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?

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

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