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 gr

Question

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 11.5 cm, and the bumps in the groove are uniformly separated by 0.374 mm. At what rate (hits per second) do the bumps hit the stylus?

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Mít Mít 3 years 2021-08-11T14:28:54+00:00 1 Answers 16 views 0

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    2021-08-11T14:29:56+00:00

    Answer:

    1063 hits/sec

    Explanation:

    -Angular velocity of the record is given as:

    \omega= 33 \ rev/min=0.55 \ rev/s

    -Radius of the record is given as:

    r=11.5\ cm=0.115\ m

    The linear speed of the record is calculated as:

    v=\omega r\\\\=0.55\times 2\pi \times 0.115\\\\=0.3974 \ m/s

    The grove bumps are uniformly separated as 0.374 mm(0.000374), the number of hits per second is calculated as:

    hits/s=\frac{v}{us}\\\\=\frac{0.3974}{0.000374}\\\\=1062\  hits/s\approx 1063 \ hits/s

    Hence, there are 1063 hits/sec

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