Emulating car battery output through home power?

[sophiecentaur]

Power is always average.

Average over whatever time interval you choose to specify. Rate of doing work may be very relevant, even though it only applies for a brief period.
But I am not 'forgiving' HI manufacturers. They are mostly selling snake oil. Their Peak Power may well be relevant to someone, somewhere. Loud impulsive sounds may get through where low organ notes will exhaust the power supply and make it sag.

 

[Averagesupernova]

The main reason I want to specify that power is average and not RMS is because we cannot take the instantaneous power at the crest of a sine wave and multiply it by .707 and expect a correct result which is what we typically do with the voltage and current. It should go without saying that average will be defined over a specific period of time and this time varies due to many reasons.

 

[jim hardy]

we cannot take the instantaneous power at the crest of a sine wave and multiply it by .707 and expect...

Sinewave is well behaved, its crest factor is √2.
So, for sine with resistive load peak power is twice true power.

Square wave would have crest factor of 1because peak = average.

In self defense speaker manufacturers defined a test signal for rating their speakers
http://www.jblpro.com/pub/technote/spkpwfaq.pdf

...at end of that document

clip a sinewave and it approaches a square wave with same peak, containing twice the power

 

[sophiecentaur]

The main reason I want to specify that power is average and not RMS is because we cannot take the instantaneous power at the crest of a sine wave and multiply it by .707 and expect a correct result which is what we typically do with the voltage and current. It should go without saying that average will be defined over a specific period of time and this time varies due to many reasons.

I think the rationale is that a typical audio signal mostly consists of bursts of mid range frequencies and impulsive sounds and it covers many octaves of spectrum. Mostly, it doesn't consist of long periods of single sinewave. For brief periods, in most audio programme, the Power level will be much higher than the Power Level that you would measure with a long term 'thermally' based Energy / Power meter. So it isn't altogether 'bad' to talk about peak power. Many circuits will cope with short peaks of high power without folding. More demanding programme material will sort them out, though.
Interestingly, to give a consistently 'loud' sounding audio signal, the phases of the various components can be tinkered with so that the high peaks are ironed out so the mean level can be turned up to avoid clipping. This, introduces some distortion and the process will also have to introduce some delay but it is useful when, as in AM, there is a fixed maximum that can be handled by the modulation process. this is referred to as Audio Compression.

 

[sophiecentaur]

I want to specify that power is average and not RMS i

To be precise, the RMS value, over a given interval is the Power. RMS is the Sum of the Squares of the Volts (say), divided by R, averaged over that time, whatever the waveform happens to be. If you do that sum on a set of samples of a waveform, you will get the same answer (i.e. correct value) as if you measured the power with a calorimeter. It is common to assume that 0.707 of peak applies to every waveform and many cheap and cheerful meters will do that, assuming a sinusoid, every time.