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Before we go any further, we need to just collect a bunch of information about vinyl records.

General Information

Min groove depth: 0.001″ = 0.039 µm
Max groove depth: 0.005″ = 0.197 µm

12″ LP’s

Outside modulation groove radius: 146 mm
Inside modulation groove radius: 60 mm
Total maximum modulation radius: 86 mm (3.4″)
Typical modulation radius: 76 mm (3″)

7″ 45 RPM

Outside modulation groove radius: 84 mm
Inside modulation groove radius: 54 mm
Total maximum modulation radius: 30 mm (1.2″)

Basic math

Pitch = (Running time x RPM) / Modulation Radius

Groove Width = (1000/LPI + 1) / 2

Peak Amplitude of Displacement = Peak Lateral Velocity / (2 π freq)

Examples

Pitch = (Running time x RPM) / Modulation Radius
Pitch = (20 minutes x 33.333) / 76 mm
Pitch = 8.8 lines per mm (LPm) = 223 LPI

Groove Width = (1000/LPI + 1) / 2
Groove Width = (1000/223 + 1) / 2
Groove Width = 2.74 mil = 2.74 x 10^-3 inches =  0.0697 mm

Peak Amplitude of Displacement = Peak Lateral Velocity / (2 π freq)
Peak Amplitude of Displacement = 70 mm/sec / (2 π 1000)
Peak Amplitude of Displacement = 0.011 mm

Reference:
“Basic Disc Mastering” by Larry Boden (1981)

On to Part 6