Sound theory: Waveforms

It has been fully described in the previous paragraphs. It is perceived as a frequency tone equal to the sinusoid's frequency. It is easily generated electronically and is often used as a testing instrument.

In the previous paragraphs the flow of sound as well as the various characteristics of sound have been illustrated [Properties of Sound ] .

As shown in the figure:

Square Wave

As we can see the harmonic content of a square wave is composed solely by even harmonics. The amplitude decreases with a flow rate of 1/f. Empirically speaking this means that the second harmonic (the one that has triple the frequency of the fundamental harmonic, the one having double the frequency not being present) has an amplitude equal to 1/3 of the fundamental harmonic, the third harmonic has 1/5 and so on.

These are the sounds of a square wave, one having a frequency of 440 Hz (the equivalent of a A note) and one having 1KHz frequency:

Square Wave (f=440 Hz)  [Track 4]

Square Wave (f=1 KHz)  [Track 5]

Saw-tooth wave

Saw-tooth waves have all harmonics present, the amplitude of every harmonic is half the precedent harmonic.

These are the sounds of a saw-tooth harmonic, one has a frequency of 440 Hz ( the equivalent of musical note A ) and one has a fequency of 1 KHz:

Saw-tooth wave (f=440 Hz)  [Track 6]

Saw-tooth wave (f=1 KHz)  [Track 7]

Triangular Wave

The triangular wave has a harmonic content that is very similar to that of a square wave. The difference is that its amplitude decreases with a flow-rate of 1/f².

These are the sounds of a triangular wave, one has a frequency of 440 Hz (the equivalent of musical note A) and one has a fequency of 1 KHz:

Triangular wave (f=440 Hz)  [Track 8]

Triangular wave (f=1 KHz)  [Track 9]

The main difference between harmonics and hypertones is that the latter have no connection with the fundamental frequency whilst harmonics are their multiples.

Hypertones strongly depend upon the musical instrument that has generated them and they contribute to characterizing sound regardless of the fact that their amplitude is inferior to that of harmonics.