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How can we measure Decibels ?
Hello everyone, I’m David, an acoustic engineer for 15 years and passionate about science and engineering.
In my job, I often have a question about what the differences are between acoustic pressure, intensity and power. So, let’s explain it !
I think you have already seen on the packaging of a washing machine, a fridge or other home equipment, some numbers like ‘XX dB’ with XX a number often between 30 and 90.
What is this number?
In this case, this number is the Decibels of the equipment in A-weighting and it should represent the power of the noise emitted by the equipment.
Another example
When you buy a loudspeaker, on the product specifications, you can see ‘ XX dB at 1m’ or just ‘XX dB’ with ‘XX’ a number between 70 and 100dB or more.
Loudspeaker Sound Pressure level (also called sensitivity)
Here, it expresses the Sound Pressure Level at 1m with 1W of electric power.
OK, so here you have 2 ways to express sound or noise, but what is it exactly?
As mentioned in the title, there are mainly 3 ways to express sound, with the ‘L’ being for ‘Level’ as all these features are often expressed on a logarithm scale.
So, let’s detail these 3 features.
Sound is a vibration in a medium.
In our case, it is air. The variation of the air pressure around the atmospheric pressure enables us to hear sound when this vibration arrives to our ears. That’s why the Sound Pressure Level (SPL) is the feature characterizing this variation of pressure from a noise source. So, the SPL depends on the environment where the sound is emitted and the distance from the source.
It’s possible to measure SPL with a standard microphone (a Sound Level Meter) and it’s expressed in ‘Pa’ or in dB on a logarithm scale (reference 2.10–5 Pa)
To come back to the example of the loudspeaker, the value expressed here is the SPL at 1m (for 1W of electrical power) and it’s measured in an anechoic room (no sound reflection). So SPL will be different if you measure it in another type of room (in your saloon) or at a different distance (at 2m in the free field, you will have 6dB less).
In sum up, for SPL it’s important to take into account the environment and the distance where the measurement has been done, and it can be measured with a sound level meter.
For information, a lot of standards exist to measure home equipment, car noise, railway noise, buildings, environment…
To be honest, few people use this feature but it’s important to understand what it is to have a better view of the acoustic power level.
Then, the Sound Intensity (SIL) from a source is the power per surface area (W/m2) emitted, perpendicular to this surface. Also, the sound Intensity is calculated by multiplying the pressure by the particle velocity (I = p x v). It s important to know to understand the next techniques to measure the sound intensity.
Sound Intensity representation (shema by author)
The technique to measure the SIL is called the ‘Intensity method’ (P-P technique) and it is a technique with 2 paired microphones that are very closed (from 6mm to 50mm depending on the frequency range).
Schema of an Intensity probe (Intensity Method)
Intensity method calculation (by author)
Also, this method consists of measuring the acoustic pressure (approximated by the average of the 2 acoustic pressures measured by the 2 mics) and the particle velocity, from the Euler equation, by considering a straight line approximation between the 2 acoustic pressures (p1 and p2). Indeed, if the microphones are very close, it’s possible to do this approximation.
The sound power (SWL) represents the sound power emitted by a source. It doesn’t depend on the environment and the distance. It’s directly linked to the source.
To calculate : multiplying the Sound Intensity by the radiating surface.
Basically, this method is the same as the SIL described above, by using the surface of measurement (W = I.S in Watt). The method with 2 microphones (P-P method) is described in 2 standards (ISO 9614–1 and 9614–2). Currently, none standard exists with the method using the measurement of the particle velocity (P-U method).
However, there are other standards (ISO 3744, ISO 3743…) that use the mapping of standard microphones around the source. From the measurement, it’s possible to have an average of the SWL around the source. In contrast, the Intensity Method enables you to have a cartography of the SWL around the source.
An example of microphone mapping (ISO 3744)
From the SWL, it’s possible to calculate the SPL by taking into account the distance, the environment around the source, … For example, if the source is at 1m in free field (without any obstacle) from the source, the difference between SWL and SPL is -11dB. But if there is a plan, the difference will be -8dB.
In sum up, for SWL it’s intrinsic data of a source and doesn’t depend on the environment or the distance. It’s possible to measure it with a mapping of microphones or a specific intensity probe. The SPL can be calculated from the SWL.
I hope to clarify the differences between acoustic pressure, intensity and power. It’s always complicated to determine the real decibels that you will have in your room at the end. No matter the type of values, the main aim is to compare products between them. To have a more detailed estimation, an acoustic study is necessary with more data (spectrum, size,…).
Thank you for reading!
David Lauret
