Design Considerations

When it comes to accurate sound reproduction, an open baffle loudspeaker design is probably the better avenue to take. Two familiar reasons are its forward and backward sound radiation pattern at all frequencies, and lack of cabinet, which through vibrations colors the reproduced sound. Admittedly, a well constructed cabinet can minimize vibrations, but never completely nullify them. One may wonder why speaker cabinets are used in the first place if life is so good without them, and the reason is, to prevent acoustic phase cancellation.

When a speaker driver is suspended in free air and allowed to operate, it behaves as an acoustic dipole in the mid-low frequency range. This means that as frequency goes lower, the sound waves that it radiates forward and backward are increasingly cancelling each other due to being increasingly out of phase with each other, hence the term “phase cancellation“. Spatially, the cancellation is most severe sideways and least severe on-axis. The end result is a forward-backward “figure of eight” sound radiation pattern, decreasing in intensity toward lower frequencies.
The purpose of the speaker cabinet is to trap the sound waves radiated backward, thus preventing phase cancellation in the mid-low frequency range where it otherwise would occur. The driver now behaves in the mid-low frequency range as an acoustic monopole, which means that it radiates sound in an omni-directional pattern – firing equally strong in all directions and also equally strong at all relevant frequencies.
Eliminating the cabinet requires the signal fed to the driver to be progressively amplified toward lower frequencies, to compensate for the decreasing sound intensity. We call this progressive amplification of the signal “dipole equalization“, and it’s easily accomplished electronically. However, it leads to a dramatic increase in the driver’s cone excursion toward lower frequencies, and very soon the driver “runs out” of available cone excursion. The situation is bad enough even with ordinary (cabinet) speakers, where equal loudness at all frequencies implies that the cone excursion quadruples with each halving of frequency. With dipole equalization added (for the purpose of maintaining equal loudness at all frequencies under open baffle conditions), the cone excursion increases eightfold with each halving of frequency, a true nightmare from an engineering point of view.
Luckily, acoustic phase cancellation occurs only below the “Baffle Step” frequency (around 600Hz For an average baffle), where wavelengths are longer than the baffle width. This means that we have to apply dipole equalization only below that frequency, which somewhat eases the demand on cone excursion at low frequencies.
Above the step frequency, where wavelengths become shorter than the baffle width, the forward and backward sound waves become increasingly confined to their respective hemispheres, hence gradually ceasing to interact. Nevertheless, this confinement leads to a “per ipsum” figure of eight radiation pattern, so we have it maintained up to a few hundred Hz above the step frequency. Going further up in frequency, the wavelengths become shorter than the driver’s cone circumference and the sound gradually concentrates on-axis, projecting forward more than backward at higher frequencies due to the driver’s rear construction.
Here we sadly lose the figure of eight radiation pattern. Were the driver smaller, the figure of eight radiation pattern would be maintained up to higher frequencies, but the volume of air it could move would be much too small for lower frequencies to sound loud enough.
As to the cabinet speaker, above the step frequency it ceases to be omni-directional, since, like with the open baffle speaker, the waves that it radiates forward become increasingly confined to the front hemisphere. Here, however, this also translates to an increase in loudness in the forward direction, commonly referred to as “baffle step” (hence the term “step frequency”). Going further up in frequency, the wavelengths become shorter than the driver’s cone circumference, and the sound gradually concentrates forward.
From the perspective of sound radiation pattern, we conclude that the main difference between the two types of speakers lies below the step frequency, where the open baffle speaker radiates sound in a forward-backward “figure of eight” pattern, while the cabinet speaker radiates sound in an omni-directional pattern. As a result, the open baffle speaker maintains axial directionality at all frequencies, albeit not in an ideal “figure of eight” form at higher frequencies, while the cabinet speaker gradually changes from omni-directional at lower frequencies to increasingly forward-directional at higher frequencies. Thus, the open baffle speaker has a rather constant radiation pattern at all but the two highest octaves. The sound on-axis is loudest and also equally loud at all frequencies. The sound off-axis is weaker, but still equally loud at all frequencies, more or less. We get a rather flat frequency response everywhere, and also a rather uniform power response, which means that the room is “illuminated” with an equal amount of energy at every frequency. Contrarily, the cabinet speaker has a radiation pattern that radically changes with frequency, thus achieving a flat frequency response only on-axis. It “illuminates” the room with much more energy at low frequencies than at high frequencies, thus yielding a very non–uniform power response.
One could argue that the large/multiple low frequency drivers required for an open baffle speaker is a heavy price to pay for merely a more frequency independent radiation pattern and its consequent more uniform power response, but the open baffle speaker has another advantage (apart from not having a vibrating cabinet, which was mentioned earlier), and that is its intrinsically low acoustic impedance at low frequencies. A sound source having low acoustic impedance couples ineffectively to room modes, therefore exciting them to a lesser degree than a sound source having high acoustic impedance, e.g. the cabinet speaker. That helps taming speaker-room interactions at low frequencies where other methods hardly ever work, and if we add to that the weaker low frequency radiation at larger off-axis angles, we get a sound source that ultimately doesn’t interact much with the listening room at low frequencies. This certainly can’t be said about the cabinet speaker.

Some points for clarification:
1)  For them to sound equally loud at low frequencies, an open baffle speaker has to move much more air than a cabinet speaker, which implies a very large cone area and/or a very large available cone excursion.
2)  For generating sound equally loud at all frequencies, the driver’s cone excursion needs to be largest at the lowest frequency to be reproduced. Thus, the lowest frequency we choose to reproduce determines how loud the driver can play music. Giving up the bottom octave of 20-40 Hz is the easiest way to enable a speaker play much louder. That’s true for both types of loudspeakers, be it a cabinet speaker or an open baffle one.
3) For a given cone excursion at a low frequency, a driver mounted in a cabinet yields more acoustic output than an identical driver mounted on an open baffle. That’s why cabinets are employed for loudspeakers.

The table below briefly compares between the open baffle Speaker and the cabinet Speaker.