You made it entirely too easy for me.
Ever heard of a true RMS meter? Ever wonder WHY they make them?
I mean, if peak is peak, wouldn't RMS be RMS? Take the peak and multiply by .707, RIGHT?
Ohh crap... then comes TRMS.
The beginning of this lesson:
"The distorted waveform is actually a summation of the fundamental frequency sine wave and a variety of harmonics. Harmonics are actually pure sine waves themselves but each has a frequency that oscillates at a multiple of 60Hz (i.e. 3rd harmonic = 3 x 60 = 180Hz, 5th harmonic = 5 x 60 = 300Hz).
To find the total RMS value of any distorted wave, you have to take "the square root of the sum of the squares" of the RMS value of the fundamental and the series of harmonics. (admittedly it's easier to see this demonstrated than to explain it!!)"
Feel free to continue reading here -
http://www.lehmanengineering.com/quiz/quiz5sol.html
Also note the EQUATION for calculating harmonics inside of a waveform is NOT Vpeak *.707, it's the square root of the net sum of the squares.
What does that mean?
PEAK SUDDENLY HAS POTENTIAL TO BE MORE THAN 1.414!!
More backup against your thought process...
"A conventional volt meter simply calculates the RMS value as A x 0.7071, where A is the peak voltage. Most conventional volt meters assume the input is sinusoidal and may introduce an error if the waveform is distorted or non-linear. "
Note the entire distorted waveform/ non-linear waveform comments given. Note where it plainly states a 'conventional volt meter calculates RMS as a simple .7071 times the apparent voltage at the time it's measuring.' Also note that it "assumes" the input is perfectly sinusoidal and may introduce an
error if the waveform is distorted or non-linear.
Then we have this link here:
http://www.voltech.com/Downloads/86050_02.pdf
Explaining thuroughly average values and how to properly calculate non-sinusoidal waveforms and as with anyone that can understand common math, you can PLAINLY see that a musical waveform will have more power under the curve.
Be sure to read up about crest factor, and be sure to note how it plainly states that the crest factor of the waveform depicted is MUCH GREATER THAN 1.414. Suddenly, peak becomes a much more sticky figure!
Go down to page 5, in black and white... It takes harmonics.. .and ADDS them to every piece of the fundamental wave, INCREASING IT.
I could go on for days with this... You clearly don't have enough electrical background though.
Class is over.