Okay. So now let's talk a little bit about volume control circuits, and typically one uses a electronic device called a potentiometer. Here's a picture of a typical potentiometer. And all it is, is a a set of wire windings, a resistor wire in there, with a wiper. So it's a resistor. It's laid out and there's a wiper that contacts that resistor at various points along the the, the resistor itself. So [COUGH] the the input of this circuit is some kind of time varying voltage that we'll call a signal. We'll say a lot more about signals later on in this course. But instead of a DC voltage, it could be a DC voltage or it could be a AC voltage, like what comes out of a guitar pickup. And so, that's going to that voltage [INAUDIBLE] is going to be dropped across this resistor. The whole volt, the entire voltage is, will appear here. And as I go down the resistor, there's a smaller segment of this resistor between the wiper location and ground. And so as, when, when the I change the position of the wiper, the voltage at the output changes. So if I move the wiper all the way to the top, I get maximum voltage and so I'll get maximum volume saying that, let's say that voltage, then, is amplified and drives a speaker. and then, if I turn the knob all the way to the other direction, I'm tapping off the minimum amount of resistance and I'm getting the minimum volume. Now, that's pretty simple but one thing that's worth noting a little bit here is that in audio applications when you're trying to control a volume of a signal that you're going to listen to, the, the potentiometers that are used, are generally not linear. They're logarithmic. And what that means is that as I rotate the knob from zero to the 100% position, if it were linear, then it would just track this straight line. The resistance would go up in proportion to the percentage of the knob rotation. But in a logarithmic potentiometer it goes up very slowly at first and then the resistance increases more rapidly as you get toward the end. Now this curve, actually, if you're observing, isn't logarithmic. This is a exponential curve. But they they, it, it's, it's referred to as logarithmic. [SOUND] so, the question is why do we do that for volume control? Well, the reason for that, is that the human perception of loudness is logarithmic. Now, what that means is that to double the perceived loudness, the sound pressure level has to increase, not by a factor of two, but by a factor that's greater than that. About a factor of 2.8, which corresponds to about 9 decibels. Now, decibels, we're going to be talking about those in other parts of the course. [COUGH] But a decibel scale is just a relative scale. So you pick a reference voltage, for example, so dB volts decibels measure of voltage. As we pick a reference voltage and then whatever voltage we're referring to, we divide that by the reference and then we take the logarithm to the base 10 and multiply by 20. Now you can invert this equation and solve for V. So if I have a certain dB Volts value divide that by 20, raise 10 to that power. And then the voltage that corresponds to that is just V ref times that. So, this 9 decibels, to give you a perceived loudness of two times is a very subjective thing. This, in fact, it's, if you really stop to think about it, it doesn't really, what does it mean when something is twice as loud as something else? So if you ask yourself that question and really ponder it for a while, it really doesn't make sense. But it's a curious thing about human perception that people are more than happy to say, yeah that's twice as loud as,as this, or that's twice as loud as that. So if you ask people to kind of play the game and, and tell you when something is twice as loud, then folks are totally happy to do that. And so if you do experiments with a large number of people and play a number of different sounds of different loudness levels, and ask them to sort off classify them, which ones are, are, how much louder is this than that. Is it two times or four times louder? if you do that, then you find out that subjectively, people well, generally consider something that is about a factor of 2.8 greater sound pressure level to be about twice as loud. So, what that means is that the let's say that I have a potentiometer like the volume control knob on your amplifier. if it's set at 1, then if I go from 1 to a position of 2, I want the voltage to go up by a factor of 2.8, not 2. And then if I turn the knob from 2 to 4, I want it to go up by 2.8 times 2.8, which is about 7.8. And if I go from 4 to 8, then it has to go up another factor of 2.8. And so the output or the voltage of the potentiometer as I change the knob position from zero to 10 the at 2, it's about 2.8. At 4, it's about 7.8 and then at 8, it's about 22. And of course, we made our potentiometer go up to 12. Just, just in case you want it to be louder yet. But the thing to remember is that loudness perception is a subjective thing. but our subjective judgement classifies loudness on a logarithmic scale. And so, one uses a logarithmic potentiometer for most audio volume control circuits.