A random entry from off by one

T [Comments] (1) Sun Oct 16 09:04:10 PST compression:

I had a brainstorm this morning. I've been copying some of my old vinyl records to the computer while I still have a record player. It occurred to me that tracks on the outer grooves of an LP will sound better than tracks on an inner grooves due to the way a record moves. This is old news to some people, but not to me. The issue is that records move at a "constant angular velocity" or CAV for short. This means that the disc always spins at the same velocity. For 12 inch LPs, that velocity is normally 33 and 1/3 rotations per minute.

If you consider that a standard LP is 12 inches, it's radius is 6 inches. Circumference is 2 Pi times the radius (or Pi times the diameter), or 2 * 6 * 3.14, which is 37.7 -- 37.7 inches around the outside groove. If the record spins 33.33 times a minute, and a minute is 60 seconds, then this translates into 20.94 inches per second (37.7 * 33.33 / 60).

By contrast, the inner grooves are only 3 inches away from the center of an LP, giving us a diameter of 6 inches and a circumference of 18.84 inches. Using the same translation to inches per second, we see that the surface of the record at that distance from the center hole is moving at 10.5 inches per second -- essentially half the speed of the outside grooves!

This matters because the more space you use to store image or sound information, the better that representation will be when you play it back -- one way to think of it is that you can draw a more detailed picture on a 3x5 card than you could on a postage stamp -- well, if the outer grooves of a record are like that 3x5 card, then the inner grooves are about half that size! Not a lot of space.

This is also basically true with computers -- the more bits of data you store, the better the representation of analog data (images and sound) can be. That's why we care about the "megapixels" of digital cameras (and that's largely why MP3s don't sound as good as a CD -- they're smaller). The way compact discs avoid the "postage stamp" problem of the inner track of LPs is that their discs spin at "constant linear velocity" (or CLV) -- this means that as the laser moves across the face of the CD, the disc changes speed so that the laser is always scanning the disc at the same speed; when the laser is on the inside "tracks," the disc spins much faster than when the laser is on the outside. The data is more "tightly packed" on the inner rings and more "loosely packed" on the outer rings -- therefore the quality is always constant!

(Incidentally, unlike LPs, CDs read from the middle of the disc out!)

This is not new news at all -- it's just a lightning bolt that hit me this morning. In fact, I'm going to guess that an article very similar to this was in Hi-Fi magazine in about 1984!


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