Chapter One: An Acoustics Primer

5. What is frequency?

The number of cycles per unit of time is called the frequency. As mentioned in the previous section, the period (units of time per cycle) is the reciprocal of the frequency. For convenience, frequency is most often measured in cycles per second (cps) or the interchangeable hertz (Hz), so 60 cps = 60 Hz (named after the 19th C. physicist). As is customary, the fully-named unit is all lower case, and the abbreviation is capitalized. One thousand Hz is often referred to as 1 kHz (kilohertz) or simply '1k' in studio parlance.

 
4 Hz image
14 Hz image
 

Ultrasonic frequency ranges: One million hertz is referred to as 1 MHz (megahertz), and one billion hertz is 1 GHz (gigahertz). Neither MHz nor GHz are normally part of audio applications, as our human hearing stops at 20 kHz at best. In fact, sound in air has a frequency limit due to propagational laws. The highest airborne acoustic frequency produced and recorded as of this writing is 10 GHz, and these waves travel extremely short distances before dying out. Medical ultrasounds range from 2 MHz to 15 Mhz and travel through solids and liquids, not air. GHz, maybe terahertz someday, however, are definitely relevant when selecting a computer by processor clock speed. My personal favorite SI frequency band (being a Seinfeld fan) is the yottahertz (YHz), which is 1024 Hz.

click video image to play/pause

An additional method for quantifying frequency, used extensively in signal processing maths, such as phase vocoding and STFT calculations, entails measuring the angular velocity of the signal, or the rate of change of angular displacement (displacement being represented by the Greek symbol theta (θ)). In this case, the angular velocity is simply the rate of phase rotation represented by a point on the circumference of the ccw spinning disk. The video above represents a single cycle of a sine wave traced via rotational change (disk) vs. time. Angular velocity is usually denoted by the Greek lower-case letter for omega (ω) and represents the rate of rotation, such that an entire cycle is equal to 2π radians rotation (equivalent to 360°). ω is normally expressed as radians per sec or rad/s. ω as rad/s is equivalent to 2πƒ expressed as Hz or cps. So 1 Hz would be ω=2π (~6.3) rad/s, and 60 Hz would be ω=~377 rad/s.

For further study, see Hyperphysics: Angular Velocity