Index Room & AcousticsBoundary Interference

Boundary Interference

The bass notch created by the wall behind a loudspeaker.

First notch123Hz

Notch depth−7.3dB

First peak245Hz

Second notch368Hz

Response at the seat

Why it happens

The wave that goes backwards returns half a cycle late at the notch frequency and cancels the direct sound.

Input

Woofer to the wall behind

d

Measure from the cone, not from the back of the cabinet.

Wall reflectivity

1.0 is bare masonry. Thick absorption on the wall lowers it at higher frequencies.

Listening distancem

How it works

Bass goes everywhere

At low frequencies a loudspeaker radiates in all directions, including backwards. That rear wave reflects off the wall and returns to join the direct sound, having travelled an extra $2d$ . When the detour equals half a wavelength the two arrive in opposite phase and cancel:

f_{notch} = \frac{c}{4d}\,(2k + 1),

k = 0, 1, 2 \ldots

Halfway between the notches, at multiples of $c/2d$ , the reflection adds instead.

Depth of the notch

With the reflection arriving at relative amplitude $a$ , the combined response is

\left|H(f)\right| = \left|1 + a\,e^{-j 2\pi f \cdot 2d / c}\right|,

a = \rho\,\frac{D}{D + 2d}

where $\rho$ is the wall's reflectivity and $D$ the listening distance. Equalisation cannot fill a cancellation: adding power feeds both the direct and the reflected wave equally.

What to do about it

Go close. Under about 30 cm the notch moves above 280 Hz, where the cabinet is already directional and a modest absorber is effective.
Go far. Beyond 2.2 m the notch falls below 40 Hz, under most music. Few rooms allow it.
Avoid the middle. Distances of 0.5 to 1.5 m put the notch between 60 and 170 Hz, right in the body of bass and kick drum.
Stagger. Make the distances to the rear wall, side wall and floor all different so their notches do not coincide.