Last edited 17 Dec 2019

### Main author

ParkerJonesAcoustics Other Consultant Website

#  Introduction

The difference between sound pressure and sound power can be tricky to appreciate. For predicting noise levels from noise-polluting sources like plant, it is very important.

Noise levels are often verbally quoted by non-acousticians with phrases like ‘this unit has a level of 60 dB’. Unfortunately, based on that alone, one cannot do a great deal, without making a lot of assumptions. If the context is that the quoted level is 140dB then there is a problem. But at 60 dB, depending on the situation, it is difficult to assess the risk without digging into the information a little more.

#  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, the SPL is 0dB.

A sound pressure level is what can physically be measured 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 by sound pressure level).

#  Why are sound power levels (SWL) necessary?

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 one measures the SPL of a fan unit inside a plant room, and one that is 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 hemispherically, the SPL will be different. Simply moving further away from a sound source will reduce the SPL, particularly noticeable when outside.

A large plant enclosure will have many different machines from different manufacturers who may all provide noise data as a sound pressure level. Same thing? Not quite. The issue is that all of these sound pressure levels could be 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). The data is just not consistent. Because of this, one has to make a lot of assumptions to predict the sum of noise levels from a plant enclosure, and then most likely get it wrong.

The sound power level (SWL) helps get around this consistency problem. 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 provides a level playing field to directly compare two sound sources. Predicting the noise levels from a plant enclosure is now much simpler - one can apply the same calculation to all the equipment.

In summary, the SWL is very useful in quantifying how noisy a source is, such as an extract fan or air handling unit (AHU), and therefore predicting the noise impact from a source in a new development, before it is built, without having to measure it. Where noise date is required, acousticians will always appreciate data given as sound power levels.

#  Can SWL be converted to SPL and vice versa?

Yes. The SWL is not directly measurable, but it is calculable from the SPL, and vice versa. So, if one has sound power level data for a plant from the manufacturer, one can predict the noise level for that plant, in a room, outside, at 1m, at 10m, at 100m…and so on.

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 the 'receptor' is from the source, the less the sound pressure level.

Secondly, Q is the radiation pattern of the source. If one suspends a fan in the air (Q=1 in diagram below), it would radiate spherically. If placed on the floor (Q=2), it now radiates hemispherically. Because the same SWL is now radiating into half the volume of before, the sound pressure energy condenses and therefore the SPL doubles. The fraction of this sphere gets smaller the more surfaces that are placed around it, as shown below. For each halving of the sphere, roughly add another 3dB to the SPL. Hence, if one measures 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 6dB louder.

So now one can predict the noise levels that we hear and measure, from a multitude of different sources, at various distances and various positions. This is 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 above 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. 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.

This article was written by ParkerJones Acoustics and previously appeared on its website. It can be accessed HERE.