###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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# Sound Waves

Jonathan Osbourne
###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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Sound waves are waves transmitted through the air or even through liquids or solids which change the pressure of that substance enough that our ears can perceive them. The pitches of sounds we hear depend on varying frequencies of these waves.

Let's talk about sound waves, sounds waves are actually very kind of strange things to go through and think about how they work. And part of the reason for that is they're associated with really small displacements of lots and lots of atoms and molecules that go back and forth, back and forth many, many times per second. So we need to think very carefully about how they work. Now what I'm going to do is I'm going to create a sound pulse and I'm going to do that by dropping this book on the table. So there we had a loud thud right? So what happened why was there a sound wave? Well let's go ahead and look at what happened with the book as it was falling towards the table. So here's the book falling down towards the table and what I've done is I've drawn little dots at locations of molecules inside the table alright?

Now the molecules inside the table aren't really bothered until the tables comes, sorry until the book comes into the contact with the table. Now at that point the book is moving down but the table is in the way. So the table got to stop it, but it can't it instantaneously because that would require an infinite amount of force. The acceleration will go to infinity, so what the table has to do is deform itself a little bit, now of course I've greatly exaggerated this here but you get the feel for it. Alright when it deforms itself, the atoms in the top layer becomes closer to each other. Now down here it's not really affected but right here look what we've got, a condensation. So we've got a nice little condensation of our molecules right here and they don't want to be that close together. So they're going to fight that, they're going to try to push apart and that means that the table is representing a medium for the propagation of a wave and that wave is going to be a sound wave.

Now here we've got the molecules very close together so that's associated with a displacement wave. Now these molecules here are going to move out that way in order to get away from the other molecules. So the wave is moving this way and the molecules are moving this way. So that means that this sound wave is a longitudinal wave, the displacement of the atoms and molecules is along the direction that the wave is moving in. Alright so we definitely got a displacement wave here, but look here we've also got these molecules that are close to each other here and we can say that, that leads to a high pressure zone. Now as they push out this table is going to reform itself it's not going to be deformed anymore and then I'm going to have a low pressure zone there. So I'm going to have both a displacement wave and a pressure wave and that's what makes a sound wave. You have a pressure wave and a displacement wave, alright now let's see a little bit more clearly how this works. So what I've got here is I've got my displacement wave plotted as the function of position. So here the displacement is maximum positive, here the displacement is 0 and here the displacement is maximum negative.

Alright now this is a little bit difficult to understand how it works the first time you see it. So what I've done here is I've drawn a column of air the black lines represent where the molecules are supposed to be. These are equally spaced because in equilibrium they're supposed to be equally spaced they're not supposed to be closer at some points and further away at others. Now maximum displacement, that means that the molecules that are supposed to be at this black line right here are actually at the red line here. they're moved over the maximum amount in the positive direction. Now as we go along here we have moved over less and less and less as we start moving down here they start moving backwards. So notice what happens, here everybody's moved over the same amount, so that means that nobody is closer together than they ought to be. They're just kind of all moved over. But look what's happening around here? The atoms on this side are moved to the right and the atoms on this side are moved to the left.

And so we've got this region right here where the red lines are closer together than they're supposed to be. So this is my condensation, now as we continue to go here we've got maximum displacement but in the negative direction, so again it's like everybody just sat there and were just moved over the same amount. So it doesn't matter, this is the same pressure nobody cares. But then as we keep on going, once we get to this point right here, all the guys on this side are moved to the left and all the guys on this side are moved to the right. So that means that we've got this area right here of rarefaction low pressure. So if I were to graph the pressure wave what I would end up with is 0 pressure here just because it's the same and then as I go we've got maximum pressure at the condensation and then minimum pressure here at the rarefaction and then back up. So if we compare the pressure wave with the displacement wave we see that we took the displacement wave and we just kind of moved it over to the right 90 degrees. So the pressure and displacement wave that we talked about over here with the sound wave are 90 degrees out of phase. And this will be very important to us when we discuss standing waves associated with sound.

Now as far as most of the problems that I've seen about sound waves go they're really just associated with this formula right here v equals f lambda but we know that one that is standard for basically always. The only thing we need to know is what's the speed of sound? Well in air at standard temperature and pressure. So that's 0 degrees Celsius 1 atmosphere of pressure. The speed of sound is 331 meters per second, so if they give me the wave length I know the speed I'll divide and that will give me the frequency. At 20 degrees Celsius which is more like room temperature again one atmosphere pressure, the speed of sound is 343 meters per second. Again same thing, so most of the time in this problems they'll say you know the temperature is this here's the frequency, what's the wave length? Alright that's sound waves.