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ngn

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- How to know if a quantity is a root-power quantity (field quantity). Is there a list somewhere? Or a helpful rule of thumb?

Hello, I am working with calculating decibels, and there is one equation when using quantities of power and another equation when using root-power quantities (which essentially just converts them to a power ratio and places them into the first equation). I know that common quantities of power are things like "power", "intensity", "energy density", and I know that common root-power quantities are things like "amplitude", "pressure", "voltage". And I know that root-power quantities are those that are proportional to the square root of power.

But I am wondering if there is a simple way to know or intuit if a quantity is a root-power quantity or not. If there is only a finite number of known root-power quantities, then is there a list I can find somewhere? Or are most quantities (other than direct measures of power) root-power quantities? This may seem like a basic question, but if you try to search online, you often find only the definition of a root-power quantity, and maybe a few examples, but no comprehensive list or comprehensive generalized definition of a root-power quantity that you can apply as a rule of thumb when encountering a quantity that is not one of the few examples listed.

Is there a rule of thumb that I can apply? I'd assume that some measures aren't root-power quantities, and I'd assume that some measures are proportional to the cube root of power and therefore the decibel equations wouldn't work (or you would have to use 30 x log(ratio)). So, what should I do if I encounter a new quantity that I want to convert to decibels?

For example, I generally intuit that amplitude is a root-power quantity based on the fact that when I push on a spring, I not only have to apply more power to move the spring a further distance in a given time period but I also have to apply more and more force to move the spring the harder I push, so work/power must go up exponentially (squared) as I push. Therefore, I have a sense that power is amplitude squared.

But what about a person's height? Here I don't think height is a root-power quantity. But could it be on some level? For example, doesn't it require more power to grow taller in a given amount of time and aren't limitations on height somewhat related to limitations on energy, and if I grow taller, would I require an exponential increase in energy to do so, which is why we don't currently have dinosaurs running around? This is a silly example, but I'm wondering if there is some intuitive way (rule of thumb) to decide on the correct equation to use when calculating decibels and whether some measures (e.g., height) just aren't able to be converted to power and used for decibel calculations.

Thank you!

But I am wondering if there is a simple way to know or intuit if a quantity is a root-power quantity or not. If there is only a finite number of known root-power quantities, then is there a list I can find somewhere? Or are most quantities (other than direct measures of power) root-power quantities? This may seem like a basic question, but if you try to search online, you often find only the definition of a root-power quantity, and maybe a few examples, but no comprehensive list or comprehensive generalized definition of a root-power quantity that you can apply as a rule of thumb when encountering a quantity that is not one of the few examples listed.

Is there a rule of thumb that I can apply? I'd assume that some measures aren't root-power quantities, and I'd assume that some measures are proportional to the cube root of power and therefore the decibel equations wouldn't work (or you would have to use 30 x log(ratio)). So, what should I do if I encounter a new quantity that I want to convert to decibels?

For example, I generally intuit that amplitude is a root-power quantity based on the fact that when I push on a spring, I not only have to apply more power to move the spring a further distance in a given time period but I also have to apply more and more force to move the spring the harder I push, so work/power must go up exponentially (squared) as I push. Therefore, I have a sense that power is amplitude squared.

But what about a person's height? Here I don't think height is a root-power quantity. But could it be on some level? For example, doesn't it require more power to grow taller in a given amount of time and aren't limitations on height somewhat related to limitations on energy, and if I grow taller, would I require an exponential increase in energy to do so, which is why we don't currently have dinosaurs running around? This is a silly example, but I'm wondering if there is some intuitive way (rule of thumb) to decide on the correct equation to use when calculating decibels and whether some measures (e.g., height) just aren't able to be converted to power and used for decibel calculations.

Thank you!