Sound Pressure and Sound Power - what's the difference?
The difference between sound pressure and sound power can be tricky to get your head around. For predicting noise levels from noise polluting sources like plant, it is very important.
As a consultant, I’m often verbally quoted noise levels by clients, i.e. ‘this unit has a level of 60 dB’. Unfortunately, based on that alone, I can’t do a great deal, without making a lot of assumptions. If you tell me it’s 140 dB I know it’s going to be very loud and problematic! But at 60 dB, depending on the situation, it’s difficult to assess the risk.
What is a sound pressure level (SPL)?
A sound pressure is the pressure deviation from atmospheric pressure caused by a sound wave, in pascals. The sound pressure level (SPL) is a logarithmic measure of the ratio of a sound pressure over a reference sound pressure (corresponding to the hearing threshold of a young, healthy ear), quoted as a dB. If these two pressures are the same, we have an SPL of 0 dB.
A sound pressure level is what we can physically measure using a sound level meter. Most noise level parameters in a report are based upon an SPL, albeit they are mostly adjusted in some way, i.e. weighted to a single number (dB(A)), or a level difference such as a Dw.
A sound power level (SWL) is theoretical. A sound power is in Watts (W), a sound power level like above, is in dB, a logarithmic ratio of the sound power over a reference sound power. W for Watts, hence SWL (as SPL is already taken!) I’ll explain more shortly.
Why do we need sound power levels (SWL)?
The sound pressure level (SPL) depends on distance, the position of the source and the environment, i.e. reflections from the ground, or if inside the surfaces of the room and therefore the reverberation time and volume of the room. So if we measure the SPL of a fan unit inside a plant room, and move this fan outside, the SPL is unlikely to be the same because of more sound energy escaping into the atmosphere. Similarly, if the unit is in the corner of a room, condensing sound radiation by the surfaces close around it, and then move this unit into the centre of the room on the floor, where it radiates more hemi spherically, the SPL will be different. Simply moving further away from a sound source, will reduce the SPL, particularly noticeable when outside.
If we take a large plant enclosure, with many different machines from different manufacturers, who all give us noise data as a sound pressure level, but all measured at varying distances, some in a lab, some outside, some in an anechoic chamber (or very often not referencing how it was measured at all which is effectively useless data as it could be measured at 1m or 10m!), we’ll have a hard time predicting the sum of noise levels from our plant enclosure.
The sound power level (SWL) helps us around this. It is not dependent on distance, position or environment. This is the crucial difference. It is a theoretical value; it is not directly measurable. A noise source will have the same sound power irrespective of where it is placed. It gives us a level playing field to directly compare two sound sources. Predicting the noise levels from our plant enclosure is now much simpler, we can apply the same calculation to all of our equipment.
In summary, the SWL is very useful in quantifying how noisy a source is, like an extract fan or AHU, and therefore predicting the noise impact from a source in our new development, before it is built, without having to measure it. If you’re asked to provide noise data for something, your acoustician will always appreciate data which is given as a sound power level.
Can SWL be converted to SPL and vice versa?
Yes. As I said earlier, the SWL is not measurable, but it is calculable from the SPL, and vice versa. So if we have sound power level data for a plant from the manufacturer, we can predict the noise level for that plant, in a room, outside, at 1m, at 10m, at 100m…
One thing to note, SPL is often written as Lp and SWL as Lw. With that in mind, a simple equation for calculating the direct component of SPL from SWL is given below:
There are two variable terms here. Firstly r, is simply the distance in meters. The further away we are from the source, the less the sound pressure level.
Secondly, Q is the radiation pattern of the source. If we suspended a fan in the air it would radiate spherically. If placed on the floor, it now radiates hemi spherically. Because the same SWL is now radiating into half the volume of before, our pressure condenses and therefore the SPL doubles. The fraction of this sphere gets smaller the more surfaces we placed around it as shown below. For each halving of the sphere, we roughly add another 3 dB to our SPL. Hence if I measured an identical source placed in a corner, compared to one in the centre of the room, at the same distance, the former will be roughly 6 dB louder.
So now we can predict the noise levels that we hear and measure, from a multitude of different sources, at various distances and various positions. This all very useful in predicting the noise impact on the occupants of our development and the neighbouring properties.
What about noise levels inside a room?
The equation we just looked at concerns the ‘direct’ component of sound. This is the sound pressure received at our ears, directly from the source, without interacting with any objects or surfaces around us. Of course in a room there are surfaces everywhere, reflecting sound towards our ears, the ‘reverberant’ component of sound. Hence the total energy is the sum of these two components. These calculations are something for a later article.
The direct equation best approximates sound propagation outside. But even then, the sound absorbing properties of the ground and the wind may affect the SPL over distance. You might notice the effect of the wind if you live or work a few hundred meters from a motorway. There is also the screening in noise levels from buildings or objects in between us and the source that obscure our view of it.
I hope you enjoyed this short article, and keep an eye out for more articles on the common questions that I get asked by clients in my job as an acoustic consultant. Feel free to connect and message me through LinkedIn, send me an email at chris@parkerjonesacoustics.com, or through our Contact Us page.
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