Wave properties

A wave front is the leading edge of a wave. It represents a continuous crest or trough. A wave ray is an arrow perpendicular to the wave front that shows the direction of motion at a particular point.

wave frontwave rays
Wave front and wave rays on a wave emanating from a point source

When an incident wave ray hits a reflective surface, it makes an angle with the normal (a line perpendicular to the surface) called the angle of incidence. The angle of the reflected ray is called the angle of reflection. According to the law of reflection, these two angles are equal:

Incident ray and reflected ray illustrating the law of reflection

When waves enter a new medium, refraction occurs. The speed of the wave either increases or decreases, and the wavelength changes with it. The relationship is v1λ2=v2λ1 when frequency is held constant.

Straight wave enters a slower medium

When straight waves pass through an opening, they can be bent. This phenomenon is known as diffraction:

Diffraction of a wave through a wide slit (left) and a narrow slit (right)

The sine of the angle of diffraction is proportional to the wavelength and inversely proportional to the width of the opening:


For example, sound is easily diffracted because its wavelength is fairly long. Light, on the other hand, requires a much narrower slit because its wavelength is shorter. In general, the wave experiences significant diffraction when w<λ.

Whenever there are two waves, we usually talk about their phase delay. Two waves are in phase if their crests and troughs line up. They are completely out of phase if crests line up with troughs and troughs line up with crests. Anywhere between and they are partially out of phase.

in phasepartiallyout of phasecompletelyout of phase
Two waves in phase, partially out of phase, and completely out of phase

When the waves are in phase, the phase delay is 0º. When they are completely out of phase, it is 180º. Often it is more useful to express it in terms of the wavelength—the range from 0º to 360º is equivalent to the range from zero to λ.

Waves don’t really collide—they just pass right through each other. While they are occupying the same space, though, they interfere with each other. That interference can either be constructive, when amplitude becomes larger because two crests or two troughs overlap, or destructive, when amplitude becomes smaller because a crest and a trough overlap.

Constructive and destructive interference with square waves