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?

(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