## What is sound ?

« vibrations that travel through the air or another medium and can be heard when they reach a person’s or animal’s ear » The New Oxford Dictionary of English, Oxford University Press, 2002.

Sound is a mechanical vibration that travels through matter, wether solid, liquid or gaseous. Sound travels anywhere but not in space, which is void of any matter. A sound wave consists of successive compressions and expansions of matter, mainly air. Sound is thus a vibrating mechanical wave. It is measured by its amplitude and frequency, where amplitude is the wave’s power and frequency is its repetition per unit of time.

### What is a basic sound wave ?

It is a sinewave which is represented by the plotting of angles on the x axis of a graph and their sine function on its y axis.

### What is frequency ?

The frequency of sound is the number of cycles per second expressed in Hertz or Hz. The human ear hears typically from 20 Hz to 20 kHz ( 20 000 Hz ), the upper limit diminishing with age. An infant hears extremely high pitched sounds to 20 kHz and even beyond, but a sixty year old adult will hear between 5 to 10 kHz. The wave period is expressed in seconds. It is the inverse function of frequency. For instance, a 1000 Hz wave has a 1 millisecond ( 0.001 second ) period.

### What are milli, micro, mega, giga … ?

**International System of Units Number Prefixes**

10^{24} yotta **Y** 1 000 000 000 000 000 000 000 000

10^{21} zetta **Z** 1 000 000 000 000 000 000 000

10^{18} exa **E** 1 000 000 000 000 000 000

10^{15} peta **P** 1 000 000 000 000 000

10^{12} tera **T** 1 000 000 000 000

10^{9} giga **G** 1 000 000 000

10^{6} mega **M** 1 000 000

10^{3} kilo **k** 1 000

10^{2} hecto **h** 100

10^{1} deca **da** 10

10^{-1} deci **d** 0.1

10^{-2} centi **c** 0.01

10^{-3} milli **m** 0.001

10^{-6} micro **µ** 0.000 001

10^{-9} nano **n** 0.000 000 001

10^{-12} pico **p** 0.000 000 000 001

10^{-15} femto **f** 0.000 000 000 000 001

10^{-18} atto **a** 0.000 000 000 000 000 001

10^{-21} zepto **z** 0.000 000 000 000 000 000 001

10^{-24} yocto **y** 0.000 000 000 000 000 000 000 001

### What are bass, mid and highs ?

Bass frequencies are usually referred to as below 400 Hz, mids are between 400 Hz and 3.5 kHz, and highs beyond 3.5 kHz. A very often mentioned frequency in music is the A440, the A in the fifth octave of the audible spectrum at 440 Hz.

### What is a pure wave ?

Music is made of sounds and one rarely hears a pure wave, which is a pure sinewave.

### What are harmonics ?

So a sound usually includes harmonics, which are multiples of the main frequency, called the fundamental. The second harmonic is double the fundamental frequency, the third the triple, and so on.

### What is the timbre of a sound ?

A note played on a music instrument has a timbre, which is the combination of the fundamental, its harmonics and other sounds produced by the instrument playing that note.

### What is wavelength ?

A wave’s length is its velocity divided by its frequency. Since sound travels at different speeds in different matters, its wavelength varies accordingly. The wavelength is an important parameter in assessing soud behavior in different places and, especially, in designing loudspeaker systems. We will get back to this.

### What is amplidude ?

In humans, the threshold of hearing is 0.000000000001 Watt per square meter. The threshold of pain is 100 Watts per square meter. Therefore, the range spans 14 decimal places, which is not very practical, mind you …

### What is decibel ?

Long ago, Bell Labs chose to measure sound with logarithms. Logarithm is the exponent of a number. It is positive for whole numbers and negative for fractional numbers. For example, 100 = 10^{2} its logarithm is therefore 2. 0.001 = 10^{-2} its logarithm is -2. In measuring sound intensity for instance, if the measured sound is 1000 times stronger than the threshold of hearing, il will be 10^{3} times stronger which is 3 Bels or 30 decibels ( dB ). Decibel is in current use, Bel is not.

### What kind of decibel ?

Decibel is a power ratio, be it mechanical or electrical. It is only a number. To use it as a measurement unit, it requires a reference at its zero point on the scale, which corresponds to 1 in absolute numbers. So, looking at the sound intensity scale in dB SPL, the zero point is 1 X 10^{-12} Watts per square meter. Since a normal conversation measures at about 60 dB SPL, one can deduce that it is 1 X 10^{-6} Watts per square meter of sound power. Don’t worry, Watts per square meter are almost never used as a sound power unit.

### What is dB SPL ?

Well, a ratio ( gain or loss ) is expressed in decibels at all, and a measurement is expressed in decibels referenced on a scale. 0 dB SPL corresponds to that 1 X 10^{-12} Watts mentioned above, which is the average hearing threshold for a pair of human ears in good shape. One often sees sound intensity measured in decibels ( dB ) without the SPL reference, which is then implied. There is also quite a lot of different dB scales, we will see this later.

### References

The New Oxford Dictionary of English, Oxford University Press, 2002

https://en.wikipedia.org/wiki/Sound

https://en.wikipedia.org/wiki/Metric_prefix

https://en.wikipedia.org/wiki/Decibel

Sound Wave image by author.

These often refer to Wikipedia sources for convenience. Wikipedia articles mention other sources that may be useful to the reader that wants to further search the matter. A word of caution, however : since Wikipedia is a collaborative encyclopedia, anyone can modify an article ; reasonable skepticism is thus recommended.