where fp is the frequency of the first resonance mode. I then reduced the length by a factor of 0.73 given by the ratio between the speed of sound in the lined TL (with 50% of volume occupied by foam) and the speed of sound in air. The lenght development of the HADO is therefore 73 cm (note that the test line, 1 meter long, is accidentally tuned at the resonance frequency of the speaker). The total volume is 4.5 litres and, from a first simulation, should allow an f3 of at least 65 Hz.
The small offset needed to mount the driver on the front panel, even if only a few centimeters, helps to control the resonance of the second harmonic (3fp), and mitigates the first dip in the system response, without practically affecting the low frequency contribution of the opening.
I added a small coupling chamber, equal to one third of the total volume, to observe the impact this would have on the TL’s behaviour. The data collected were fundamental to integrate the coupling chamber into the simulation model. It turned out that the best way to represent the compliance of this additional volume of air is a simple parallel capacitor, with the only care taken to place it correctly along the line at a distance equivalent to that of the driver offset. In our 73 cm long line each of the 50 sections is worth about 1.5 cm; in the HADO the driver is mounted with about 6 cm offset, so the capacitor should be replace the one in the fourth RLC section.
The model already contains the directives that automatically determine the capacitor value by simply inserting the volume of the coupling chamber (VCC).