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 14.6 cm, and the bumps in the groove are uniformly separated by 0.202 mm. At what rate (hits per second) do the bumps hit the stylus

The rate at which the bump hit the style is   hits per second

Explanation:

From the question we are given that

             Velocity of the record is 33 rev/min

             The radius of the grove  14.6 cm =

            distance of  separation  of the bumps in the groove  is d =  0.202 mm

Now since we know the radius to obtain the circumference of the record would be

 Since each of the bump is separated from one another by 0.202 mm the number of bumps can be obtained mathematically as

 Where n is the number of bumps

             C is the circumference of the record

              d is the distance between bumps

We are told from the question that the rate a record turn is 33rev/min

Hence the rate at which the bumps hit the style would be

        =  Rate at which record turn in seconds × The number of bumps

Since 1 minute is equal to 60 seconds

  This means each and every bump  would hit the style  at the rate of

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