# Crest and trough meet

### Constructive and Destructive Interference - Video & Lesson Transcript | ommag.info

destructive interference, the crest of one wave overlaps the trough of another wave, making a smaller wave. cancel, If waves with equal amplitude meet cres to . Depending on how the peaks and troughs of the waves are matched up, Although the waves interfere with each other when they meet, they. A crest is the point on a wave with the maximum value of upward displacement within a cycle. A crest is a point on a surface wave where the displacement of the .

If two objects bob up and down with the same frequency at two different points, then two sets of concentric circular waves will be produced on the surface of the water.

These concentric waves will interfere with each other as they travel across the surface of the water. If you have ever simultaneously tossed two pebbles into a lake or somehow simultaneously disturbed the lake in two locationsyou undoubtedly noticed the interference of these waves.

### Two Point Source Interference

The crest of one wave will interfere constructively with the crest of the second wave to produce a large upward displacement. And the trough of one wave will interfere constructively with the trough of the second wave to produce a large downward displacement. And finally the crest of one wave will interfere destructively with the trough of the second wave to produce no displacement.

In a ripple tank, this constructive and destructive interference can be easily controlled and observed. It represents a basic wave behavior that can be expected of any type of wave. Two-Point Source Interference Patterns The interference of two sets of periodic and concentric waves with the same frequency produces an interesting pattern in a ripple tank.

The diagram at the right depicts an interference pattern produced by two periodic disturbances.

The crests are denoted by the thick lines and the troughs are denoted by the thin lines. Thus, constructive interference occurs wherever a thick line meets a thick line or a thin line meets a thin line; this type of interference results in the formation of an antinode. The antinodes are denoted by a red dot. Destructive interference occurs wherever a thick line meets a thin line; this type of interference results in the formation of a node.

The nodes are denoted by a blue dot. The pattern is a standing wave pattern, characterized by the presence of nodes and antinodes that are "standing still" - i. The antinodes points where the waves always interfere constructively seem to be located along lines - creatively called antinodal lines.

The nodes also fall along lines - called nodal lines. The two-point source interference pattern is characterized by a pattern of alternating nodal and antinodal lines.

There is a central line in the pattern - the line that bisects the line segment that is drawn between the two sources is an antinodal line. This central antinodal line is a line of points where the waves from each source always reinforce each other by means of constructive interference. Depending on how the peaks and troughs of the waves are matched up, the waves might add together or they can partially or even completely cancel each other. We'll discuss interference as it applies to sound waves, but it applies to other waves as well.

Linear superposition The principle of linear superposition - when two or more waves come together, the result is the sum of the individual waves.

## Two Point Source Interference

The principle of linear superposition applies to any number of waves, but to simplify matters just consider what happens when two waves come together.

For example, this could be sound reaching you simultaneously from two different sources, or two pulses traveling towards each other along a string. When the waves come together, what happens? The result is that the waves are superimposed: Although the waves interfere with each other when they meet, they continue traveling as if they had never encountered each other.

When the waves move away from the point where they came together, in other words, their form and motion is the same as it was before they came together.

### Crest and trough - Wikipedia

Constructive interference Constructive interference occurs whenever waves come together so that they are in phase with each other. This means that their oscillations at a given point are in the same direction, the resulting amplitude at that point being much larger than the amplitude of an individual wave. For two waves of equal amplitude interfering constructively, the resulting amplitude is twice as large as the amplitude of an individual wave.

For waves of the same amplitude interfering constructively, the resulting amplitude is times larger than the amplitude of an individual wave.

Constructive interference, then, can produce a significant increase in amplitude. The following diagram shows two pulses coming together, interfering constructively, and then continuing to travel as if they'd never encountered each other.

## Interference - Key terms

Another way to think of constructive interference is in terms of peaks and troughs; when waves are interfering constructively, all the peaks line up with the peaks and the troughs line up with the troughs. Destructive interference Destructive interference occurs when waves come together in such a way that they completely cancel each other out.

When two waves interfere destructively, they must have the same amplitude in opposite directions. When there are more than two waves interfering the situation is a little more complicated; the net result, though, is that they all combine in some way to produce zero amplitude.

In general, whenever a number of waves come together the interference will not be completely constructive or completely destructive, but somewhere in between.

It usually requires just the right conditions to get interference that is completely constructive or completely destructive. The following diagram shows two pulses interfering destructively. Again, they move away from the point where they combine as if they never met each other.

Reflection of waves This applies to both pulses and periodic waves, although it's easier to see for pulses.