RMS Power from Waveforms

Sine wave:

P_rms = V_peak² / (2R) = V_rms² / R
V_rms = V_peak / √2 ≈ 0.707 × V_peak

Square wave:

P_rms = V_peak² / R  (100% duty cycle)
V_rms = V_peak

Music signal (approximate):

Crest Factor ≈ 10–15 dB (typical pop/rock)
V_rms ≈ V_peak / (crest factor linear)
P_average ≈ P_peak × (1/crest_factor²)

Practical implication:

An amplifier rated 1000W RMS delivers that power continuously with a full sine wave. With music at 10 dB crest factor:

P_average = 1000 / 10² = 10W average

The amplifier only works hard during peaks — which is why thermal design must handle peaks, not averages.