Types of noise

In everyday language, the word "noise" indicates something indistinct and chaotic. However, in a scientific context, various types of noise can be quantitatively characterised by studying their spectral content. The classification of noise is of fundamental importance in the study of all signals that contain random components and is heavily used in sound technology, as is illustrated in the following paragraph.

For a discussion on the differences between sound and noise, see the page Sound or noise?

White noise

By analogy with white light, which is the superposition of electromagnetic waves of all visible frequencies, if a noise has a roughly "flat" spectrum, with waves of all frequencies and similar intensity at each frequency, it is called white noise. White noise, with its high-frequency "shrill" sound, has an excess of brightness that is very annoying. The reason is that each octave contains twice as many frequencies as the previous one: with the same intensity per hertz, the highest audible octave (from 10,000 to 20,000 Hz) alone contains half the energy of the whole noise. If you wish to listen to an example, click on the audio file below.

rumore_bianco.wav White noise

Alternatively, you can hear an example by connecting to our virtual laboratory and selecting Wave forms: Noise. Observe the extension of the spectrum on all the frequencies with a variable amplitude (remember that intensity is proportional to the square of the amplitude) but, on average, constant in the various regions of the spectrum. A remark: the app is programmed only to generate sounds having multiple fundamental frequencies, therefore, what you are hearing is not true white noise, which should contain the full range of frequencies. As explained on the related page, a wave obtained by superposing harmonics of the same fundamental repeats with the period of the fundamental (the least common multiple of the periods of the harmonics is exactly the period of the fundamental). What you obtain is therefore a "periodic noise": a wave that is very irregular within each period but repeats identically in every period. This is why, as also explained in the frequently asked questions of the app, instead of a hiss you hear a note of definite pitch.

Coloured noises

There are various types of "coloured" noises, which are characterised by having several components of the spectrum more prevalent than others. For example:

• pink noise, which has larger amplitudes (and, therefore, intensities) at low-frequency components. It can be obtained from white noise by filtering out the high frequencies. Pink noise is often created according to the following rules (even if it is a bit of an oxymoron to state rules for creating a random event such as noise):
  • the intensity per hertz of bandwidth (the spectral density) decreases as the inverse of frequency. This means that it is halved when passing from one octave to the next (in the logarithmic scale this is equivalent to an attenuation of 3 dB). Since each octave is twice as wide as the previous one, the energy contained in each octave stays the same.
  • the intensity profile within an octave is repeated for each octave.

It seems that noise built this way has relaxing properties similar to many natural sounds (rain, waterfalls, etc.). There are even CDs with pink noise!

You can try to build pink noise with the Fourier app by reducing the amplitudes by a factor ${\displaystyle \sqrt{2}\approx 1.41}$ from one octave to the next, in such a way that the intensity, which is proportional to the square of the amplitude, decreases by 3 dB per octave. The first octave includes one partial, the second two, the third four, the fourth eight, etc. You will find the results very disappointing: the further regularisation introduced in the spectrum (apart from the one caused by the software itself) will not allow us to mimic the randomness that a noise, even a pink one, should have.

Pink noise is used in recording studios and in acoustics to calibrate sound systems and rooms, because it contains the same energy in every octave and its spectral distribution is closer than that of white noise to real sounds (and to the sensitivity of our ears, see the page on isophonic curves).

rumore_rosa.wav Pink noise

• brown noise

This type of noise contains more dominant low frequencies than pink noise. Its intensity per hertz of bandwidth decreases as the inverse of the square of the frequency (an attenuation of 6 dB from one octave to the next in the logarithmic scale). Brown noise sounds like the rumbling of thunder.

rumore_marrone.wav Brown noise

• red noise

The name "red noise" is often used as a synonym of brown noise; sometimes it indicates instead noise in which low frequencies have even higher intensity (without precise mathematical rules as with pink and brown noise). It sounds like a very low rumble (similar to a subway train or the noise of a motor that causes walls to vibrate due to resonance) and is at the lower threshold of audible frequencies. It is often used in electronic music and film soundtracks.

• blue noise

This sound is the complement of pink noise. High frequencies are its strongest spectral components with an increase in intensity of 3 dB per octave. It is obviously obtained by filtering out the low frequencies. It sounds like a shrill, artificial hiss.

• purple noise

This is the complement of brown noise and its spectral content is the highest at high frequencies. Its intensity increases by 6 dB per octave. Its hissing effect is even more irritating then that of blue noise.

Check your understanding

In-depth study and links

• The terminology used for noise comes from the spectrum of electromagnetic waves. We encourage you to visit the corresponding page to fully appreciate the analogy with those waves.

• Many sound phenomena that we classify as noise are more due to the "confusion" perceived by our auditory system rather than the spectral composition of the sound phenomena themselves. Visit the page on critical bands and beats, if you wish to hear some examples.