Clearing The Air: Defining A Host Of Commonly Used Audio Terms

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Decibels, Phons & SPL

A decibel is a unit of measurement for sound, one tenth of a Bel, named after Alexander Graham Bell, the inventor of the telephone. One decibel is said to be the smallest difference in sound detectable to the human ear (although any monitor engineer who’s been asked for a “tenth of a dB” change knows that there’s more than physics at play when it comes to that!).

But a decibel isn’t a thing in and of itself, an absolute – it’s a ratio, a relative measurement. You can turn something up by a decibel, but something cannot be x-many decibels loud without a suffix such as dB(A), dB(C), or dB SPL.

SPL, of course, stands for sound pressure level, and 0 dB SPL represents the threshold of hearing, below which even the most perfect human ear cannot detect a sound. It’s measured by the Pascal (Pa); however, it’s impractical to employ this reference in every day use because it’s a tiny unit and we can hear across a wide range, from 0.00002 Pa (threshold of hearing) to 200 Pa (where it’s better not to find out what happens).

Enter the dB SPL measurement. If physics is your thing, sound pressure level in decibels is defined as 20 log (p/po) where p is sound pressure, and po is the reference sound pressure of 0.00002 Pa or 0 dB SPL, a.k.a., the threshold of hearing.

Without getting too bogged down in physics and equations, SPL is a sound field quantity and uses a 20-log factor, meaning that:

+/- 6 dB is a doubling/halving of sound pressure
+/- 10 dB is multiplying/dividing by a factor of 3
+/- 20 dB is multiplying/dividing by a factor of 10

And what’s a phon? Because of our non-linear hearing, a standard measurement is needed for perceived intensity. The phon is a unit of loudness for pure tones that is matched to the perception of a reference frequency of 1 kHz – is the sound pressure level that matches the perceived loudness of a 1 kHz tone. If a sound is perceived to be equally loud as a 1 kHz tone at 70 dB SPL, it is said to have a loudness of 70 phons.

Sign, Square & Sawtooth Waves

That same noise generator on the console may have an option to generate tone – a sine wave that oscillates evenly at a certain number of times per second (1000 Hz = 1000 oscillations per second). A sine wave is a smooth, continuous wave whose peak is equal and inverse to its trough, like an ocean wave; its sound is a pure, single-frequency tone – the pure tone of a flute sounds like a sine wave. This is nature’s waveform.

A square wave, by contrast, is something not generally found on a console but often heard in electronic music. Square waves are made up of harmonics – really sine waves with added odd harmonic frequencies in inversely proportional quantities (Figure 4).

Figure 4: Top to bottom: sine, square and sawtooth waves.

Like a sine wave, the amplitude of a square wave oscillates at a steady rate between peaks and troughs, with the same time spent at each extreme. The “perfect” square wave is not actually physically attainable because technically it requires that the switch between peak and trough occurs instantaneously – not possible without messing with the time-space continuum!

Square wave = fundamental frequency + (3rd harmonic at 1/3 level of fundamental) + (5th harmonic at 1/5 level of fundamental) + (7th harmonic at 1/7 level of fundamental), and so on to infinity. In the real world, we can’t go to infinite frequency, and so our bandlimited systems produce an imperfect version of a square wave.

The sound quality of a square wave is “buzzy” and hollow sounding when compared with a sine wave of the same frequency, which sounds warm and smooth. As noted, it’s frequently used in EDM and was also common in 1980s pop music. Electric guitar distortion also resembles a square wave the more it’s applied, and reed instruments such as saxophone have square wave qualities.

Finally, staying with musical instrument comparisons, bowed instruments such as a violin and cello create a sawtooth-style wave, which consists of both odd and even harmonics of the fundamental.

Sawtooth wave = fundamental frequency + (2nd harmonic at 1/2 of level of fundamental) + (3rd harmonic at 1/3 level of fundamental) + (4th harmonic at 1/4 level of fundamental), and so on to infinity.

This creates the characteristic dense “rasp” of a bowed instrument and is also the basis of synthesized string sounds that are common in many forms of music.

The bottom line: do we need to know most of this to mix a show? Probably not. But when we play instruments and mix audio, we’re fundamentally playing with physics, shaping energy and creating new forms – isn’t it pretty cool to understand what’s going on under our fingertips.