A vibration is the back and forth AND BACK motion or "oscillation" which is a cycle of movement. A wave is basically a transfer of energy. What it moves in is called the medium.
We were working a lot with slinkies today because they're a really good example of different sizes and types of waves! There are two types of waves that we created, transverse and longitudinal. Transverse waves are when the energy is moving in the direction perpendicular , and longitudinal is when they travel parallel (in the same direction). So when we were working with the slinkies, to make a longitudinal wave, you would push the slinky forward and pull it back to create a wave. To make a transverse on, you would move it left or right and return to the same spot, this causes the energy to travel side up and down, while it goes to the side until the end of the slinky. The wavelength is the distance or length of wave from two equal spots, usually from trough-to-trough or crest-to-crest. The amplitude would be the distance from the starting point to either a trough or crest!

As you can see in the photo I'm holding the slinky with both hands and having a pretty even curve. The area that is compressed is the part hat bends. It's compressed because that is where the slinky wires come together, and the areas where it's looser is the long end. This is the rarefaction. By using slinkies we can conclude that the tension of the slinky affects the speed of the wave because a higher tension makes the energy move faster. Also that the amplitude of the wave doesn't affect the speed, along with the wavelength because they still end up being the same! The parts that don't move in a wave are called nodes, and the areas that move are antinodes. We used a lot of this equation: V=F(lambda) I don't know how to do the squiggly line...but Velocity equals frequency times lambda!
Another way of looking at waves is to look at the ocean! I learned today that waves do NOT bounce off of each other (even though it may look that way), but travel through them and continue on their merry way! A period of a wave is the time it takes for one cycle to occur, or for it to return to its original spot. A water wave would be an example of a dispersive wave. This is when a wavelength will affect the speed, compared to a non-dispersive wave which is one that has all waves travel at the same speed in the same medium, not matter what your frequency is (like a sound wave). There are also constructive and destructive waves. Constructive are when two waves come together to create a larger one. A destructive wave is when they are opposite, one positive and one negative, and they cancel each other power out to create a flatline.

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