How much amplifier power do you really need?

[thumb5]

This statement contradict's itself.  Peak power "by definition" is the √2 (which is 1.414) times the RMS power as you say but is NOT twice RMS power as you also say. Calculus proves this, what math are you using?

My statement does not contradict itself; you seem to be confusing power with amplitude.  What calculus are you using to derive your (incorrect) conclusion?

Negative.  I managed to dig up a video tutorial for you...  RMS vs Peak

Sorry to be blunt, but you are simply wrong about this.

As its title says, the video you linked to above explains why the relationship between RMS and peak value of a sine wave is a factor of root 2.  That means a sine wave of amplitude (value) 1 has an RMS value of ~0.707, or conversely if the RMS value is 1, the peak value (amplitude) is ~1.414.  Since power depends on the square of the value, the relationship between RMS and peak power is a factor of 2.

Since you are apparently fond of tutorial links, here's one for you: https://en.wikipedia.org/wiki/Root_mean_...rage_power.  Note that for a sine wave both Irms and Vrms are ~0.707 times the respective peak values so when multiplied together (P = IV) the RMS power is a factor of 0.707 x 0.707 = 0.5 times the peak.