As acoustic engineer at Jigsaw Acoustics I often get asked ‘What’s the difference between White Noise and Pink Noise?’ or when conducting sound insulation testing, if someone hears the speaker that generates the sound for the Airborne sound test, they may ask ‘Why do you use White Noise for the sound testing?’ (In fact it's Pink noise that the speaker is generating, more on that below)
White noise is sound that has equal energy per constant bandwidth (Hz) and Pink Noise has equal energy per percentage bandwidth (octave).
The diagram below shows how the two types of broadband noise look when plotted on a Linear (unweighted) frequency scale. The white noise remains flat through the frequency range, whilst the pink noise falls by 3dB per octave.

When plotted on a Log Frequency scale, however, the white noise increases by 3dB per octave and the pink noise remains flat, as shown below. This is the main reason that we use Pink noise in sound insulation testing. The Pink noise is calibrated to how a human hears sound, on a logarithmic scale. This is the same as how the decibel is calculated, read more about the terminology on my Acoustics glossary page here

The Guardian published an article around using white noise as a sleep aid: https://www.theguardian.com/lifeandstyle/2020/oct/18/white-noise-as-sleep-aid-may-do-more-harm-than-good-say-scientists?CMP=Share_AndroidApp_Other
The paper found that ‘the quality of evidence for continuous noise improving sleep was very low, which contradicts its widespread use. Additional research with objective sleep measures and detailed descriptions of noise exposure is needed before promoting continuous noise as a sleep aid, especially since it may also negatively affect sleep and hearing.’
The paper can be found here https://www.sciencedirect.com/science/article/pii/S1087079220301283
One of the reasons for white noise apps being popular may also be that they provide a certain amount of masking noise for the user. In situations where the person is attempting to sleep during the daytime or in an environment that is disrupted by background noise this may be beneficial. Think of shift workers or long distance lorry drivers.
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