Control around the cabinet.
A ring of tweeters can be steered: delay the ones at the back and the wavefronts line up in one direction. The Field chapter computes that beam from the geometry, and lets you turn it.
Computational acoustics / Interactive companion
Two compact speakers, rebuilt part by part, then driven with real acoustics: what the drivers are, how a voice coil moves a cone, how five tweeters make a beam, and what a room does to all of it.
The explanations and part descriptions still work. Try a browser with WebGL 2 or WebGPU enabled.
Open the 2D acoustic diagram →The cabinets follow the published envelopes and photographs, and the drivers, motors, horns and duct are placed and sized to the manufacturers’ own cutaway renderings and, for HomePod, to Apple’s patent; how each part is built inside is generic. Each part says which. The sound fields are computed from ideal point sources. What the model can and cannot show →
The architectural difference
A ring of tweeters can be steered: delay the ones at the back and the wavefronts line up in one direction. The Field chapter computes that beam from the geometry, and lets you turn it.
A driver pointed at the ceiling adds a second, later copy of the sound at the listener. The Field chapter computes the two together and shows the comb filter that results.
The visual evidence
Sources & model boundaries
This companion extends the published technical investigation. The two cabinets follow the published envelopes (Apple: 168 × 142 mm; Bose: 184.7 × 121.1 × 167.5 mm) and their outlines are read off the product photographs. Inside, every driver, motor, horn, board and duct is placed and proportioned to the manufacturers’ own cutaway renderings, scaled against the published height, and the HomePod tweeter tilt and horn height follow the ranges in Apple’s patent US12192698B2. How each part is built (cone, surround, spider, voice coil, magnet and plates, the horn passages, the duct section) is a first-principles reconstruction drawn in Blender, so the mechanism can be taken apart and explained; the part panel says, for each part, what is proportioned to a source and what is generic. Nothing is either company’s CAD, and no interior dimension is a measurement of a production unit.
The sound fields are linear acoustics of ideal point sources: monopole sums with delay-and-sum steering for the tweeter ring, and Allen and Berkley image sources for the room and the ceiling bounce, at 343 m/s. They model interference and geometry exactly for those idealised sources and nothing else: no driver directivity beyond a simple cardioid weighting, no diffraction, no absorption spectra, no room modes, and none of either manufacturer’s processing. The functions are tested in Node; the tests are in the repository beside the page.
Bose’s FCC internal-photo exhibit is listed for release on 11 November 2026; the model therefore relies on the public marketing cutaway, not an inspected production unit.
Detailed model and reference notes →