This was my first attempt at a 4th order "bass reflex" tuned speaker. The principle is to tune the back pressure from the speaker driver to add to the low frequency output, which takes more energy to produce and is therefore usually lacking. I first chose the components, a 4 inch woofer and soft dome tweeter crossed over at 5 kHz, ensuring the driver was suitable for such a design.
I used the BassBox 6 Pro software for modelling output and other parameters, learning as I went. My aim was to tune the speaker slightly lower than "optimal" to extend the frequency range at the cost of some output power. I found this to work quite well for small rooms where less output power is needed, and room gain makes up the quieter bass before it drops off.
The top graph of output power against frequency shows the driver modelled in a sealed enclosure (white line) compared to the tuned enclosure used (green line). The effect of the tuned enclosure is to add bump in lower frequency output as can be seen. The consequence is that below the tuning frequency the output loses power twice as steeply. The lower graph shows the air velocity at the vent opening. High levels can be audible and described as a "chuffing" sound. In general, keeping at around 20 m/s and below keeps the turbulent sound inaudible.