Editing Audio power (section)

== Power calculations ==
[[Image:Peak-power-average-power-tau-T.png|thumb|A graph of instantaneous power over time for a waveform, with peak power labeled P<sub>0</sub> and average power labeled P<sub>avg</sub>]]

Since the [[instantaneous power]] of an [[alternating current|AC]] waveform varies over time, [[AC power]], which includes audio power, is measured as an average over time.  It is based on this formula:<ref>{{cite web|url=http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ACCircuit/AC-AvePower.html|title=Average Power in an AC Circuit|last=Vawter|first=Richard|archive-url=https://web.archive.org/web/20100327161721/http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ACCircuit/AC-AvePower.html|archive-date=2010-03-27|access-date=2016-04-22}}</ref>
:<math>
P_\mathrm{avg} = \frac{1}{T}\int_{0}^{T} v(t) \cdot i(t)\, dt \,
</math>

For a purely [[resistive]] [[Electrical load|load]], a simpler equation can be used, based on the [[root mean square]] (RMS) values of the voltage and current waveforms:
:<math>
P_\mathrm{avg} = V_\mathrm{rms} \cdot I_\mathrm{rms} \,
</math>

In the case of a steady sinusoidal tone (not music) into a purely resistive load, this can be calculated from the [[peak amplitude]] of the [[voltage]] waveform (which is easier to measure with an [[oscilloscope]]) and the load's resistance:
:<math>
P_\mathrm{avg} = \frac{{V_\mathrm{rms}}^2}{R} = \frac{{V_\mathrm{peak}}^2}{2R} \,
</math>

Though a speaker is ''not'' purely resistive, these equations are often used to approximate power measurements for such a system. Approximations may be used as reference on a specification sheet of a product.

=== Example ===
An amplifier under test can drive a sinusoidal signal with a peak amplitude of 6 V (driven by a 12 V battery). When connected to an 8 [[ohm]] loudspeaker this would deliver:
:<math>P_\mathrm{avg} = {(6~\mathrm{V})^2 \over 2(8~\Omega)}\,\ = 2.25~\mathrm{W}</math>

In most actual car systems, the amplifiers are connected in a [[bridge-tied load]] configuration, and speaker impedances are no higher than 4 Ω.  High-power car amplifiers use a DC-to-DC converter to generate a higher supply voltage.