A word about sound pressure levels (SPL) - in simple terms how loud will it be? PA speakers usually have an SPL rating quoted in decibels (dB) at a reference power level of 1W at a distance (from the speaker) of 1metre. For a typical PA speaker the SPL at 1m for 1W is usually between 96dB and 102dB with a typical value being 100dB. To give you an idea of how loud this is, it's often quoted as being the same as if you were standing 2m from a pneumatic drill - i.e. pretty damn loud! So 100dB is quite a good reference level for working out how loud it will be at a given distance from a PA speaker at a given power level. The other thing to note is that SPL decreases in inverse proportion to the distance from the speaker. At each doubling of the distance from the speaker, the SPL reduces by 6dB. At 10m from the speaker, the SPL will have reduced by a tenth (1/10) which is equivalent to a 20dB reduction. It's possible to calculate SPL levels at various distances for different amplifier power levels.
The Pascal (Pa) is the unit of pressure, defined as 1 Pa = 1 N/m2. 0dB(SPL) is defined as 20 micropascals (µPa) = 2 x 10-5 Pa, the quietest sound a human can hear. One Pascal is equal to 94 dB(SPL). This level is used to specify microphone sensitivity. For example, a Shure SM58 microphone has a sensitivity of -54.5dBV/Pa, equivalent to 1.85mV.
The relationship between pressure and SPL is logarithmic so SPL = 20 * Log (P/Pref) where Pref = 20 micropascals (µPa) so a doubling of the pressure from 1 to 2 Pa results in an SPL of 100dB.
The following table shows the amplifier power required to achieve 100dB and 94dB at various distances, based on PA speakers with a sensitivity rated at 100dB for 1W @ 1m.
| Power | Max O/P @ 1m | 100dB | 94dB |
|---|---|---|---|
| 1W | 100dB | 1m | 2m |
| 10W | 110dB | 3.16m | 6.31m |
| 100W | 120.0dB | 10.0m | 20.0m |
| 300W | 124.8dB | 17.3m | 34.6m |
| 600W | 127.8dB | 24.5m | 48.9m |
| 1000W | 130.0dB | 31.6m | 63.1m |
| 3000W | 134.8dB | 54.7m | 109.4m |
| 10,000W | 140.0dB | 100.0m | 200.0m |
These figures ignore any contribution from the on-stage amplifiers, which will, of course, add to the overall SPL. The actual SPL in any given situation or venue will depend on a lot of factors, so these figures can only be used as a guide. The only real way of determining the (average) SPL is to measure it with a meter!
Always try to provide a sound level appropriate to the venue. Expect to achieve a listening level at the back of the room (i.e. furthest from the stage) of between 90dB and 95dB - if it's too loud you can always turn it down! The volume will, of course, be greater nearer the stage and will vary within the room depending on the size and shape of the room and many other factors such as the size of the audience (people absorb sound), the height of the ceiling, the floor covering and if the windows have curtains.
You can use the calculator below to find out the amplifier power required to produce a desired Sound Pressure Level db at a given distance. It's usual to allow 3dB of "headroom" to keep the amp out of clip.
Example: If the furthest listening position from the stage is 50 meters, and the desired Sound Pressure Level is 95 dB SPL, and the loudspeaker has a sensitivity rating of 98 dB. With the minimum recommended amplifier headroom of 3 dB, then the amplifier will need to supply at least 2,500 watts.
Note: if the Max Listening Level Achieved is less than the Level Required, the amplifier output needs to be higher. The results above also, in effect, show the SPL which can be achieved for a given amplifier power at a given distance.
Equations used to calculate the data:
dB = Lspl - Lsens + 20 * Log (Dist/Dref) + Ahrm
Pw = 10 to the power of (dB/10)
SPLmax = Lsens + 10 * Log (Amp)
dBdist = 20 * Log (Dist)
SPLout = SPLmax - dBdist
Where:
Lspl = required SPL at listener
Lsens = loudspeaker sensitivity (1W @ 1m)
Dist = loudspeaker-to-listener distance
Dref = reference distance (1m)
Ahrm = desired amplifier headroom
dB = ratio of power referenced to 1 watt
Pw = power required
The Lenard Audio Institute has a very comprehensive web site dealing with all aspects of sound systems.
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Page updated 04/10/22