question about water waves?

Question

so my theory is,
the reason why water waves bend toward the normal line and slow down when it enter from a deeper region to a shallow region is that the density of water increases.
since density=mass/volume,the volume decreases,the mass remains,then the density will increase.
and when the density increases,the water particles increase too which slows down the speed.
but when i think of it again,
shouldnt the density of water be the same as it's the same water?
and the mass of water should decrease when it enters a shallow region since it's volume decrease.
now i am totally confuse about this whole thing...

Answer 1

Water is, to a good approximation, incompressible. Therefore it isn't density changes that cause the bending of the water waves. It is much simpler. The velocity of the wave is proportional to the depth, so if a plane wave comes towards a shore at an angle to the normal, the part closest to the shore will start moving slower first and the part of the wave further from the shore will still be moving at a higher speed. So the latter part of the wave crosses the distance faster and the wave comes closer to the normal.

Compare this to a car where the left wheals are experiencing more friction than the right wheels at any given moment. The car will turn left.



Haarlet's answer invokes Snell's law of refraction. That law is not a cause for bending, but Snell's law is a consequence of light waves traveling slower in an optically denser medium.

Answer 2

The other contributors have correctly explained the reasons for the wave propagation effects you describe.



So to clear up the issue of water density - water and all fluids (in this case liquids) are 'compressible'. The value is called the 'Bulk Modulus' this is generally defined as the pressure required to reduce a specified volume by 1%. However, these values (the pressures) are extremely high. e.g. For 'fresh water', I believe that the bulk modulus is about 300,000 p.s.i. - a huge pressure.



Consequently it is therefore generally accepted that for normal everyday calculations water can be regarded and considered as incompressible.



The bulk modulus becomes more important when dealing with very large and 'confined' volumes and things like pressure 'transients' (pressure surges) etc.



Hope this small contribution helps clarify things for you.l

Answer 3

Water's density doesn't change. You're looking for Snell's law. The wave is propagating through the water. Water is just the medium. A sudden depth change in the water is an interface between 2 media of different refractive index. The wave refracts at the interface according to Snells Law, which is



sin(theta_1) / sin(theta_2) = v_1 / v_2 = eta_1 / eta_2