The average distance between, you know, the human ears is about 22 to 23

centimeters, okay? And so, you know, I've given myself a

head start because drawing circles for me is a little bit difficult.

But if we assume this is someone's head, and we sketch on a couple of ears.

And we'll assume that they're listening to music they enjoy, so we'll put a smile

on here. the point I wanted to make was, is that a

wave length of 1500 hertz fits precisely between the two ears, okay?

So, what happens when you know, I shouldn't say the wave length of 1500

hertz, it's the wave length corresponding to a frequency of 1500 hertz.

So the wave length is on the order of 22 to 23 centimeters, it's exactly the

distance between the two ears, at corresponding to 1500 hertz in air,

alright? So what happens at much lower frequency?

Well, at much lower frequency, the wavelength gets much longer, so it's much

greater than the distance between the ears.

At much higher frequency, the corresponding wave length can become much

shorter, okay? And so now the question is, is how do the

ears and the brain use that in terms of localizing sound.

And that's what we're going to see a bit more of on the next that I have here.

So in details in the range of frequencies below 1500 hertz, will cause that

wavelengths larger then the dimensions, between the ears.

And, above 1500 hertz where the wave length is smaller then the dimensions

between the ears. that ends up defining kind of a, a

fracture point, if you will. In terms of the way we do, do, we

determine directionality as sound. And there's two basic mechanisms that

have been identified or discussed in, in, with respect to the wavelength of, of, of

sound waves. And one is called the Interaural Time

Difference or ITD. And the other is called the Interaural

Intensive difference or IID. the ITD, the time difference in the sound

propagation, is related to frequency, wavelengths for, corresponding to

frequencies less than 1500 hertz. And the IID or Interaural Intensive

Difference is corresponds to wavelengths at frequencies greater than 1500 hertz.

And I promised I would bring this back and discuss it relative to loudspeaker

design. And this is fairly simplified, but you've

probably seen satellite speaker systems. Where you have, you know, two small

satellites and one larger sub woofer in the room.

And that became a very popular design, and it became popular.

Because the recognition was is that the wavelength of sound associated with the

subwoofer Was very long compared to the distance between the ears.

This is the low frequency sound radiation.

And the wavelength associated with the satellite speakers was obviously shorter.

Now, the break point is in 1500 hertz. But, basically, you know, most of the

subwoofers you know range between 20 hertz up to maybe 400 hertz or so.

And to have full bandwidth audio you would have to have satellite speakers

that at least had a minimum of 400 hertz to 20 kilohertz for this example.

sometimes this is much lower, sometimes 20 hertz to order of 100 hertz.

And your satellites will be from 100 hertz up to 20 kilohertz.

but the point is, most of the directionality of the sound, really in

room acoustics can be localized based upon the satellites.

And at low frequency the sound waves appear somewhat omnidirectional in

acoustics. Now, we can localize low-frequency sound.

And I'm going to talk about that a little bit.

But you tend to be more sensitive to the higher frequency.

in room acoustics. So, I mentioned earlier the ITD and the

IID. So, the interaural time difference, and

I've sketched on a speaker here. so we have a speaker and a sound wave

that propagates. In this case, the wavelength of the

sound, if this is if this is our little sketch of the hat and the ears, the

wavelength of the sound is very large, okay?

Compared to that of the ears. And so, if that's the case, you know, I

don't sketch this perfectly. But the bottom line is, is that the sound

wave is going to arrive at this ear, just a little bit sooner than it arrives here.

But the magnitude of the sound wave won't be significantly different.

So the way you auralize, or localize, I should say, the, the sound the direction

of the sound is based upon the amount of time it takes.

so this is time to the left ear, and this is the amount of time It takes to get to

the right ear. And so the way you localize the sound is

basically is your ear and brain actually can determine which ear the sound arrived

at first. And that's, that's why it's called the

time difference, the interaural time difference, alright?

So now let's compare that to the interaural intensive difference.

And it means pretty much what, what it says.

In this case, we tend to think about wavelengths that are much shorter than

the distance between the ears, okay? So we'll sketch our ears on here.

and in this case you know you may have several wavelengths changes before you

actually, you know, the sound arrives at at this ear.

this side of the head and further more if the source is on.

if the source is on this side of the head your, the cause of the dimensions of the

head and the absorptive properties of the skin.

There will actually be a reduction in the sound pressure level by the time the

sound wave reaches this ear. And so, the intensity of the sound wave

will, will have decreased, or the measure of the sound pressure will have

decreased. And so, you're me, your ears, basically,

at this point, are able to determine that it's effectively louder here than it is

here, and localize the source. So, two very different ways, and you have

to think about that. Because, you know the for a sine wave

that would propagate to this ear and this ear.

It could be that the sine waves were perfectly in phase when they were

reached, reached the ears. the difference here again, is the fact

that it'll be reduced in amplitude on this side of the head versus this one,

okay? So that's a little bit about how we

actually localize sound. there's one other component that's very

significant, and it played a huge role in 3D audio along with understanding the

shape of the ear. which is known as the pina and it's the

head related transfer function, okay? HRTF, the Head Related Transfer Function,

so, it turns out that if you look, you know, if you touch your own ear, it's

cupped. And so sound waves that come from behind

the ear we're going to have, at the same frequency.

And particularly at the higher frequencies are going to have a lower

amplitude response as perceived by the sensing mechanisms here in the ear.

Then they will if the same frequency content comes from the front.

And furthermore, it actually depends whether the sound waves are propping,

propagating from the ground, or even propagating from above.

in the front or the back of the ear. And a lot of the gaming systems,

particular computer gaming for a while and some of the sound cards incorporated

head related transfer functions. In other words, what they did is they

figured out how the ear filtered the sound to give you a sense of direction.

And then basically would take sounds that they were trying to artificially move,

and would effectively apply that filter of the way your ear would hear it.

Or it would change if the sound were behind you.

And so it could give you the illusion that you were in a, in a 3D sound or

could literally move the sound around you kind of in a surround field approach.

Very interesting approach to technology. but it requires, you know, that your,

your head sits at a pretty well defined distance between the speakers.

And that your proximity to the speakers are pretty accurate because these things

become fairly sensitive in the design of 3D audio sound fields.

the last thing I think we should discuss relative to hearing is the dynamic range

of the ear. Which extends from 0 dB up to about 140

dB, which happens to be the threshold of pain.

So, but what's, what's dB? well in measuring sound we have something

that we call sound pressure level, alright, and that's commonly recognized

as SPL. and it's a common measure of sound, and

there are what are known as sound pressure level meters that are

specifically designed to measure sound. For those of you who have iPhones or

Android devices there are apps that you can download for the devices that will

measure sound pressure level. now they're not calibrated in terms of,

of you know, instrument quality systems that are used in profession applications

that are, that are calibrated for accuracy.

But [COUGH] it gives you some indication of what the the house sound pressure

levels vary in, in a given room or, or in a given conversation of music.

You could, you can loo, you can use, use the apps.

But sound pressure level is computed as 20 log base 10, so 20 times log base 10.

basically, our measured pressure, the effective measured pressure at some point

in, in space or in your room and relative to a reference pressure.