Amplifier power

dcbingaman

Joined Jun 30, 2021
1,065
Hello there,

I think you meant Steven's Power Law?

Anyway, the way the ear responds to amplitude is extremely complex and i believe it is still an active area of research. To start with, a PDE with two spatial dimensions and one of time, then a bunch of other stuff following that. That is because the human ear is so complicated with several structures inside. I dont think anyone here wants to go that deep though and really would be looking for an approximation of some kind maybe similar to Steven's Power Law but i did not check that out yet.

However, the signal frequency is also a key factor which i will illustrate shortly. But first, the unit of signal intensity is dB and the unit of sound loudness is the phon. 2 phons seems twice as loud as 1 phon to the human ear for example, and since this is independent of frequency we have a scale to measure the perception of sound loudness if we know the loudness in phons.

A signal at 1000Hz at 10dB intensity would require 20db to sound twice as loud. That is because if we place the reference in phons at 10dB we get 10 phons, and at 20dB we get 20 phons. So there is a direct relationship between intensity in dB vs phons now.
Now to see how different this can be at a different frequency, at 100Hz it would take around 50dB to sound as loud as 1000Hz at 20dB because it takes 50dB to produce 20 phons, so we see a bigger change at the lower frequency. At 10000Hz, it would take about 30dB.
If we use this information to create a smoothed scale of phons vs frequency we might end up producing Steven's Power Law but i did not try that yet. It would be approximate, but very usable i believe.

So we see a very wide change in perceived sound level depending on frequency. The actual relationship is even stranger than that but it gets too complicated to talk about here.
But you can see that @Audioguru was right about the 10x law, just only at 1000Hz.
To make things even more complicated. Every human being hears differently and children hear differently than adults. I liked your post. Very educational.
 

Audioguru again

Joined Oct 21, 2019
6,672
Remember Fletcher-Munson curves?
Our hearing is most sensitive at about 3.2kHz maybe so that we can hear a baby cry. At low levels our hearing's sensitivity is very poor at low frequencies and a little poor at high frequencies which is why many amplifiers have a "loudness contour" switch that boosts bass a lot and boosts treble a little when the volume control is set low.
 
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