Phase Relationships
Interference
Interference is when a propagating wave encounters another object that may alter its path or change the amplitude in the medium. There are two types of interference: constructive and destructive. Two or more waves cross paths but do not interrupt the separate wave structure and as a result they either create a larger displacement or cancel each other; this is called the superposition of waves.
In constructive interference, waves that cross paths while traveling in the same direction are considered to be in phase. This means the crests are in phase within the medium resulting in an amplitude equal to the sum of the separate amplitudes. If both amplitudes are equal, this doubles the resulting amplitude. Destructive interference is exactly opposite of constructive interference. Assuming that both waves have the same amplitude, when the crest and the trough line up, that is to say, when the two waves are out of phase, the result is an amplitude equal to zero.
Destructive intereference created by two pulses:
Constructive interference created by two pulses:
Here are two java applets demonstrating interference:
You can best view constructive and destructive interference when two water waves cross paths. Destructive interference occurs when there is no motion. This is because the waves cancel each other out and leave the wave resting at the equilibrium position. The point of maximum oscillation would be where constructive interference occurs because the addition of the two waves superimposed create a larger displacement in the water.
Reflection
An intervention of a wave by a fixed boundary that causes it to reverse direction with respect to the normal is reflection. When a wave strikes a fixed object, some of the energy is absorbed and converted into thermal energy. However, some of the original energy reflects off of the surface. The direction of travel before contact is called the incident ray. The angle that the reflected ray makes with the normal is the angle of incidence. The direction of travel once it is reflected is called the reflected ray. The angle that the reflected ray makes with the normal is the angle of reflection. The angle of incidence is always equal to the angle of reflection.
Refraction
When a wave hits a medium, some of the energy becomes thermal energy, and some of the energy continues to travel through the medium. Once it enters a medium, the direction is slightly altered since there is a change in velocity. The velocity depends on the optical density of the medium. If the medium is more dense, the velocity will decrease because it will take longer for the wave to travel through it. The velocity will increase if the medium is less dense because it makes it easier for the wave to travel through.
Here is a flash demo demonstrating refraction:
Diffraction
Imagine a straight water wave approaching a small gap between two objects. When the water goes through the gap, it spreads out into a cone, where the gap is the point of the cone. The smaller the gap in comparison to the wavelength of the wave, the more noticeable the spread. This is known as diffraction. If the gap is smaller than the wavelength of the wave, there will be no noticeable diffraction pattern, though there will always be diffraction.
Here is a flash demo demonstrating diffraction:
Standing Waves
A standing wave is one that does not travel in one direction or another. This occurs when two identical traveling waves move in opposite directions through a medium and combine according to linear superposition. In the case of a string, which has one fixed end and one vibrating end, the wave hit the fixed point and reflects back. At a fixed end, there will always be a node, or an area of zero displacement. Halfway between nodes are antinodes, which are areas of maximum displacement. There are only certain frequencies which produce standing waves, known as natural frequencies. The lowest frequency that produces a standing wave is called the first harmonic, or the fundamental. For more on this topic, see harmonics, under sound.
