SBIR calculator

SBIR and floor bounce calculator

With the availability these days of room measurement software, digital equalization (EQ) and even automatic equalization EQ systems as fitted to some amplifiers and speaker systems it's really easy to go for the quick fix and use these to try and correct errors in a systems frequency response. The problem being of course that a systems frequency response at any one point in a room is determined by a combination of factors the most obvious of which is the room itself.

The size, ratio and amount of damping in a room all conspire to create a wild variation in a rooms frequency response depending on where you are in the room. These are called "Room Modes" and are beyond the scope of this piece but a quick bit of background. When sound waves bounce off two opposing walls you get standing waves at certain frequencies and harmonics. With three parallel sets of walls in a normal rectangular room all these resonances interact with each other and the result is Room Modes and below 200hz they tend to dominate a rooms response.

However even at these lower frequencies and certainly at higher frequencies speaker placement and their interaction with the room can create wild swings in the response all on there own. There's little to be gained from attempting to fix these with EQ without first trying to understand what is going on with the speaker/room interaction or for that matter speaker placement and listening position. EQ, even if implemented using the latest wizz bang linear phase FIR (finite impulse response) DSP (Digital Signal Processing) is probably the last thing you should use to fix a systems problems as there are some issues that you cannot fix with EQ.

Speaker Boundary Interference Response (SBIR)

But first a discussion of the Baffle Diffraction Step (BDS) transition which is where a speaker goes from 2pi hemispherical radiation pattern to a 4pi spherical radiation pattern. It is in effect a 6db loss in sound output at lower frequencies and the point at which this occurs is determined by the width of the baffle that the driver is mounted on.

The loss occurs over four octaves and the centre of it, -3db down, f3 is defined as f3 = 115824/W, where W is the width of the baffle in millimeters.

BDS response for a 500mm wide baffle

So at low frequencies a speaker radiates its acoustical energy in an omnidirectional pattern where it strikes the walls, floor and ceiling and is reflected back. The reflected sound has a longer travel path and therefore arrives at the listening position slightly later in time than the direct sound.

When the distance from the driver to the wall is 1/4 of a wavelength you get complete cancellation at that frequency and then reinforcement, cancellation etc. at multiples of this frequency. At other frequencies the front radiation combines with the reflected rear radiation and causes constructive and destructive interference. This is known as comb filtering and creates a series of very deep nulls and +6db peaks which decrease slightly with each null and peak as does the spacing between them (they get closer together).

As the distance from the wall increases this frequency lowers and vice versa so like many things in audio you have a bit of a dilemma. By moving the speaker closer to the wall, hard up against it or even sunk into the wall so it's flush mounted you can remove SBIR completely at least for the wall behind the speaker.

This is why the best place for sub woofers is hard up against a wall and on the floor as it raises the 1/4 wavelength frequency above the operating range of the driver.

It's also why 1100mm is a really bad distance for any full range speaker if you're a fan of the kick drum with it's 60hz - 100hz "thump", so a deep null at 80hz is the last thing you want.

The problem is of course that the best place to put stereo speakers for soundstage depth and imaging in general is not near the front wall but a fair distance from it. And at this point satellite speakers crossed over to stereo subwoofers at a fairly high frequency start to look really good.

It should also be noted that SBIR is also applicable to the side wall, the floor and for that matter and to a much lesser extent the ceiling, the rear wall and even the wall on the other side of the room. This is why you should try and avoid placing a speaker an equal distance from the front and side walls because the SBIR effects are additive causing bigger peaks and nulls. SBIR is also applicable for driver mounting heights for bass and mid bass drivers. In a worst case scenario where the distance to the drivers centre from the front and side walls and the floor are all equal the peaks in the response will be +6db and the nulls as deep as -24db.

Floor/Ceiling Bounce

If there's a hard reflective surface adjacent to you and a speaker such as the floor then you not only hear the direct sound but also a reflected sound. This is usually referred to as "floor bounce" but is equally applicable to ceilings and for that matter adjacent walls.

This reflected sound because it's travelling a greater distance takes longer to get to you and when combined with the original causes constructive and destructive interference comb filtering in much the same way that SBIR does.

These nulls and peaks from the floor, ceiling and walls will all combine with each other and create even more complex interference patterns. As the floor is usually the closest boundary to a speaker floor modes should dominate though.

For multi driver speaker systems you should probably measure the height to the centre of each driver and run the calculator for each and then taking into account the crossover frequencies for that driver determine if floor/ceiling bounce is applicable to it.

Heavy thick rugs will help with floor bounce as will removing such things as coffee tables that may be between you and the speaker(s). Diffusion rather than absorption is probably more practical and useful for ceilings.