# Two pulses meet

### Interference of Waves

Page 1. When two pulses meet Solution: The correct answer is c.) The principle of superposition and conservation of energy. The problem statement, all variables and given/known data. A g wire is held under a tension of N with one end at x = 0 and the other at. Wave interference is the phenomenon that occurs when two waves meet while To begin our exploration of wave interference, consider two pulses of the same.

This is shown in the diagram below for two downward displaced pulses. In this case, a sine pulse with a maximum displacement of -1 unit negative means a downward displacement interferes with a sine pulse with a maximum displacement of -1 unit.

These two pulses are drawn in red and blue. The resulting shape of the medium is a sine pulse with a maximum displacement of -2 units. Destructive Interference Destructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction.

• Wave interference

This is depicted in the diagram below. In the diagram above, the interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting displacement of the particles of the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading.

When it is said that the two pulses destroy each other, what is meant is that when overlapped, the effect of one of the pulses on the displacement of a given particle of the medium is destroyed or canceled by the effect of the other pulse.

Recall from Lesson 1 that waves transport energy through a medium by means of each individual particle pulling upon its nearest neighbor. When two pulses with opposite displacements i.

Once the two pulses pass through each other, there is still an upward displaced pulse and a downward displaced pulse heading in the same direction that they were heading before the interference. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave.

The two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur.

The resulting displacement of the medium during complete overlap is -1 unit. This is still destructive interference since the two interfering pulses have opposite displacements. In this case, the destructive nature of the interference does not lead to complete cancellation.

### Wave interference (video) | Waves and sound | Khan Academy

Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. This only becomes an astounding behavior when it is compared to what happens when two billiard balls meet or two football players meet. Billiard balls might crash and bounce off each other and football players might crash and come to a stop.

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

## Homework Help: When do two pulses begin to meet?

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.

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.

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.

## Interference of Waves

Consider what happens when a pulse reaches the end of its rope, so to speak. The wave will be reflected back along the rope. If the end is free, the pulse comes back the same way it went out so no phase change.