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It comes from huygens principle. Each point of a wavefront can be treated as a point source for a wavefront. They seems to form a common wavefront because they interact with each other through a phenomenon called interference.

This leads to a wave entering into a lower impedence media to be refracted away from the normal of the surface, you can view it as a car which comes from driving in mud into driving on good ground with one wheel first, that wheel will get better traction and the car will turn as it is now moving faster than the other wheel. At a certain angle the car will turns so much that the other wheel never passes the boundary, the car is deflected.

You could see it as the first wheel being a part of the wavefront which passes the boundary then starts interfering with the wave point sources still inside the media causing the aggregate wave front to not pass the boundary. Maye one could say that they interfere with their own potential to travel faster beyond the boundary.

Sound is not my speciality though I'm more used to thinking probablity waves so someone else may have a better explanation. But it should work the same, all waves act in the same way.

Edit: Also something about the energy being indestuctible and dependent on the frequency (which means the frequency cannot change) and the sound moving quicker and/or slower which means that the wavelength change in diffrent media. It's been almost ten years since I worked with waves.

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Sound results from a combination of particle motion and pressure. The motion changes the pressure, the pressure changes the motion. Impedance is how those two are related; a high impedance means that acoustic waves have higher pressure with lower motions, low impedance means low pressures and high motions. With the exception of things like firm barriers (which can be seen as regions with infinite impedance), neither pressure not motion can make a discontinuous jump.

When a wave encounters a barrier, waves face a dilemma. First, since impedance is changing, and impedance is the relationship between motion and pressure, one or both of those must change. Second, neither can change suddenly. The solution to this is that the discontinuity applies to the wave as a whole, not one particular ray, so if you have two waves within the two different mediums (Ie one reflected and one transmitted), there is a wave combination that satisfies both requirements.

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A more physics based answer: Consider the case of an open-closed tube. You are intuitively seeing why the sound bounces off the closed end, because the particles cannot physically move through that barrier. That barrier will provide an additional pressure to ensure that the motion at that point goes to zero. If you send a wave pulse to that end of the tube, the back of the tube will push back hard enough to stop the displacement of the particles, but it cannot do that without also pushing back hard enough for the velocity of those particles to go back, causing a reflected wave pulse going the other way. The open end would seem to let particles move freely, but the open end is fixed to atmospheric pressure*, so the (gauge) pressure of the wave at that point will have to be zero*. The wave pulse sent that direction will not have the expected resistance to its motion that it had in the tube, and as a result the air will move in mass out of the tube, but will do so in the form of a pulse traveling back into the tube. The pulse traveling back into the tube will have the same direction of particle motion, opposite direction of pressure.

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*In reality the atmosphere does not have zero impedance, just a lot less than the air in the tube, which is why mouth effects comes up when trying to apply this

So when going from a high impedance medium to a low impedance medium, shouldn’t all that energy be transmitted into the particle motion? How can a reflected wave be generated?

Waves are oscillatory motions. You can't have all the particles just leave and create a vacuum. So when the wave enters the lower impedance area there is low pressure in the high impedance area, and so particles must be drawn back in to balance it out forming a new reflected wave.

the energy doesn't just disappear, the reflected wave also carries some energy.

No, for the same reason that going from low to high doesn't transmit all that energy into the pressure. Neither pressure nor motion can have a sudden discontinuous change.

Here's an intuitive approach.

Consider the source of the vibrations in the middle of the medium. It's a combination of the inertia of the particle and the forces applied by neighboring particles.

When a particle at the boundary vibrates, the properties of the particle at the different medium applies a different force to the boundary particle. This changes the oscillation period of the boundary particle, which in turn applies a different force to the other particles in the original medium.

Essentially, the boundary particle goes out of sync, which reads as a reflection when scaled up to the entire boundary

The high impedance medium can carry more energy than the low impedance medium. So when a wave goes from high impedance to low impedance some of the energy is reflected back because it can't go forwards.

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Got it! So the reflected wave at an interface going from high to low impedance just has a lower intensity than it would if it hit gone from low to high, but the reflected wave is the same frequency as the incident.