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What's wrong with CDs? (Posted on 2005-03-30) Difficulty: 3 of 5

The diameter of a long playing vinyl record is 12 inches. The unused center has a diameter of 4 inches, and there is a smooth outer edge that is 1 inch wide. If there are 91 grooves to the inch, how far does the needle travel within the groove during playback of the record?

See The Solution Submitted by Erik O.    
Rating: 4.0000 (1 votes)

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An Aside--trivia | Comment 4 of 10 |
(In reply to Non-Calculus Approximation--spoiler by Charlie)

According to http://history.acusd.edu/gen/recording/speeds.html, real LP records have a pitch of 300 grooves per inch and a 1/4-inch guard band (the "smooth outer edge"). To quote:

<<
For the 33-1/3 12-inch LP, only the arithmetic is different. For a 23-minute record, 766 grooves are needed. At a pitch of 300 per inch, this is a music groove band of 2.553 inches wide for the maximum music groove diameter of 11-1/2 inches on a 12-inch record with a 1/4-inch guard band. This leaves a minimum music groove diameter of 6.394 inches; more than needed but found useful for progress. On the basis of such a calculation, the decision was to stay with the 33-1/3 r/min speed. The average wavelength for the top frequency reproduced was 0.0055 inches for the 78 r/min compared to 0.0012 for the 33-1/3. The improvement in compound had more than offset this difference. >>

This apparently means 23 minutes on a side, rather than for the whole 2-sided record.

But http://www.smartdev.com/glossary.html  has

<<
Groove Pitch or Pitch of Grooves:
The physical spacing of the record grooves across the surface of the disc. Groove pitch is usually specified in "lines per inch" rather than "grooves per inch," since a record has only one groove which spirals continuously from the beginning to the end. 78-rpm records have a coarse groove pitch, typically about 75 lines per inch. Modern long-playing records average about 225 lines per inch, but can be as high as 300.
>>

Edited on March 30, 2005, 3:55 pm
  Posted by Charlie on 2005-03-30 15:53:06

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