# 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.  with:

• 𝑆𝑃𝐿: Sound Pressure Level
• 𝑆𝑊𝐿: Sound Power Level
• 𝑊: Power
• 𝑝: Pressure
• : (Power reference)
• : 20µPa (Pressure reference)
• log: logarithm in base 10 (obtained with log10 in Matlab)
• 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: + with:

• 𝑆𝑃𝐿: Sound Pressure Level
• 𝑆𝑊𝐿: Sound Power Level
• 𝑄: Directivity Factor
• 𝑑: Distance from the observer to the center of the source
• 𝑙𝑜𝑔: logarithm in based 10 (obtained with log10 in Matlab)

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

with:

• : Room constant

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 constant 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 + [dB] Knowing that +  Then  + +  Finally + [dB]

### 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 in semi-anechoic chambers.

### Application to MANATEE

MANATEE software allows to use several post-processing to plot SWL (plot_SWL_fft, plot_ASWL_fft) as well as SPL (plot_ASPL_fft) of a rotating machine.

The distance of the microphone and the directivity factor are set using

Input.Simu.directivity_coeff = 2;   % directivity coefficient (machine radiates 1: without obstacle, 2: from a plane, 4: from an angle, 8: from a corner) Input.Simu.d_micro_source = 1;      % distance [m] from the center of the machine (center along axial direction and on the rotation axis) for SPL calculation