Refraction occurs when a wave bends as a result of entering a new medium. Remember when we discussed that velocity is controlled by the medium? Well, since the wave is going from one substance in which it has one speed, and then enters another substance in which it will speed up or slow down, it must bend. The only time this will not happen is if the wave hits the new medium exactly perpendicular to it. Read on to find out why.
It would be helpful to look at the diagram (above) while reading the following explanation. Points A and B in the picture are both located on the same wave crest. However, due to the way the depicted wave will hit the boundary (as in the angle), Point A will reach the new substance first. In this example the second medium is the one in which the waves travel slower, but in life this is not necessarily true (it can be the other way around). As Point A starts to slow, Point B will still have a little distance to travel before it does so too. This delay between two parts of the same crest is what causes the wave to bend. A wave will not bend if it hits the second medium at a perfect right angle, because all parts of a crest, for example, will slow at the same time. Another point to note is that the delay between one crest and the succeeding crest, for example, causes the wavelength of the wave to decrease as it slows. With A having just entered Medium 2 and begun to slow, the next part of the wave (which can be represented by Point C) behind A is still moving faster in Medium 1. Thus, C "catches up" in effect with A, reducing the distance between them. With this happening all along the wave, we see that its wavelength decreases. This is also mathematically true. Since v = f(Lambda), with a decrease in speed and a constant frequency, the wavelength must decrease.
At this point it is necessary to introduce the ray diagram (above), a type of depiction of a refracted wave that shows all relevant angles. A wave (incident ray) hits a boundary between two media and refracts (refracted ray). A dashed line perpendicular to the boundary is drawn in. It the "normal line" and is a tool physicists created to allow for analysis of the angles involved. The angle between the incident ray and the normal line is the angle of incidence. The angle between the refracted ray and the normal line is the angle of refraction. As a wave travels from one substance to another and slows, it bends towards the normal line, while from slow to fast it bends away from the normal line. Ray diagrams are more helpful in the context of light waves because a mathematical formula can be used to determine at exactly what angle the wave will refract. But this does not apply so much to sound.
So how does this work with sound? Well, different media sound often travels through are warmer and cooler air. Sound travels faster in warmer air than colder, so when you're sitting in a boat at the crack of dawn getting ready to fish, you can clearly hear someone speaking far away from you. This is because the air just around you is cold from the cool water. The air above that is becoming heated by the sun, in effect creating two media. When the person far away speaks in your direction, the sound travels from a medium it is slow in to one it is faster in. From slow to fast means away from the normal line, and therefore more towards where you are sitting. Thus the bending of sound waves sometimes allows for them to be heard in places they normally would not have been detected.