If you take a given amplifier, let's say 100 watts and operate it just below clipping with music material, the "Crest Factor" of the amplifier's output is equivalent to the "Crest Factor" of the program material.
"Crest Factor" is the difference between the average level of the signal and its peak level. For example, a pure sine wave has a "crest factor" of 3dB, meaning that it's peak level is 3dB higher than its average level. We all know that 3dB represents a power factor of 2, so another way to look at it is that the peak power of the signal is twice that of its average level. So, if we play a sine wave on our 100 watt amplifier, just below its clipping level, the average power (over time) the speaker is needing to dissipate is 50 watts.
A true square wave, by comparison, has a crest factor of 0db, so it has equal average and peak power. Our 100 watt amplifier, playing a square wave, unclipped, into our speaker requires that the speaker dissipates 100 watts of power (twice the heat as a sine wave).