I use sound to study whales in the ocean. Understanding sound is absolutely essential to my research, and to understand sound, you've got to understand the wave equation.
We're not going to actually derive the wave equation, but it's important to know what goes into it. (if you want to see the real math, look here). In order to understand waves, you need to understand four other fundamental laws. The great thing about these laws is that they pretty much are telling you that waves obey the laws of physics. By the combined powers of these laws, Captain Wave equation emerges!
Conservation of Mass: This means that even though the number of molecules in any part of the volume that sound passes through may change, the total number of molecules in the volume stays the same.
|In the sound wave, molecules get more |
compressed, but don't appear out of thin air.
Equation of Motion (Newton's Second Law): This means that we can calculate the force acting on particles by multiplying their density when a sound is passing through them by their acceleration.
|Force = Acoustic Density * Acceleration|
Equation of Force: With this, we can use the total density of the fluid (which is different from the acoustic density) and divide it by the x movement of the particles to find the force acting on the particles.
|Force = Total Density differential * x differential|
Pressure = (squishiness / acoustic pressure) * pressure
When you put these four equations together, you get the wave equation, which uses all four to describe the movement of a wave. This equation factors in pressure, time, the speed of sound, and the movement of particles.
I warned you this was going to be dense. And that was only chapter 1.2.1.
Also, if I made a math mistake, and I messed up on understanding any of the equations, please comment!