Why do sound waves travel faster in water than in air, but for light waves, it is the opposite? (At least, according to a Cassini-Huygens scientist being interviewed on a TV show.)
Because they’re different kinds of wave: sound waves are oscillations in a medium, whereas light waves are electromagnetic emanations.
Sound waves are transmitted by the atoms/molecules of the medium they’re in; since water, as a liquid, is considerably denser than air, then the energy transfer between particles is much quicker.
However, light is actually energy on the move: i.e. light can travel through a vacuum, whereas sound cannot. As to why different substances slow light down, I refer my right honourable friend to Wikipedia, because it’s been years since I studied physics and optics. (Seems that the electromagnetic waves get slowed down by subatomic energy fields as the EM wave passes ?)
I’m sure more knowledgeable people will be along soon both to shoot me down and complicate matters… 
In a deeper sense, both waves travel through media as a mechanical interaction involving masses and stiffnesses. In the case of sound the masses are the collective molecular weights in a wavefront and the stiffnesses are the compressibilities, and the speed depends on their ratio which is called the acoustic impedance. Since liquids are many orders of magnitude less compressible, but only around a thousand times denser, the acoustic impedance goes (up? down? forget which way) favoring faster transmission. In the case of light going through solids and liquids the masses are pretty much electrons shifting a little and the stiffnesses are their freedoms, which together determine the index of refraction, or in more detail nearly the product of the dielectric constant and the density.
Light travels through a solid or liquid in an odd way, not really as “light” in the same sense that’s implied in a vacuum. Light in a vacuum is purely electromagnetic, whereas in solids and liquids it’s electromechanical too. In a gas it’s mostly like it is in a vacuum.
Since the electromagnetic part of light, or equivalently its behavior in a vacuum, can spread as quickly as causality itself, the electromechanical version of it in a solid or liquid is slower.
Napier, keep in mind that matter is mostly vacuum, studded here and there with (essentially) dimensionless point particles. What slows light down in a medium is scattering. A photon traveling through, say, glass, is going to run into the electromagnetic fields of the glass molecules. Essentially, the photon collides with the electrons. See Compton scattering, which amounts to photons and electrons colliding like billiard balls.
So if I have billions of photons traveling through glass, each one goes through many collisions, each of which takes time. (What’s more, some of the photons are scattered back or to the side. The only ones that get through are the ones that happen to be scattered in the forward direction.)
Upon reading both of the Wiki links already given, I think I need to adjust my statements: What slows light down isn’t that each collision with an electron takes some amount of time, but rather that the collision sends it off in a different direction. The net effect of many collisions is that the light has traveled a greater distance (bouncing all around inside the material) before exiting than it would have had there been a vacuum instead.
Hmm… would that explain why it takes so long for a photon to emerge from the center of the sun?
By that token, if a photon has bounced off a particle in a different direction once, how does it “know” in which direction to continue to exit the glass? IMO that explanation doesn’t wash: it seems like the light would merely be reduced in intensity (i.e. fewer photons exiting the glass, and many bounced off in different directions) than “slowed”.
Yes, the many thousands of years it takes for a photon created in the sun’s core to escape to the photosphere is due to scattering events which occur every millimeter or so as it makes its random walk outward.
And when Mr. Sunbeam finally gets to Earth, he gets beaten up by greenhouse gases in the upper atmosphere, where his rotting corpse contributes to global warming.
(Now more informative and less flippant.)
**Napier **has given a really excellent description of the difference between light and sound waves traveling through a medium. The interaction of light and matter is not an easy topic, and jjim’s concern about directionality is significant. Say you have a photon in a vacuum heading towards some solid material. Any number of things can happen when it impinges on the material:
It can interact with the material lattice and can be either transmitted or reflected. Or, if it approaches at an angle other than 90 degrees to the material surface (90 degrees = “normal incidence”), it can be refracted (sent off in a different direction).
The most convenient way to describe these interactions is to think of the material lattice as a set of planes with which a wavefront can interact. At normal incidence, you can naively think of transmission as the interaction of the wavefront with successive planes, and Spatial Rift 47’s picture is of the slowing-down is not too misleading. Reflection can occur if the lattice planes are spaced such that they create constructive interference in the outward direction.
Thus, each scattering event does send the photon off as a spherical wave in all directions. It is the constructive and destructive interference that occurs as the sum over all possible scattering paths that keeps the light going straight through (or straight back). You could argue that this is only valid for a wavefront (many photons in a coherent beam) but keep in mind the weird nature of quantum mechanics: electrons interfere with each other (themselves) in the two-slit experiment even if you send them through one at a time.
Now, if the wavefront comes in at an angle, the interference becomes more complicated. Here is a nice applet illustrating such interference. The light ray bends because the frequency has to stay the same along the wavefront (otherwise it would build up or decay somewhere) so the wavelength changes, but then the speed also has to change, so you can get a spatial separation of wavelengths as through a prism.
But as I said at the outset, it’s only a convenient model. The material lattice can just as well be described using a math-heavy phonon-based description (phonons, by the way, are lattice vibrations, also knows as sound waves!) Here, the full beauty of quantum mechanics comes into play, but this is not my field of expertise so I’ll leave this intriguing connection to be fleshed out by others.
Let’s return to our photon for a minute. If it’s really energetic, it can interact not only with the material lattice but with the atoms of the material themselves. It could knock out one of the electrons, for example (the photoelectric effect). Or if could give up only a part of its energy to an electron and go off poorer (Compton scattering, as occurs in the sun, where gamma rays from fusion get down-scattered into visible light on their long journey to the photosphere, as opposed to the Thomson scattering described above, where the photon keeps all its energy). If the light has a really low energy, on the other hand, that is, if it has a wavelength on the same scale as the material sample, it behaves more like a static electric field, and the whole of the material responds to it based on the intrinsic electrical resistivity.