acousticsrefraction
When sound waves go from air to water what will happen to the wavelength and the angle of refraction?
I used the approach that we apply to light waves and concluded the wavelength will decrease and the wave will bend toward the normal since water is a denser, but the answer given in my book was the opposite. There was no explantion given, could you please explain.
The frequency of a sound wave cannot change as it crosses the water-air boundary. The wavelength can, and does, change but the frequency cannot because if it did there would be no way to match the two waves at the interface. This means that the higher frequency is not some quirk of the sound propagation, but that the colliding stones emit a higher frequency when in water.
To see why this is we need to consider how the sound is generated. When the two stones collide this generates a shock wave that propagates into the interior of the stones and makes them vibrate. At the surface of the stones the vibrations propagate into the surrounding medium as a sound wave, and that's ultimately what we hear. A stone will have some set of normal modes, and the shock wave will transfer energy into these normal modes exciting them in some probably rather random way that will depend on the details of the impact. The sound we hear is the combination of the frequencies and amplitudes of all these normal modes.
The reason that the sound of the impact is different in water is simply that the normal modes of an object in a medium like water are different to the normal modes of the same object in air. This is because water has a (much!) high bulk modulus than air and the surrounding water resists being moved by the surface of the vibrating stone far more than air does. It would be a brave physicist who would predict exactly how the sound would change because this will be complicated. Vibrational modes that cause lateral displacement of the water will tend to be slowed because the water has a higher density than air. On the other hand vibrational modes that cause compression of the water will shift to a higher frequency because water has a higher bulk modulus than air.
It might be possible to calculate exactly how the bulk modulus and density of the medium affect the normal modes for some idealised object like a perfectly elastic sphere. I've Googled for such calculations but with no luck - if anyone finds a relevant link please feel free to edit it in or add it as a comment. For now all i can say is that experiment shows the normal modes that shift to higher frequency dominate the sound we hear.
I think that this question is why sound waves are non-dispersive whereas gravity waves on the surface of water are and also depend on the depth of the water.
In fact if the depth of the water is less than about half a wavelength, the speed of the gravity waves is $\sqrt{gd}$ and not dependent on the wavelength of the waves. The speed of gravity waves depending on the depth of the water is really no different than the speed of sound in air depending on the pressure, density etc.
Also sound waves can show dispersion as is illustrated in the article about the dispersion in concrete.
We find that at low ultrasonic frequencies the arrival velocity of ultrasonic pulse, in such a material, increases with the grain size. At the high ultrasonic frequencies a decrease of the pulse velocity with frequency and grain size is observed.
In the chapter The Origin of the Refractive Index Feynman explains that electromagnetic waves interact with the bound electrons of a dielectric. The bound electrons undergo forced oscillations under the influence of the incoming electromagnetic waves. If the frequency of the electromagnet wave is not close to that of a natural frequency of the material then the dispersion is very small but near resonance the material will be highly dispersive.
So what you must look at is the interaction of the wave with the medium and its surroundings.
In the link from HyoerPhysics that you quoted you will have noted that the motion of the gravity waves are as shown below.
If the depth of water is restricted (shallow water waves) then you can imagine that the speed of the waves might well be affected.
This dependence of velocity on depth is explained in this poor video quality but excellent content Waves in Fluids which is one of a series of videos on fluid dynamics made by the National Committee for Fluid Mechanics Films.
In deep water the gravity waves do become dispersive as the phase velocity is $\sqrt{\dfrac{g\lambda}{2 \pi}}$ which depends on the wavelength.
As is explained in the video gravity waves are the result in a difference in hydrostatic pressure which causes horizontal forces resulting in wave propagation.
I am afraid that I cannot simply explain by "hand waving" why it is that longer wavelength gravity waves travel faster than shorter wavelength waves which is shown in the Ripples in a Pond video in which capillary waves are also described.
So perhaps the answer to your question is that when one starts to study wave motion the examples used tend to be relatively simple and dispersion tends not to be mentioned except in the splitting up of white light into its component colours by a prism. More advanced courses then show that the assumptions made in the less advanced course are not necessarily valid.
The book by Willard Bascom "Waves and Beaches" is available on free e-loan from Archive.org if you register with them.
Best Answer
Refraction occurs because of a change of speed of propagation of the wave. When light passes from air to water it slows down, whereas when sound travels from air to water it speeds up. Therefore sound is refracted away from the normal, whereas light is refracted towards the normal.