Now we look at the wave equation. And our standard equation we're going to be using here in physics for a traveling sinusoidal wave is this one you see here. There's a lot of information here, so let's pull it apart piece by piece. First of all, the y over here is our vertical position. And it's a function of two other variables, x and t. Here, the x is the horizontal position, and t is the time variable. So we're looking for what's the vertical position of the wave at some horizontal position along the wave at some particular time. Now in addition to those variables, we've got some sort of problem-specific constants. For example, the amplitude A, the phase phi, the angular frequency, and the angular wave number. So for these problem-specific constants, meaning for a particular wave, it starts with A set of these values. We need to take a look at these quantities in a little more detail. Start with the easy one, the amplitude. It's got the symbol of a capital A. If you don't use a lower k-say, make sure it's a capital A. It represents the maximum displacement of the oscillator, and it can be measured in any distance units. A standard unit would be meters, but I could use other distance measurements like centimeters or feet as well. Then we get to the angular wave number. Now the symbol for this is k. And be careful because this is a new use for the symbol k. Obviously we use the symbol k as the spring constant. This is not the spring constant. It's just another type of variable called the angular wave number that we happen to be using the same symbol for. It's related to the wavelength, and we'll take a look at that in a little bit more detail in another video. And my units, it has to be in units of radians per meter. And we get to my angular frequency, which is very similar. It's got a symbol here of omega. And yes, this is the Greek letter omega, it's not a w. Remember, the Greek letters referred to our rotational properties. And like the angular wave number was related to the wavelength, this is related to the period of the wave. And this angular frequency is then measured in units of radians per second. Let me get to the phase. And it's got the symbol here, which is the Greek letter phi. And it could be called the phase, but it can also be called the phase shift or the phase constant. And it's a measure of where the oscillation started in the cycle. So it can range between zero and two pi radians. And it has to be in units of radians for this equation. So now we can look at the overall units, starting with focusing on this purple box here. K, the angular wave number, is going to have units of radians per meter, followed by meters for the horizontal position, radians per second for the angular frequency, second seconds for the time, and then radians for my value of phi, the phase constant. Now my meters and my seconds on each of the first two terms, they end up canceling each other out because I've got the same thing on the top and the bottom. And that leaves me with radians minus radians plus radians, or just radians overall. So that means when I do the sine calculation here, I've got a number that's in radians and my calculator has to be in radian mode to do the sine. But once it's done the sine of that number in radians, there's no units on it anymore. Sine is a dimensionless unitless type of quantity. So that means whatever unit I have for the amplitude, like meters, I'm going to have the same unit for the vertical position on my wave. Why? The standard is meters, but I could have other length measurements here as well. So that's your wave equation.