## 5. What is frequency?

The number of cycles per unit of time is called the frequency. For convenience, frequency is most often measured in cycles per second (cps) or the interchangeable Hertz (Hz) (60 cps = 60 Hz), named after the 19th C. physicist. 1000 Hz is often referred to as 1 kHz (kilohertz) or simply '1k' in studio parlance.

The range of human hearing in the young is approximately 20 Hz to 20 kHz—the higher number tends to decrease with age (as do many other things). It may be quite normal for a 60-year-old to hear a maximum of 16,000 Hz.

 Amazing factoid #2: For comparison, it is believed that many whales and dolphins can create and perceive sounds in the 175 kHz range. Bats use slightly lower frequencies for their echo-location system.

Frequencies above and below the range of human hearing are also commonly used in computer music studios. We refer to these ranges as:

 <20 Hz 20-20kHz >20kHz sub-audio rate audio rate ultrasonic

Sub-audio signals are used as controls (since we can't hear them) in synthesis to produce effects like vibrato. The lowest 32' organ pipes also produce fundamental frequencies below our ability to hear them (the lowest, C four octaves below 'middle C' is 16.4 Hz) — we may sense the vibrations with our body or extrapolate the fundamental pitch from the higher audible frequencies (discussed below), but these super-low ranks are usually doubled with higher ranks which reinforce their partials.

The perceived pitch of a sound is our ear/mind's subjective interpretation of its frequency. As will be discussed in a later chapter, an increased frequency is perceived by us as a higher pitch, although not linearly. A frequency lowered by 400 Hz will not be perceived by us as a change equivalent to a pitch to raised by 400 Hz. Therefore, frequency and pitch should not be considered interchangeable terms.

Frequency is directly related to wavelength, often represented by the Greek lambda (). The wavelength is the distance in space required to complete a full cycle of a frequency. The wavelength of a sound is the inverse of its frequency. The formula is:

wavelength ( ) = speed of sound/frequency

 Example: A440 Hz (the frequency many orchestras tune to) in a dry, sea level, 68°F room would create a waveform that is ~2.5 ft. long (2.56 = 1128 (feet/sec) / 440). Be certain to measure the speed of sound and wavelength in the same units. Notice how if the speed of sound changed due to temperature, altitude, humidity or conducting medium, so too would the wavelength.

As can be seen from the above formula, lower frequencies have longer wavelengths. We are able to hear lower frequencies around a corner because the longer wavelengths refract or bend more easily around objects than do shorter ones. Longer wavelengths are harder for us to directionally locate, which is why you can put your Surround Sound subwoofer most anywhere in a room except perhaps underneath you. At 20°C, sound waves in the human hearing spectrum have wavelengths from 0.0172 m (0.68 inches) to 17.2 meters (56.4 feet).

One particularly interesting frequency phenomenon is the Doppler effect or Doppler shift. You've no doubt seen movies where a police siren or train whistle seems to drop in pitch as it passes the listener. In actuality, the wavelength of sound waves from a moving source are compressed ahead of the source and expanded behind the source, creating a sensation of a higher and then lower frequency than is actually being produced by the source. This is the same phenomenon used by astronomers with light wavelengths to calculate the speed and distance of a receding star. The light wavelengths as stars move away are shifted toward the red end of the spectrum, hence the term red shift.

 The formula for an approaching sound source is: The formula for a receding sound source is: fobserved=frequency we hear, fsource=frequency of source, v=speed of sound, vsource=speed of approaching or receding sound source

 Example: At 20°C the speed of sound (v) is 343.7 m/s. An oboist in a convertible traveling at 29 m/s (vsource ) or 65 mi/hr is tuning to A440. As the convertible approaches your position, you hear 480 Hz and as the car passes and moves away, you hear 405 Hz.

It is particularly important for musicians to have their hearing tested regularly, where audiograms may depict both the maximum frequency heard and any loss of sensitivity in certain frequency ranges. Many audiologists will test only up to 8kHz, because that is considered the high end of what is necessary for speech perception. Composers should insist on tests for the full hearing spectrum if possible.

For further study, see Hyperphysics->Periodic Motion

An Acoustics Primer, Chapter 5
URL: www.indiana.edu/~emusic/acoustics/frequency.htm