I remember those from the early 1970s. At the time, I thought JBL was hot stuff, and like you, I wondered how those lenses worked. But home audio was still in its infancy. I can’t really explain the physics behind them, but I’ll take a few guesses
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The link you found said this on the front page:
The JBL family of acoustical lenses was originally designed for stereophonic audio systems for motion picture theater application. They were first presented to the industry in 1954. The acoustic lens, which had been described by Bell Laboratory scientists Kock and Harvey in 1949, had not previously been applied to commercial sound reproduction. The acoustic lens, as engineered by JBL, was the first real Innovation in high-frequency sound reproduction since the early 1930’s.
Remember that JBL’s main business was sound systems for theaters and large auditoriums – not home audio. In the 1950s, when they developed these devices, sound from compression drive tweeters rapidly dissipated in auditoriums. Apparently, using horn loaded waveguides was not enough, so they added these lenses. Their goal, as far as I understand it, was not to achieve broad dispersion, but to project the treble sound out further into the room. Think of light from a bare light bulb compared to light from a spot light with the same bulb and a reflector.
Something about these acoustic lenses reminded me of the
Fresnel lenses you can see on old lighthouses. They had what appears to be a similar goal, to take the weak light from an oil lamp, focus it into a larger beam that projected out to much farther distance.
These acoustic lenses are designed to work for acoustic waves with much longer wavelengths than visible light. They look odd to our eyes, but to sound waves, they look just like a Fresnel lens.
While searching Google, I found this picture. That was what made me think of a Fresnel lens on a lighthouse. The sound source is the small horn at the guy's right shoulder.