Comparisons can also be made between the characteristics of the transmitted pulse and those of the incident pulse. Once more there are several noteworthy characteristics. First, observe that the transmitted pulse is not inverted. In fact inversion only occurs for the reflected pulse (if it occurs at all). Second, observe that the transmitted pulse has a smaller speed and a smaller wavelength than the incident pulse. This is always the case for boundary situations in which a pulse in a less dense medium reflects off the boundary with a denser medium. Since wave speeds and wavelengths in strings are always greatest in a least dense medium, it would be expected that there is a decrease in wave speed and wavelength as the pulse crosses the boundary. Finally, when waves cross boundaries the frequency of the incident pulse is the same as the frequency of the transmitted pulse (though it is not evident from the above animation). The fact is that the vibration of the last particle in the incident medium creates the vibration of the first particle on the opposite side of the boundary. These two particles are adjoined in such a manner that the frequency at which one particle vibrates is equal to the frequency at which the other particle vibrates. Like two hands shaking with each other, the frequency at which one hand shakes can never be any different that the frequency at which the other hand shakes (assuming they remain adjoined to each other). Thus, it is this handshake principle that explains why the frequency of the incident pulse and the transmitted pulse must be the same.

In conclusion, the boundary behavior of waves is best summarized by the following statements:

• the wave speed is always greatest in the least dense medium,
• the wavelength is always greatest in the least dense medium,
• the frequency of a wave is not altered by crossing a boundary,
• the reflected pulse becomes inverted when a wave in a less dense medium is heading towards a boundary with a more dense medium,
• the amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.
• The transmitted pulse into a denser medium has a slower speed and smaller wavelength than the incident pulse or the reflected pulse
• The reflected pulse has the same frequency, wavelength, and speed as the incident pulse.

There are additional principals that must be considered for a light wave traveling in a three dimensional medium. For example, what would happen if a light wave is traveling through air and reaches the boundary with a glass surface? How can the reflection and transmission behavior of a light wave be described? First, the light wave behaves like the wave on the rope: a portion of the wave is transmitted into the new medium (glass) and a portion of the wave reflects off the air-glass boundary. Second, the same wave property changes which were observed for the wave on the rope are also observed for the light wave passing from air into glass; there is a change in speed and wavelength of the wave as it crosses the air-glass boundary. When passing from air into glass, both the speed and the wavelength decrease. Finally, and most importantly, the light is observed to change directions as it crosses the boundary separating the air and the glass. This bending of the path of light is known as refraction. A one-word synonym for refraction is "bending." The transmitted wave experiences this refraction at the boundary. As seen in the diagram at the right, each individual wavefront is bent only along the boundary. Once the wavefront has passes across the boundary, it travels in a straight line. For this reason, refraction is called a boundary behavior. A ray is drawn perpendicular to the wavefronts; this ray represents the direction which the light wave is traveling. Observe that the ray is a straight line inside of each of the two media, but bends at the boundary. Again, refraction is a boundary behavior. The idea that a light wave can be represented by a ray is known as the ray model of light.