Our pop group releases a single on an old-fashioned vinyl 45 record. As part of their work, for their first single, the band begins by playing a single pure tone of approximately 666Hz. For your information, a 45 record revolves on a turntable at 45 times a minute (rpm). The information on the record is read by a needle resting in a small groove. The way the record reproduces a sound is that the groove will contain a series of small bumps that the needle will hit, making it vibrate. Assume the grooves start right at the edge of the disc.
a) How far apart are the bumps along the groove at the beginning of the single? A vinyl 45 record is read from the outside in, and you’ll need to know the diameter of a vinyl 45 record.
b) Suppose there are bumps separated by the same distance near the very end of the recorded area. What is the frequency heard when playing the end of the record? (You’ll need to know the diameter of a 45 at the end of its play time.)
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Please show all your work :) How far apart are the bumps along the groove at the beginning of the single?