, there are some models of loudness perception. One is from Zwicker which extracts a continuous function representing loudness over time. You can get info about it either from Zwicker's book or a review on the model here (free to download). The other one I know of is from Glasberg and Moore and actually calculates the short-term loudness of consecutive overlapping frames. It also "kinda" emulates the temporal integration of the auditory system between adjacent time frames. You can have a look at this one here (also free to download).

According to the first reference (Pulkki) none of the current models can fully explain loudness perception. Without having extended experience on the matter I assume that this is referred to audio codecs mostly, where "arbitrary" signals have to be coded yielding consistent results (which so far I personally, haven't managed to experience).

So, depending on your intended application the aforementioned models may or may not be sufficient. What is to be taken home from this here though is that loudness is way too complex to be able to characterise (or measure it) with just a pressure (or particle velocity) RMS value.


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