Thermodynamic beta: it directly tells you how energy will be exchanged between objects to reach thermodynamic equilibrium. This proportionality to volume is how we were able to first define the concept of temperature in the first place. Under ideal gas, it's proportional to mean kinetic energy, and, assuming constant pressure and amount of gas it also proportional to volume. We have a few different quantities that all tells you how hot something is: We have these different quantities because our physical processes are not linear, so depending on context some quantities will be more directly usable for the job. More generally, there are always many different quantities that are non-linearly related. And can you really say which quantity is more fundamental? Energy/power is proportional to square of amplitude, so anything linear with amplitude is not linear with energy/power and vice versa. Everything is non-linear from a different perspective. Just want to point out that there are really no units that are "linear". When ratios matter and the absolute numbers increase at a rapidly increasing rate, a logarithmic scale can capture what really matters. Remembering that 10 is quiet and over 100 is really loud is easy. You'd need very large numbers to describe common things, and would end up having to count zeroes. It wouldn't be obvious that going from 10 to 100 was a bigger perceptual difference than going from 50,000,000,000 to 100,000,000,000. If you had a linear scale, the units wouldn't make sense. Slightly increasing the volume of your voice may still be a 10-fold increase in pressure, a normal conversation may be 10,000 times the pressure intensity of soft breathing, and a rock concert is 100,000,000,000 the intensity of soft breathing. For it to be useful, it needs to reflect that our ears can notice a large difference at low levels (whisper->soft speech->conversation) but also keep scaling up. This means that to measure sound intensity, you need a system of units that covers a gigantic range. Human ears have an impressive range, able to hear soft breathing yet tolerate a rock concert. Their apparent brightness doesn't scale linearly with their distance from us because of how energy dissipates over distance. What about other things that aren't tied to human perception, like the Richter scale? Well, to be honest, that's a bit complicated but it boils down to "Because Richter liked it that way."Īnother example that isn't explained by "just because" is the apparent brightness of stars. In order to perceive it as the same, it would have to go from 2 to 4 - doubled - since 1 to 2 is a doubling. We perceive a change from 2 to 3 as being less than a change from 1 to 2. So, why do we measure decibels logarithmically in the first place? If you scaled it out to have all the values there wouldn't be enough space between the smaller values to distinguish them, and huge gaps of nothingness between the larger values. The value for 20 decibels would be where the 100 decibel value is and the value for 30 decibels wouldn't even be on the chart. If we both measured and graphed it linearly, the chart would basically be too large to depict. Logarithmic scales basically take something that isn't linear by nature and makes it appear linear when scaling.įor example, here is a basic decibel chart:Īs depicted, it is "linear", because we measure decibels logarithmically.
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