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2 January, 08:36

As the drawing illustrates, a siren can be made by blowing a jet of air through 20 equally spaced holes in a rotating disk. The time it takes for successive holes to move past the air jet is the period of the sound. The siren is to produce a 2087.8-Hz tone. What must be the angular speed ω (in rad/s) of the disk?

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Answers (2)
  1. 2 January, 08:38
    0
    Given:

    n = 20 holes

    f = 2087.8 Hz

    1rev = 20 hole

    = 20 cycle/rev

    ω = (2π * f) * n

    n = number of cycles per revolution

    = 1/20

    = 0.05 rev/cycle

    ω = 2π * 2087.8 * 0.05

    = 655.9 rad/s
  2. 2 January, 08:58
    0
    Answer: 656 rad/s

    Explanation:

    Angular frequency is also called radial circular frequency. It measures angular displacement per unit time. It's unit is rad/s. It is also greater than the regular frequency by a factor of 2π. Hence, angular frequency, ω = 2πf

    If 1 revolution (20 hole) = 20 cycle per revolution.

    Then, 2087.8 (cycle) = x revolution

    X revolution = 2087.8/20)

    X revolution = 104.39 revolution

    ω = 2πf

    ω = 2 * π * 104.39

    ω = 655.98676

    ω ~ 656 rad/s
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