 Remember for for vision we had perception of motion, perception of depth. So, we are up to the high level now perception of sound. Now, way back near the beginning of the course you may recall um Stevens power law which takes the magnitude of a stimulus and and maps it to the perceived um magnitude of the stimulus. So, um let me make sure I get that and it should be fine. So, let me change that just a little bit let us say um P the perceived magnitude of the stimulus is some constant times the magnitude and there is some exponent there. So, M is the magnitude of stimulus and P is the perceived magnitude. And so, one very simple example in the perception of sound where this becomes important is loudness at a pure tone of let us say 3000 hertz. So, in this particular case we get a plot like this where the exponent is 0.67. So, this is the magnitude of the stimulus and the perceived magnitude of the stimulus. So, in other words if you double the magnitude of the sound it does not necessarily get perceived as being double the magnitude. In fact, it is significantly less than that. So, as as the sound pressure waves get louder and louder the incremental amount of extra loudness that we perceive is significantly less. So, this is ends up being a nice example of Stevens power law in the context of audio perception um. Here is another um interesting um result in the perception of sound you can talk about loudness as a function of frequency. I will just use some rough idea of the plots here. So, we put frequency here um it is in log scale, but I am not going to worry about the exact um coordinates. I just want to show you that there is a interesting shape to the plot. So, here is what I do I I take a sound at um fixed amplitude or fixed dB fixed ah decibels at 1 kilohertz right. So, I have sound at I have a 1 kilohertz tone and you get a custom if you are participating in this experiment you get a custom to the loudness of that and now you listen to a tone at a different frequency and you are asked to turn the loudness up or down until it sounds like it is just as loud as this base tone. Does that make sense? So, you just trying to compare and say ok I have I may have a sound at 2000 hertz this one is at 1000 hertz I may have a sound at 2000 hertz and I have to tune it so that it seems like it is just as loud. But in terms of decibels we can measure scientifically exactly whether or not it is the same loudness level. And so, in this particular case um the curves end up being quite interesting I guess I will just draw there is like some kind of plot like this let us say. So, it ends up being non constant. So, I just want to say that we have very unusual perception of equal amount of loudness it varies as a function of pitch. So, this would be a um equal perceived loudness contour. And finally, as I um I am not finally sorry, but next as I mentioned before um very early in the course there is adaptation. So, it may be the case that um perceived loudness over time generally decreases. This also happens throughout the day for us I I do not know about you, but when I wake up in the morning um I am very sensitive to sounds if I was suppose was listening to some music the night before had it at a certain volume level. I wake up the next morning and I think wow I had it that loud how could that be you know. So, it seems to take some time for us to adjust to um or adapt to loudness levels throughout the day. So, adaptation as well um here is another interesting result pitch perception and this makes use of a powerful idea from a psychophysics which is called just noticeable difference I need to point this out. So, right before getting into pitch perception let me mention just noticeable difference just noticeable difference or J and D. So, the question is in that case if I have a stimulus and I have the ability to change its magnitude how much do I have to change the magnitude by before you notice there is a difference right that is the question what is the smallest amount reason ah it is different now. I could do this in many ways I could do this by slightly changing colors you know I could do this by changing brightness levels in um in um in the case of of vision right I could do this by changing the pitch I could do this by changing the amplitude. So, a lot of cases where I have a linear stimulus let us say and I just want to ask the question when do you notice that it is different right that I have done something different to it. So, this is a just noticeable difference and um here is one interesting general result called Weber's law which if I look at the um the change in the magnitude of the stimulus divided by the overall magnitude of the stimulus. So, and let us say delta m is the just noticeable difference that was obtained through some experiment and suppose delta m is this small change that was the just noticeable difference anything smaller would not be perceived then um Weber's law says that this amount delta m over m um is a constant right which means that if I were to all of a sudden cut the um the overall magnitude of the stimulus in half then the delta t would cut in the delta m sorry would cut in half as well. So, it is really the um the percent difference let us say in the in the in the um stimulus magnitude that seems to be at the thresholds of perception um. So, this is a common law that seems to occur very frequently in these types of just noticeable difference experiments. Let me go back to the case of pitch perception and mention this interesting experiment which I find this result surprising. So, you start off with a pure tone you have a um center frequency. So, I generate a pure tone and I will make a logarithmic scale here. So, I will put it at 100,000 and 10,000. So, I start off here with a pure tone I generated at that frequency and then we start varying the frequency and we try to determine when you the the subject can actually tell that it is a different tone right. So, I may give you random tones and I ask you to press a button is this the same or different? The time over? In in what in what sense? Oh I think it is very interesting observation. So, so that is right you may not um if I if I present to you a stimulus today and then we come back tomorrow when I say is this at the same level um I bet that would make a much larger delta m. So, so that is that is reasonable um. So, this as it is formulated does not it is not saying a delta m is going to be the same across all of these. So, let us just hold time fixed and then say this law holds and and most of the time in these kind of experiments the one stimuli one stimulus is presented right next to the other a temporally. So, they are very short in time, but you are right your ability to remember how close those were um that ends up that ends up involving memory let us say yeah in in these types of experiments usually it is one and then the other um, but that is a very good point. So, in this particular experiment here what we have is the um the differential threshold in other words the delta m and what I find surprising. So, we have like 0.1 hertz here 1 hertz 10 and 100 certainly a lot of room for my axes here I will put it on this side um. The plot is about like this which means that when we are in the range of a few 100 hertz we can perceive a tone difference of 1 hertz that is quite incredible I mean it is amazingly sharp. So, but then as the frequencies get higher it gets more difficult. So, I find that really interesting alright um. So, these are just some basic audio perceptions you know I cannot talk about things like um perception of scale or perception of the shape of objects and things like that right we do not have these kind of this level of complexity as we have for vision, but um this gives some idea of perception it also is remind you of something that is very important which um I encourage you to look up more about this I do not have enough time in this course, but um yeah to look up psychophysics which is the science of connecting stimulus to perception right you want to we want to understand we have a stimulus coming in we want to understand the perception coming out. If you are building virtual reality systems it is very important to understand what the user is going to perceive based on the stimulation that you are providing and. So, there is there is an entire field literature devoted to this and entire um methodologies for designing experiments that involve human subjects. So, that you get the right results out you do not have artificial bias and um other problems that are introduced right. So, so this is worth looking up and studying um um in conjunction with this course especially if you are interested in doing user studies to develop to determine whether or not um you have done the right thing right or done something sufficient for your task or whether or not you have made a comfortable virtual reality experience alright.