How to Calculate an Angular Frequency

By John Brennan
Different pitches of sound have different frequencies.

The frequency of a wave measures the number of times a complete wave cycle will pass a given position. Angular frequency is similar, except that it's been converted to a form that's easier to use in trigonometric equations. While frequency measures cycles per second, or Hertz, angular frequency measures radians per second, where radians are a measurement of an angle similar to degrees. There are 2π radians in a circle, so a frequency of 1 Hertz is equivalent to an angular frequency of 2π.

Determine the frequency of the wave you're working with. Frequency for waves like sound waves and electromagnetic waves is typically measured in cycles per second, or Hertz, and is equal to the speed of the wave divided by its wavelength.

Multiply the frequency by 2π to obtain the angular frequency. The symbol ω in a wave equations stands for angular frequency.

Plug the angular frequency into the wave equation to model the wave. The wave equation is y(x, t) = A cos ( kx + ωt ), where A is the amplitude of the wave or its maximum height, k is the wave number (equal to 2π divided by wavelength), x is the distance from the y axis and t is the length of time elapsed.

Tip

Since the wave speed is equal to the wavelength times the frequency, the wave speed will also be equal to the angular frequency divided by the wave number, ergo v = ω / k.

About the Author

Based in San Diego, John Brennan has been writing about science and the environment since 2006. His articles have appeared in "Plenty," "San Diego Reader," "Santa Barbara Independent" and "East Bay Monthly." Brennan holds a Bachelor of Science in biology from the University of California, San Diego.