The speed of a wave does not depend on the amplitude or frequency of a wave.

• Instead, the speed of the wave is determined by the properties of the medium it is traveling in.
• Some examples of how the properties of the medium can affect the speed of the wave are:
  1. Speed of water waves depend on the depth of the water.
  2. Speed of waves in a rope depend on the force exerted on the rope and the weight of rope used.
  3. Speed of sound in air depends on the temperature of the air.
• A wave with a bigger amplitude does transfer more energy, but it will still travel at the same speed as a smaller amplitude wave in that same medium.

Quite often a wave will move from one medium to another, like sound traveling through the air and then into water.

• This will definitely change the speed of the wave, and may also cause it to be somewhat distorted (changed randomly). We will assume no distortion happens in our examples.
  • The original wave that was in the first medium = incident wave.
  • The wave that continues into the new medium = transmitted wave.
  • Any wave that bounces back = reflected wave.

Different things will happen when the incident wave hits the boundary between the two media, depending on the densities of the media compared to each other…

Change in Density is BIG

If there is a big difference between the densities of the media, the following will happen:

1. The incident wave will come moving in towards the boundary.

2. When it hits the boundary, almost all of the wave will be reflected back the way it came! Almost none of the wave will be transmitted.

• Notice that the reflected wave is still right side up (we call this “erect”), and so is the little bit of the transmitted wave.

This is an example of what happens when the wave is going from more to less dense media. A different set of rules apply if it goes from a less to more dense media.

• If the wave is going from a more to less dense media then the reflected wave is erect.
  • Any part of the wave transmitted will be erect and speeds up.
• If the wave is going from a less to more dense media then the reflected wave is inverted (upside down).
  • Any part of the wave transmitted will still be erect and slows down.

Example 1: I hang a giant slinky spring from the ceiling (using very light string). I then make a wave travel through the slinky towards the other end, which is just dangling there. Describe the waves at the boundary.

The change from the original media (the spring) to the second media (the air) is definitely a BIG change in density, so most of the wave will be reflected back through the slinky.

• Since it is going from more to less dense, the reflected wave will be erect.
• The little bit of the wave that is transmitted into the air will be erect and speed up.

Change in Density is SMALL

If the change in density is small, things are a lot easier to remember.

• Quite simply, almost all of the incident wave will be transmitted and stay erect.


• It’s hard to see the boundary between the two media in the middle, but they are slightly different densities (thickness of line).
• That’s it! The transmitted wave is (almost) the same as the original incident wave.
• Only a very little bit of the wave will be reflected (I didn’t even bother drawing it in).