![]() Some of you might not be all that used to logarithms (maybe skip the next section if you are). ![]() We’ll see why the caveat ‘when dealing with power quantities’ is relevant soon. When dealing with ‘power quantities’ the decibel (dB) expresses the ratio of two power values as 10 times the logarithm to base 10 of the ratio of the quantities. We have described qualitatively how logarithmic scales work to get any further with the decibel, we’ll need to define it properly… Indeed, the rock concert at 120 dB represents a rate of energy transfer to your eardrum ten billion times that provided by rustling leaves at 20 dB (you will see where ‘ten billion’ comes from soon). Logarithmic scales are useful when trying to display values with wide variation. But if you are 1.5 times as wealthy as me, then you do not have $40 billion more than me. The difference in their wealth is $40 billion. In the same way, Jeff Bezos is approximately 1.5 times as wealthy as Mark Zuckerberg (, 2018). But those two steps are not the same number of Watts of power. So is the difference from 100 dB to 120 dB. The difference from 40 dB to 60 dB is a step up of 100 times the power. The graph of decibels is labelled in increments of 20 dB. A logarithmic scale doesn’t step up in equal intervals, but instead in equal ratios. Logarithmic scales are common, but often people are not shown how they work, why they are used, or when they are in use – hence this post. The decibel scale cannot be a ‘linear scale’ – we have already described that 120 dB must be much more than twice the sound level of 60 dB. ![]() In addition, 120 metres is twice as far as 60 m. So, when measuring length, the difference between 6 metres and 7 metres is the same number of metres (one) as the difference between 78 metres and 79 metres. Many scales are ‘linear’, so that equal shifts along the scale represent equal differences in the quantity concerned. The next question is ‘how do the numbers on the scale work?’ We will see this in the section ‘power quantities and field quantities’. In fact, even for the term ‘sound level’, there are two different ways of calculating decibels, depending on the meaning you give to it. For those who think those two terms are synonymous, we will provide a discussion of the problem with the term ‘loudness’ toward the end of the post. Quite often, you will see use of the cunning term ‘sound level’ (well, I did mention ‘signal levels’ for electronics…). We will base this post in the realm of acoustics, since it is probably in connection with sound that most people are familiar with this unit, but the principles can be applied to other applications such as signal levels in electronics, and amplification.Ī tempting answer to our question might be ‘loudness’. The first question is what decibels measure. ![]() There is more than one layer of demystification to take place, too, so stop at whichever point suits you best (hopefully, though, not this point right here!). This post aims here to demystify the decibel scale. And instinctively, you might realise this cannot possibly be the case. But unless you know how the scale works, you might be led to think that a rock concert is twice as loud as a conversation. We have probably all seen charts of the decibel scale like the one below. ![]()
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