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A vinyl record is played by rotating the record so that an approximately circular groove in the vinyl slides under a stylus. Bumps in the groove run into the stylus, causing it to oscillate. The equipment converts those oscillations to electrical signals and then to sound. Suppose that a record turns at the rate of 33 rev/min, the groove being played is at a radius of 14.2 cm, and the bumps in the groove are uniformly separated by 0.499 mm. At what rate (hits per second) do the bumps hit the stylus?

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Answer:

983.400345675 hits per second

Explanation:

Radius = 14.2 cm

Record turn rate = 33 rev/min

Bump separation = 0.499 mm

Circumference of the record = [tex]2\pi 0.142=0.89221231362\ m[/tex]

Number of bumps in the groove = [tex]\dfrac{0.89221231362}{0.499\times 10^{-3}}=1788.0006285\ bumps[/tex]

The rate which the bumps hit the stylus = [tex]33\times\dfrac{1788.0006285}{60}=983.400345675[/tex]

The rate at which the bumps hit the stylus 983.400345675 hits per second

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