Are there exceptions to the rule of speed and energy for waves?

[mahrap]

Today I was presented with dispersion in my introductory physics class. Before this topic was presented we were told of two important rules for waves: 1) The speed of a wave is dependent on the medium in which it travels and 2) the frequency of wave does not change when going from one medium to another. Now back to dispersion. I am able to see several trends from dispersion: EM waves with higher frequencies and therefore higher energy will travel slower in a medium and therefore bend more towards the normal. Now rule 1 is clearly violated here because there seems to be a inverse relationship between the frequency of a wave and its speed in a medium. To resolve this I though well, EM waves are special in that their energy is directly proportional to their frequency. Therefore, perhaps the reason the EM waves end up traveling slower in a medium based on their frequency is a direct result of their energy which makes sense since the only reason EM waves slow down in a medium is due to the atomic interactions of photons with electrons in the medium resulting in a cycle of absorption and emission. With this in mind, the natural question that came into mind was will the relationship between speed and energy also hold for other waves?

Let's consider sound waves. Well there are no photons there but sound waves are due to the the pressure of molecules. So let's sound there was a sound wave in a Helium medium and a sound wave in a Fluorine medium and that both these sound waves were traveling at the same speed. The Fluorine medium sound waves would therefore have a greater kinetic energy since they have greater mass. Now let's say these two sound waves were to be transmitted through the ocean. Would the sound wave in Fluorine bend more towards the normal and ultimately travel slower does this not make any sense?

 

[olivermsun]

Why is rule 1 violated in the case of EM waves? the speed is dependent on the medium, which is true. It doesn't say that the speed is directly proportional to the medium.

As for kinetic energy -- are you comparing two waves with the same pressure amplitude? How about frequency?

If you have two waves transmitted through the ocean, are they both being conducted into the ocean, one from Helium and one from Fluorine? Are you just assuming "what if" those same waves got transplanted into the ocean?

 

[nasu]

Regarding the two sound waves, they don't have the same speed in the two gases.
Besides this, the KE energy of the wave depends on the speed of the particles in the medium and not on the propagation speed.
Actually, as the energy density is proportional to the density of the medium whereas the propagation speed is inverse proportional to square root of the same, is perfectly possible. to have more energy "in" a wave with lower propagation speed. But in the end the energy depends on amplitude too so you cannot make such general statements anyway.

Dispersion means not that the speed "depends on the medium" but that the speed is different for different frequencies. Of course, dispersion can only happen in a medium.