Wall behind the Loudspeaker Cancellation

The mechanism of cancellation is very simple. When two identical signals are in anti-phase (180 degrees out of phase), they cancel each other. If the loudspeaker is a quarter wavelength away from a reflective wall, the reflected wave comes back to the loudspeaker in anti-phase (phase difference of half a cycle, see Figure 1) and thus cancels the original signal at that frequency. How complete the cancellation is depends on the distance and the reflection coefficient of the wall. Longer distance means that the amplitude of the reflected signal is lower and thus the cancellation is not complete.

back wall cancellation

Figure 1 - Wall behind the Loudspeaker Cancellation Phenomena (Distance to wall = ¼ Wavelength distance)

In real life the depth and width of the first cancellation dip varies depending on the level of the reflection, but in most cases it is well audible. No equalisation will cure this situation because it originates from interference; adding amplitude at the dip frequency will also boost the reflection and thus their sum remains the same.

This simple case deals with one mode only: the reflection from one wall behind the loudspeaker which usually generates a set of cancellation dips (comb filtering effect). Typically the first frequency response cancellation dip is 6...20 dB deep.

cancellation dips

Figure 2. The frequency response dips caused by a single wall reflection.

The first and best cure for the ‘wall behind the loudspeaker’ cancellation dips is to flush mount the loudspeakers in a hard wall – also called ‘infinite baffle’ mounting - which totally eliminates this wall reflection and cancellation.

Second best is placing the loudspeaker very close to the wall, which raises the cancellation frequency higher. This works well when the loudspeaker is not too small. The risk is, with small loudspeakers which inherently are less directional in mid frequencies that the dip just moves to the low mid-band and causes even worse coloration. As seen above, the distances between 0 and 20 cm from the wall let the loudspeaker response to be, in most cases, unaltered; i.e. the directivity of the loudspeaker is high enough so that the rear radiation cannot cause a severe cancellation. Additionally, the low frequency boost should be compensated for when the loudspeaker is mounted close to the wall (+6 dB).

Alternatively, the third cure is to move the loudspeaker considerably away from the wall: the cancellation frequency goes down so far that it is below the low frequency cut-off of the loudspeaker. Thus, the minimum distance ‘loudspeaker/wall behind’ depends on the loudspeaker low frequency performance. However, at low frequencies and for large loudspeakers, the minimum distance becomes very long and impractical. At the same time, the distances to other boundaries in the room become similar to the desired distance to the wall behind the loudspeaker, and the reflections from these other surfaces start to dominate the response.

The fourth cure is to make the wall so absorptive that the reflected energy becomes negligible and hence does not cancel any of the direct sound. The thickness of a porous absorber has to be one quarter of the wavelength of the frequency to be absorbed to become effective. This is the same distance that determines the frequency of the cancellation dip and therefore the absorber has to be very thick. Usually, the required absorbing thickness is so high that such solution is practically not implemented.