Thank you for the detailed explanations, much appreciated. As long as we have numbers, we can discuss what they actually mean.Instead of using a single frequency sine wave, here is what you'll get with a signal that is representative of the characteristics of music -- M-Noise, AES Standard AES75-2022.
AES Standard » AES75-2023: AES standard for acoustics — Measuring loudspeaker maximum linear sound levels using noiseThis standard details a procedure for measuring maximum linear sound levels of a loudspeaker system or driver using a test signal called Music-Noise. In order to measure maximum linear sound levels meaningfully and repeatably, a signal is required whose RMS and peak levels as functions of...www.aes.orgM-Noise is a new test signal that promotes standardized measurement of a loudspeaker system’s maximum linear output.m-noise.org
M-Noise crest factor = 7.832 (= 17.9 dB). See below (reference):
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Assuming the short term transient power of the Schiit Rekkr is 1.5x its rated output, its clipping voltage is 6.928 V.
Rated output power (Schiit Rekkr) = 2 W @ 8 ohmV_rms @ rated power = sqrt(2 * 8) = 4 VV_pk @ rated power = sqrt(2) * V_rms = 5.657 VAssuming a short term power headroom of 1.5x rated powerClipping voltage = V_pk * sqrt(1.5) = 6.928 V
With M-Noise, for a speaker with 88 dB SPL sensitivity, that means a maximum of 77.9 dB SPL, 1 m, free field, before the on-set of clipping.
M-Noise V_rms = V_pk / Crest Factor = 6.928 / 7.832 = 0.8846 VM-Noise SPL at clipping = 20 log10(0.8846/2.83) + 88 = 77.9 dB
See also Charles Sprinkle's comments on amplifier power rating:
Excerpt:Finally saw it. Looks like we finally got a good and "cheap" monitor. H2 is a bit high, but who cares, H3 stays under 0.5% at 96 dB and under 0.2~0.3% after 500 Hz; not even changing with SPL! And as already said, the diffraction is moved in a much more benign area and with a lower level. Will...www.audiosciencereview.com
...So which way is the right way to measure power? I have something to say about that. The traditional way of rating "power" as V^2/R with sine waves is in my opinion complete nonsense. Power amplifiers don't amplify power. They amplify voltage. People don't hear watts. They hear SPL. We provide output "power" ratings as a reference, and yes, they are honestly measured and specified as described above. But I hope we all understand that actual power produced into a reactive load with complex impedance using real music or program material is going to be substantially less than headline "power" ratings.
I'm not so sure aboutyour last line of calculations:
This formula, calculating peak SPL using Vrms is valid for a uniform signal, it shouldn't be applicable to such a non-uniform signal.M-Noise SPL at clipping = 20 log10(0.8846/2.83) + 88 = 77.9 dB
Just as you quoted it yourself:
Power amplifiers don't amplify power. They amplify voltage. People don't hear watts. They hear SPL.
For any given Vrms, V_pk (thus peak SPL) can very wildly from one audio signal to the other. Therefore it's not accurate to calculate peak SPL with Vrms alone for coplex audio signals (as opposed to a uniform signal).
So let's look at those voltages more closely:
First of all, I measured Rekkr's clipping voltage as 9V using a digital oscilloscope, so I'll refer to that value rather than 6.928V you assumed. Now, as long as the amplifier provides V_pk=9V, the peak SPL (which is at the point of clipping) should be at that power level, regardless of the shape of the signal. In other words, peak SPL at any given V_pk is a fixed value, becuse they both represent the same ceiling (I don't know how to calculate peak SPL from V_pk, so if anyone knows, any help would be much appreciated).
The only difference between signals with high and low crest factors at equal peak SPL (thus equal V_pk) should be the mean SPL (that of high crest factor signal being lower).
So for a signal with such high crest factor, instead of trying to calculate the peak SPL from Vrms, we should be doing it the other way around: Calculate the mean SPL when V_pk is at clipping point.
Above is an audio signal from Rekkr output with a V_pk/Vrms value of 3 (7.4V/2.48V). I don't know what value it corresponds to in terms of crest factor (help, anyone?), but it's certainly lower than M-noise, which has a V_pk/Vrms value of 4.5 at roughly the same peak voltage. This is what M-noise looks like with a very close V_pk:
Vrms = 1.60V compared to the Vrms = 2.48 for the track above for roughly the same V_pk values.
(Actually it was 1.62V excluding the second of silence at the end, but let's discard that error).
I took quick and dirty SPL measurements (at around 1.2m distance) for both tracks using an Android app with signal levels (with almost matching V_pk levels) as shown above.
Music file: 93dB SPL peak and 81dB SPL average
M-noise: 94dB SPL peak and 77dB SPL average
Now I'm not claiming these values are perfectly matching with calculated numbers, but this little experiment shows SPL peak is one and the same for a given V_pk value. It also reflects the difference between average SPL values differing with differing Vrms. The fact that difference between peak and average SPL for M-noise (17dB) matches almost exactly with 17.9dB crest value gives me even more confidence.
Therefore, I believe we can confidently say that peak SPL for a given V_pk is the same regardless of the source (signal). What differs from one signal to the other (one crest factor to the other) is the average SPL for a given peak SPL. Since max V_pk (hence peak SPL max) is determined by the clipping point of the amp, the only thing different between tracks with different dynamic range would be the average SPL at clipping point (again, peak SPL being the same).
So, at what point does "loss of fidelity" occur? It occurs when peak of the audio signal reaches the clipping voltage of the amplifier and you keep on incerasing the volume, at which point you have reached (maybe even exceeded) the peak SPL of your system already.
Here is a high dynamic range music track with even higher crest value than M-noise, with V_pk/Vrms = 5
When there's no clipping, Rekkr can reproduce the entire audio signal under V_pk = 8.6V
Again taking a quick and dirty SPL measurement:
High dynamic range music track: 101dB SPL peak and 81dB SPL average (notice the measured difference is 20dB)
Here is what happens when I push the volume further up:
V_pk doesn't go any higher than 9V but Vrms goes on rising (up to 4.84V in this example), first compressing the dynamic range, then turning the audio signal into utter garbage past the red line.
But none of this ever happens before you hit 101dB SPL peak (or whatever the actual max SPL peak level of the amp is), which is already annoyingly loud in my opinion, and that's the only opinion I have ithroughout this write-up.
I hope this helps. Now, I'm no audio engineer, so it would certainly help me if anyone can show me the error of my ways as they catch them.