Editing Audio power (section)

== Power and loudness in the real world ==
{{unreferenced section|date=January 2015}}
Perceived "[[loudness]]" varies approximately [[logarithmic scale|logarithmically]] with the acoustical output power. The change in perceived loudness as a function of change in acoustical power is dependent on the reference power level. It is both useful and technically accurate to express perceived loudness in the logarithmic [[decibel]] (dB) scale that is independent of the reference power, with a somewhat straight-line relationship between 10&nbsp;dB changes and doublings of perceived loudness.

The approximately logarithmic relationship between power and perceived loudness is an important factor in audio system design. Both amplifier power and speaker sensitivity affect the maximum realizable loudness. Sensitivity is typically measured either suspended in an anechoic chamber in 'free space' (for full range speakers), or with the source and receiver outside on the ground in 'half space' (for a subwoofer).

While a doubling/halving of perceived loudness corresponds to approximately 10&nbsp;dB increase/decrease in speaker sensitivity, it also corresponds to approximately 10X multiplication/division of acoustical power. Even a relatively modest 3&nbsp;dB increase/decrease in sensitivity corresponds to a doubling/halving of acoustical power. When measuring in 'half space', the boundary of the ground plane cuts the available space that the sound radiates into in half and doubles the acoustical power at the receiver, for a corresponding 3&nbsp;dB increase in measured sensitivity, so it is important to know the test conditions. ±3&nbsp;dB change in measured sensitivity also corresponds to a similar doubling/halving of electrical power required to generate a given perceived loudness, so even deceptively 'minor' differences in sensitivity can result in large changes in amplifier power requirement. This is important because power amplifiers become increasingly impractical with increasing amplifier power output.

Many high-quality domestic speakers have a sensitivity between ~84&nbsp;dB and ~94&nbsp;dB, but professional speakers can have a sensitivity between ~90&nbsp;dB and ~100&nbsp;dB. An '84&nbsp;dB' source would require a 400-watt amplifier to produce the same acoustical power (perceived loudness) as a '90&nbsp;dB' source being driven by a 100-watt amplifier, or a '100&nbsp;dB' source being driven by a 10 watt amplifier. A good measure of the 'power' of a system is therefore a plot of maximum loudness before clipping of the amplifier and loudspeaker combined, in dB SPL, at the listening position intended, over the audible frequency spectrum. The human ear is less sensitive to low frequencies, as indicated by [[equal-loudness contours]], so a well-designed system should be capable of generating relatively higher sound levels below 100&nbsp;Hz before clipping.

Like perceived loudness, speaker sensitivity also varies with frequency and power. The sensitivity is measured at 1 watt to minimize nonlinear effects such as [[power compression]] and harmonic distortion, and averaged over the usable bandwidth. The bandwidth is often specified between the measured '+/-3&nbsp;dB' cutoff frequencies where the relative loudness becomes attenuated from the peak loudness by at least 6&nbsp;dB. Some speaker manufacturers use '+3&nbsp;dB/-6&nbsp;dB' instead, to take into account the real-world in-room response of a speaker at frequency extremes where the floor/wall/ceiling boundaries may increase the perceived loudness.

Speaker sensitivity is measured and rated on the assumption of a fixed amplifier output voltage because audio amplifiers tend to behave like voltage sources. Sensitivity can be a misleading metric due to differences in speaker impedance between differently designed speakers. A speaker with a higher impedance may have lower measured sensitivity and thus appear to be less efficient than a speaker with a lower impedance even though their efficiencies are actually similar. Speaker efficiency is a metric that only measures the actual percentage of electrical power that the speaker converts to acoustic power and is sometimes a more appropriate metric to use when investigating ways to achieve a given acoustic power from a speaker.

Adding an identical and mutually coupled speaker driver (much less than a wavelength away from each other) and splitting the electrical power equally between the two drivers increases their combined efficiency by a maximum of 3&nbsp;dB, similar to increasing the size of a single driver until the diaphragm area doubles. Multiple drivers can be more practical to increase efficiency than larger drivers since frequency response is generally proportional to driver size.

System designers take advantage of this efficiency boost by using mutually coupled drivers in a speaker cabinet, and by using mutually coupled speaker cabinets in a venue. Each doubling of total driver area in the array of drivers brings ~3&nbsp;dB increase in efficiency until the limit where the total distance between any two drivers of the array exceeds ~1/4 wavelength.

Power handling capability is also doubled when the number of drivers doubles, for a maximum realizable increase of ~6&nbsp;dB in total acoustic output per doubling of mutually coupled drivers when the total amplifier power is also doubled. Mutual coupling efficiency gains become difficult to realize with multiple drivers at higher frequencies because the total size of a single driver including its diaphragm, basket, waveguide or horn may already exceed one wavelength.

Sources that are much smaller than a wavelength behave like point sources that radiate omnidirectionally in free space, whereas sources larger than a wavelength act as their own 'ground plane' and beam the sound forward. This beaming tends to make high frequency dispersion problematic in larger venues, so a designer may have to cover the listening area with multiple sources aimed in various directions or placed in various locations.

Likewise, speaker proximity much less than 1/4 wavelength to one or more boundaries such as floor/walls/ceiling can increase the effective sensitivity by changing free space into half space, quarter space, or eighth space. When the distance to boundaries is > 1/4 wavelength, delayed reflections can increase the perceived loudness but can also induce ambient effects such as comb filtering and reverberation that can make the frequency response uneven across a venue or make the sound diffuse and harsh, especially with smaller venues and hard reflective surfaces.

Sound absorbing structures, sound diffusing structures, and digital signal processing may be employed to compensate for boundary effects within the designated listening area.