White And Pink Noise: What You Should Know

Noises are sound effects, they have nothing to do with the light. So, why are we talking about white and pink noise?

The reason comes from the knowledge that white light is the composition of all the colors in the visible spectrum. By association, a noise composed by all the frequencies in the audible spectrum was defined as white as well. From there, it became easy to extend this concept to other kind of audio noises, and assign a different color to each one of them.

The reality as we know today, however, is quite different. Today we know that any audible noise is obtained by mixing together all the possible frequencies of the audible spectrum. The difference lays in the perceived intensity of the sound at each frequency or interval of them.

We know know that the white noise is characterized by having a constant amplitude at all the frequencies, which translates in saying that the power of the various frequency of the white noise is constant. Or, even better, the power spectral density of the white noise is the same at all frequencies.

Or is it?

Well, the problem of us humans is that we do not believe in something unless we can prove it to be true.

The fact is: our ear does not perceive the sound linearly. The ear perceives the sound logarithmically. In particular, our ear can perceive much better the high frequencies than the low frequencies. As a result, when we listen to the white noise, we perceive it as very rich of high frequencies, but that is just because we cannot hear well the lower frequencies of the white noise spectrum.

The proof of that? Look at the screen of a spectrum analyser for the white noise.

Look at the top crests. Those are the ones that represent the amplitude of the signal at each frequency. Do you see how it remains constant at all the frequencies?

Let’s now talk a little bit about the so called pink noise. When we listen to the pink noise we perceive it as filled of all those low frequencies that were missing from the white noise.

However, the reality is quite different. The pink noise intensity changes with the frequency. In particular, it is such that it decreases with the increase of the frequency at a rate of -3dB per octave. Incidentally, this is the same rate at which our ears work, but in the opposite direction: when the frequency increases, our ear becomes more sensitive to the intensity of the sound at a rate of about +3 dB per octave. The two rates are the exact opposite and so they cancel each other and, to our ear, the pink noise seems to contain all the frequencies of the audible spectrum and all with the same intensity. Weird, isn’t it?

Here is the proof of that.

Do you see how the top crests at the various frequencies become smaller and smaller at the increase of the frequency?

So, contrary to the white noise, the pink noise presents a reduction in the intensity of the sound that is inversely proportional to the frequency of the sound itself and, specifically, when the frequency doubles, the signal becomes 3dB smaller. in other words, the power spectral density of the pink noise decreases with the increase of the frequency with a ratio of -3dB per octave.

If you like, go watch this video on YouTube, where I describe how to build a generator of white and pink noise for the lab. You’ll be able to hear both the white and the pink noise several times throughout the video, so you can get an idea on how we perceive each one of these noises.

Let’s now talk about how these noises are actually used in lab and in the real world.

Let’s begin from the white noise. Because of its characteristic of providing a constant intensity at all the frequencies, it becomes really useful when we want to measure the frequency response of an audio amplifier, for example. We inject the white noise into the input of the amplifier and we attach to the output a spectrum analyser. The analyser will tell us the range of frequencies that the amplifier is capable of handling, but it will also tell us if the amplifier has a flat frequency response, or if it amplifies better certain frequencies rather than others. This information can then be used to tune the amplifier to make it work with a flat response at all frequencies.

Another usage is in filters measurements. Again, putting at the input of the filter the white noise and attaching the output to a spectrum analyser, we can actually visualize in a single shot if the filter works in the required range of frequencies and if it provides the right attenuation at each frequency.

And what about the pink noise? Pink noise becomes very useful when installing professional sound systems in a room. Such systems normally posses what is called a graphic equalizer, which allows to change the response of the system to various frequencies. We input a pink noise into the sound system and we let it fill the room with its sound. Then, using some microphones in the strategic places of the room, we can convert the actual sound back into electrical signals and send them to a spectrum analyser. Then we start playing with the graphic equalizer to obtain a flat response on the analyser. Because the pink noise has a distribution of power density which is a complement of the sensitivity of our ears, when we obtain a flat response we have actually adapted the sound system to the most appropriate way to generate sound pleasant to our ears. Without doing so, the sound system would amplify the sound linearly, therefore changing it from what it was originally intended during its recording. Remember, we want the electronic instruments behave like our ears, because that is how we perceive the musical instruments and the voice of people, not linearly. The pink noise allows us to tune the sound system in exactly that way.

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