### Constructive and Destructive Interference

What happens when two waves meet while they travel through the same medium ? What effect will the meeting of the waves have upon the appearance of the. As it turns out, when waves are at the same place at the same time, the amplitudes of the Often, this is describe by saying the waves are "in-phase". . If 2x happens to be equal to l /2, we have met the conditions for destructive interference. For the second question, I'm not entirely sure what you mean but i When 2 out of phase pulses meet, the pulses will cancel each other out ie.

This is known as constructive interference, in which two waves of the same wavelength interact in such a way that they are aligned, leading to a new wave that is bigger than the original wave. Figure of constructive interference However, if two waves are not perfectly aligned, then when the crest of one wave comes along, it will be dragged down by the trough of the other wave.

The resulting, combined wave will have crests that are shorter than the crests of either original wave, and troughs that are shallower than either of the incoming waves.

### Diffraction and constructive and destructive interference (article) | Khan Academy

This is known as destructive interference. In fact, if the two waves with the same amplitude are shifted by exactly half a wavelength when they merge together, then the crest of one wave will match up perfectly with the trough of the other wave, and they will cancel each other out. The resulting combined wave will have no crests or troughs at all, and will instead just look like a flat line, or no wave at all! Figure of destructive interference of two out of phase waves creating no wave Double slit interference Say you have a laser pointer.

A laser is basically just a bunch of light waves that all have the same wavelength and are all lined up with one another.

**THE PRINCIPLE OF SUPERPOSITION OF WAVES_PART 01**

Suppose you place a card in front of the laser beam with two slits in it, such that waves can only pass through two spots. You then measure the amount of light that hits the wall on the other side of the room at various points.

Figure of laser beam passing through two slits towards opposite wall For the experiment to work, the slits have to be tiny compared to the distance from the card to the wall, but they have to be larger than a single wavelength of the light. That means that if we choose a spot on the wall, two light waves will be hitting it; one from the top slit and one from the bottom slit. As they get close to the wall, and close to one another, they will start to interfere. Figure of waves in phase passing through slits and becoming out of phase as they near the opposite wall above the top slit The light coming from the bottom slit has to come much further than the light from the top slit, so more wavelengths will be needed to travel the longer distance.

The key is to compare the number of wavelengths it takes for each light wave to travel from the slit to the wall. For constructive interference, the difference in wavelengths will be an integer number of whole wavelengths.

For destructive interference it will be an integer number of whole wavelengths plus a half wavelength. Think of the point exactly between the two slits. The light waves will be traveling the same distance, so they will be traveling the same number of wavelengths. That means that there will always be constructive interference at that spot, so we will always see a bright spot on the wall in the middle. At that point, one of the waves will hit the wall with a crest when the other hits with a trough, so they will effectively cancel one another out, resulting in a dark spot there.

This will result in another bright spot on the wall.

- Interference of Waves
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This pattern will keep alternating so that we get a pattern of light spots and dark spots, both above and below our center bright spot. Figure of diffraction pattern on the opposite wall If your slits are further apart, the light waves will be coming from spots that are further apart. That means that their path lengths will be more different from one another, giving bright spots that are closer together.

We can pretend to divide our slit into pieces, and compare the path lengths of the light coming from these pieces to one another to discover what sort of interference pattern we will get when they interact. They are an equal distance from the center of the slit, so their path lengths to the center point on the wall will be the same. These questions involving the meeting of two or more waves along the same medium pertain to the topic of wave interference.

Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium.

To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped.

At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units. The diagrams below depict the before and during interference snapshots of the medium for two such pulses. The individual sine pulses are drawn in red and blue and the resulting displacement of the medium is drawn in green.

### Superposition of Waves

Constructive Interference This type of interference is sometimes called constructive interference. Constructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction.

In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses.

Constructive interference is observed at any location where the two interfering waves are displaced upward.

## Acoustics and Vibration Animations

But it is also observed when both interfering waves are displaced downward. 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. 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.