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What is the difference between Sound Pressure Level (SPL) and Sound Power Level (SWL)?

Definition

In acoustics, Sound Power Level (SWL) characterizes the intrisic acoustic power of an acoustic noise source, whereas Sound Pressure Level (SPL) characterizes the acoustic noise level observed at a certain distance from the source in a certain acoustic environment.

    \begin{equation*}$SWL = 10 \log\left(\frac{W}{W_0}\right)$ [dB]\end{equation}

    \begin{equation*}$SPL = 20 \log\left(\frac{p}{p_0}\right)$ [dB]\end{equation}

with:

  • SPL: Sound Pressure Level
  • SWL: Sound Power Level
  • W: Power
  • p: Pressure
  • W_0 = 10^{-12} [W] (Power reference)
  • p_0 = 20 [µPa] (Pressure reference)
  • log: logarithm in base 10
  • dB: decibel

When including A-weighting the notation ASPL or ASWL is used.

Link between SPL and SWL

The expression linking those two quantities in free-field is:

    \begin{equation*}$SPL = SWL + 10 \log \left( \frac{Q}{4\pi d^2} \right)$\end{equation}

with:

  • Q: Directivity Factor
  • d: Distance from the observer to the center of the source

The expression linking the SPL and the SWL in reverberant field is:

    \begin{equation*}$SPL = SWL + 10 \log \left( \frac{Q}{4\pi d^2} + \frac{4}{A}\right)$\end{equation}

with:

The directivity factor of a source placed on the floor equals 2; for a source placed on the floor close to a wall, Q=4 and for a source placed on the floor in a corner, Q=8.

The room equivalent absorption depends on the total surface area of the room and the average absorption coefficient in the room. This latter parameter can be obtained from reverberation time measurements inside the room.

Application case in free-field condition

A variation of 5dB in SWL leads to a variation of 5dB in SPL. Note that dB or dBA variations are the same.

Explanation:

– If

    \begin{equation*}$SWL_2 = \mathrm{SWL}_1 + 5$ [dB]\end{equation}

– Knowing that

    \begin{equation*}$SPL_2 = \mathrm{SWL}_2 +10 \log\left(\frac{Q}{4\pi d^2}\right)$\end{equation}

-Then

    \begin{equation*}$SPL_2 = \mathrm{SWL}_1 + 5 +10 \log\left(\frac{Q}{4\pi d^2}\right)$\end{equation}

-Finally

    \begin{equation*}$SPL_2 = \mathrm{SPL}_1 + 5$ [dB]\end{equation}

Application to e-NVH

Sound Pressure Level is easier to measure compared to Sound Power Level, which explains why NVH requirements of electrical machines are sometimes given in Sound Pressure Level. However Sound Pressure Level is affected by the acoustic source directivity and free-field conditions are generally not satisfied in buildings where Factory Acceptance Test are carried.

The SWL measurement with 5 microphones is described in standard ISO 3746 | Acoustique – Détermination des niveaux de puissance acoustique in semi-anechoic chambers.

Application to Manatee

Manatee software allows calculating both sound power and sound pressure levels.

Read more

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