SBIR: the reflection you cannot treat, only move

A speaker near a boundary radiates towards the listener twice: once directly and once after bouncing off the wall behind it. The two arrivals are the same signal a fraction of a millisecond apart, so they sum as a comb filter — reinforced where the delay is a whole period, cancelled where it is half a period.

Unlike a room mode, this one is not a property of the room. It is a property of where the speaker sits, and moving the speaker moves it. That is the whole reason it is worth calculating rather than treating.

The image source, and one subtraction

A reflection off a flat, rigid boundary behaves as though there were a second identical source on the other side of it, mirrored, radiating in phase. That is not an approximation for this purpose; it is exact for an infinite plane, and a wall is a good enough plane over the low-frequency range where the effect matters.

So the problem reduces to two sources separated by twice the distance to the wall, and the question is only how much further one of them has to travel. Where that extra distance is half a wavelength the two arrive in antiphase and cancel; where it is a whole wavelength they add.

Front wall: the number is fixed

With the speaker in front of a wall and the listener on the speaker's axis, the listener lies on the line joining the source and its image. The reflected path is longer by exactly 2d at any listening distance — there is no far-field correction to make, because the geometry never changes shape.

The consequence is a table worth memorising, because it turns a placement decision into a frequency:

• 0.3 m — first null at 286 Hz, right in the presence region.
• 0.6 m — 143 Hz, and the reinforcement at 286 Hz.
• 0.9 m — 95 Hz. The classic small-monitor thinning.
• 1.5 m — 57 Hz, which is usually below where the speaker is doing anything anyway.

That is why "keep the speaker away from the wall" is bad advice and "choose the distance deliberately" is good advice: 1.5 m pushes the null below the band, 1.0 m drops it into it.

Side wall: it is not 2d

A side wall is a different geometry, and the difference is no longer fixed. The image source sits off to one side, so the reflected path is the hypotenuse of a right triangle with legs L and 2d, and the excess over the direct path is that hypotenuse minus L. It is at most 2d, reached only when the listener is almost on top of the speaker; as L grows the excess falls away, which is why sitting further back pushes the side-wall null upwards rather than leaving it where it was.

At 3 m out and 0.6 m from the side wall the difference is 0.23 m, not 1.2 m — a factor of five. The first null lands near 743 Hz rather than 143 Hz, which is a completely different part of the spectrum and a completely different remedy. Applying the front-wall formula to a side wall is one of the most common errors in placement advice.

The practical reading: side-wall interference is a mid-frequency problem and front-wall interference is a bass problem. They need to be reasoned about separately, and the speaker's own directivity decides how strongly each one is excited.

What you actually hear

Two things stop this from being a textbook notch. First, the reflection is not the same amplitude as the direct sound — it is attenuated by the wall's absorption and by the speaker's own off-axis rolloff towards the wall, so the cancellation is partial. A 6 dB dip is typical rather than an infinite null.

Second, the comb fills in as the frequency rises: the nulls get closer together, and above a few hundred hertz the room's reverberation and the ear's own resolution smear them into a general timbral shift rather than a set of discrete dips. The low ones are the ones you hear as a hole.

Placement versus treatment

Absorption works from roughly a quarter wavelength, so at 95 Hz it needs to be about 0.9 m thick. A 50 mm panel does nothing there and is the wrong tool for the problem. This is the single most useful thing to understand about SBIR: it is a geometry problem, and geometry is cheaper to change than a wall.

Moving the speaker changes the null frequency predictably. What you cannot do by moving is remove it — every distance produces a null somewhere. The design question is which part of the spectrum you are willing to spend, and the answer is usually below the crossover, where the subwoofer can be placed separately.

Five mistakes worth avoiding

1. Using 2d for a side wall. The error is a factor of two to five, and it moves the predicted null by more than an octave.
2. Measuring from the baffle. The acoustic centre of a driver sits behind the baffle, further back for a woofer; at 0.9 m the difference is not negligible.
3. Treating a 95 Hz null with 50 mm panels. Absorption needs a quarter wavelength of depth to do anything at all.
4. Assuming the null is infinite. The reflection is attenuated, so the dip is finite and the fix is proportionally smaller than the theory suggests.
5. Forgetting the floor and the ceiling. They are boundaries too, and the floor is usually the closest one.

Summary

Front wall: the path difference is 2d, the first null is at c/4d, and the only real control is where you put the speaker. Side wall: the difference is a hypotenuse and depends on how far away you sit, so it lands much higher in frequency than the shortcut predicts. Calculate both, and treat the answer as a placement constraint rather than a treatment problem.

Values shown are engineering aids rather than measurements; see the disclaimer and the tool index.