Destructive Interference

Waves are found everywhere in our daily life. Sound waves, visible light waves, radio waves, microwaves, sine waves, cosine waves, stadium waves, earthquake waves, waves on a string and so on are some of the examples of waves. 

The repeating and periodic disturbances that are practiced through a medium from one end of the location to another is referred to as a wave. The wave is a transverse wave if the wave is moving perpendicular to a medium, in which the particles of the medium are displaced in a direction perpendicular to the direction of energy transport.

A medium is a substance or material by which the wave is carried; also called wave medium. In general, a wave transports energy and not matter. The particles of the medium get temporarily displaced from its rest position. The force acting upon the particles will restore them to their original positions. So, waves are said to be transporters of energy. The disturbance in the position of one particle will pass to its nearby particles in a repeated and periodic way. Thus the energy is transported from one end to the other.

Anatomy of Wave:

Wave has the crest and trough. The crest is the point on the medium that exhibits the maximum amount of positive or upward displacement from the zero position or rest position. The trough is the point on the medium that exhibits the maximum amount of negative or downward displacement from the zero position or rest position.

A wave has many crests that are often followed by other crests; same happens in the case of trough. Every crest is broken by a trough to create an alternating pattern of crests and troughs. 

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Amplitude: The amplitude of a wave refers to the maximum amount of displacement of a particle from its rest position.

Wavelength: The wavelength of a wave is simply the length of one complete wave cycle, comprising a crest and a trough. 

When two waves travel through the same medium and meet one another, depending upon the medium their effects may vary. Explaining this is the explanation of interference of waves.

When two waves meet while traveling along the same medium where interference occurs, this phenomenon is called wave interference. The interference of waves forms particle in the medium to take a shape and that results from the net effect of the two individual waves. To begin the exploration of wave interference, consider two waves of the same amplitudes are traveling in different directions in the same medium. Consider that each wave displaces an upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, eventually there will be a moment in time when they will be completely overlapped. At that time, the obtained wave shape would be an upward displaced sine pulse with amplitude of 2 units. The figures below depicts the before and during interference snapshots of the medium for two such wave pulses. The individual sine pulses are drawn in red and blue colour, and the resulting displacement of the medium is drawn in green colour.

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You know depending upon the direction of the waves’ displacement or any two waves’ displacement direction, their interference is identified as constructive interference and destructive interference.

This interference occurs at any location along the medium where the two interfering waves have a displacement in the same direction. Here an upward displacement is greater than the displacement of the two interfering pulses. Simply, a constructive interference is observed at any location along a medium where the two interfering waves are displaced upward. It is also observed when both interfering waves are displaced not only upward, but also downward. This is shown in the figure below for two downward displaced pulses.

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Here a sine pulse with a maximum displacement of –1 unit, negative sign explains that the displacement is downward. Again, the interference is with a sine pulse with a maximum displacement of –1 unit. These two pulses are shown in red and blue colour. The resulting shape of the medium is a sine wave with a maximum displacement of –2 units.

Destructive Interference

Destructive interference can take place at any location in the medium where the two interfering waves have a displacement in the opposite direction; that the two waves are travelling in an opposite direction when they get into interference. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of –1 unit, a destructive interference takes place. This is shown in the figure below.

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In the above figure, the interfering pulses have the same maximum displacement but are in the opposite directions. The result is that the two pulses completely destroy each other when they completely superimpose or overlap each other. At the instant of complete overlap, there will not be any resulting displacement of the particles in the medium. This "destruction" is not a permanent condition though. In fact, the two waves destroying each other can be partially misleading. When it is said that the two pulses destroy each other, what is meant is that when superimposed, 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 one. As we know that waves transports only energy through a medium by means of each individual particle disturbing upon its nearest neighbor particle. When two pulses with opposite displacements, i.e., one pulse displaced up and the other down, both meet at a given location, the upward pull of one pulse is balanced by the downward pull of the other pulse. Once the two pulses pass through each other, there still remains both an upward and downward displaced pulse that head in the same direction where they were heading before they got into the interference. Destructive interference perfectly leads to only a momentary condition. Here, the medium's displacement is less than the displacement of the largest-amplitude wave.

There is no need of having same amplitudes when two waves interfere in opposite directions for destructive interference to occur. Say for instance, a pulse with a maximum displacement of +1 unit could meet a pulse with a maximum displacement of –2 units. The resulting displacement of the medium during complete overlap would be –1 unit.

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This is also destructive interference, since the two interfering pulses have opposite displacements. In this case, the destructive nature of the interference could not lead to a complete cancellation.

The meeting of the two waves along a medium might not alter the individual waves or even deviate them from their travelling path. Yet the two waves will meet to produce a net resulting shape of the medium, and then just continue their travel as before the interference took place.

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