Peter, as John has nicely explained, slew rate is essentially another way of describing the top-end frequency response of an amp. As long as the amp's frequency response is quasi-flat up to 20kHz, you don't have to worry about the slew rate.
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100% equivalent?! Absolutely not. Manufacturers choose very different ultrasonic frequencies at which to begin rolloff; some begin the rolloff below 20kHz, even with solid state amps.
Cooper, the third sentence above is, of course, entirely true. Accordingly, I never stated that all amp designs are 100% equivalent at all. What I stated was, various methods of deriving the formal "transfer function" of an amp are 100% equivalent from each other. Some of these methods use steady-state test signals; others use transient/dynamic signals. But in the end, they derive an identical transfer function for a given amp. This is mathematically guaranteed. My whole point is, as far as we are discussing the amps, their dynamic/transient behavior can be accurately predicted from the measurements that use steady-state test signals. This is almost counter-intuitive but true, AS LONG AS we do not go beyond the maximum continuously-available power.
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So as you increase power levels, the instantaneous peaks of required power grow exponentially.
Of course. That's the very definition of the dB unit, which is based on the logarithmic raw of human auditory perception. Your calculations are accurate, except for two rather unrealistic assumptions: (1) An in-room sensitivity of 88dB/W/m is really close to the bottom end (you are assuming something like the Maggies). For instance, the Axiom M22 is rated at 93dB/W/m in-room. This alone cuts the power demand down to one third. (2) The sound level does NOT decrease with distance in accordance with the inverse square law in a typical listening room and position (since it is not strictly "near-field"). So, at 3m distance, the sound level will NOT drop by -9.5dB -- it will realistically be more like -6dB (exact figure depends on the room size, reflectivity, speaker placement, etc). This cuts the required power output further by half. So, the realistic power demand at 100dB musical peaks would be more like 25W (rather than 145W). And then, all this assumes that you are driving only one channel. If you are talking about a 2-channel stereo system, the power demand per channel will further decrease by 2-3dB, down to 15W/ch or so. Therefore, if you have a good-quality 100W/ch amp, you will still have a healthy ~8dB headroom. In fact, this is exactly why some astute audiophiles are perfectly comfortable with a 30W/ch "pure Class A" power amp, when combined with relatively efficient speakers.
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At this point we have established that all amps measure differently, though typically the resulting frequency response should be within a decibel.
I agree, EXCEPT that the resulting frequency response (with a real-world load) would be, in the worst case, within 0.1-0.2dB for today's SS amps. And this is indeed an important fine point: I don't know what your psychology textbook has to say, but people with well-trained ears can discern a 0.5dB hump on the frequency response (and, perhaps, a 1dB dip), if the hump/dip is broad enough to encompass 1-2 octaves.
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SOOOO, for those of you still here, I will hypothesize that with constantly changing music, our sensitivity to frequency response is higher than with fixed tones.
Your analogy with the human vision is nice, but unfortunately, it is a wrong analogy. The human visual and auditory systems work very differently in many aspects [one example is the "intra-scene" concurrent dynamic range: the visual system easily handles ~1,000,000:1, whereas the auditory system can do only ~1,000:1 at best]. In fact, on the contrary to your hypothesis, our sensitivity to deviation of frequency response is BETTER when we are listening to a steady-state, wide-spectrum tone. Alan will tell you that a pink noise is a perfect example; try it if you are in doubt. Trust me, I do systems neuroscience as my day-job, when I am not loitering in this forum.
