Interference In Physics, Types Of Interference, Analysis Of Interference, Important Topics
Interference in physics occurs when two or more waves superimpose, resulting in a new wave pattern. This phenomenon, crucial in optics and acoustics, leads to constructive or destructive interference, affecting wave amplitudes and creating patterns of light and dark or sound variations.
Shrivastav 24 Jun, 2024
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Interference In Physics : When two coherent waves of the same frequency moving in the same direction superpose, they give rise to variation of intensity in space – positions of maximum and minimum intensities appear alternately in the whole region of super position.
The positions of maxima and minima are fixed and this phenomenon is called Sustained Interference . The use of the term “interference” is generally restricted to this case only. When a material object such as a rock will not share its space with another rock, more than one vibration or wave can exist at the same time in the same space. If we drop two rocks in water, the waves produced by each can meet and produce wave interference. The overlapping of waves can form an interference pattern. Within the pattern, wave effects may be increased, decreased, or neutralized.Interference Of The Waves
Interference Of The Waves : When two waves of equal frequency and nearly equal amplitude travelling in same direction in a medium superimpose, intensity is different at different points. At some points inter is large even greater than the sum of the intensity of individual waves, whereas at other points it is nearly zero.
It is to be ne that there is no creation or destruction of energy in the medium In fact, energy has been redistributed due to its transference regions of low intensity region to the regions of high intensity. This redistribution of energy due to superposition of two more) wave trains is called interference.Mathematical Analysis Of Interference
Consider two harmonic waves of same frequency (coherent waves). Suppose A 1 , and A 2 , be the amplitudes of the waves and
is the phase difference between them. It is assumed that the waves are plane and move almost along a line. Thus, wave equations are
………..(i)
……….(ii)
Here,
When both the waves travel simultaneously, the resultant wave at
P
can be obtained by principle of superposition.
Let,
…………(iii)
and
………..(iv)
Squaring and adding Eqs. (iii) and (iv), we get
……….(v)
As
……….(vi)
Also
……..(vii)
The resultant wave becomes
….(viii)
Clearly the resultant wave has the same frequency and speed as the interfering waves
Constructive Interference In Physics
These are the points where resultant amplitude or intensity is maximum or
or
and
or
at those points where
or
Destructive Interference In Physics
These are the points where resultant amplitude or intensity is minimum or
or
and
or
at those points where
or
Principle Of Superposition
When more than one wave occupies the same space at the same time, the displacements add at every point. This is the superposition principle. So, when the crest of one wave overlaps the crest of another, their individual effects add together to produce a wave of increased amplitude. This is called constructive interference. When the crest of one wave overlaps the trough of another, their individual effects are reduced. The high part of one wave simply fills in the low part of another. This is called destructive interference. Suppose there are two sources of waves S 1 and S 2
Now, the two waves from
S
1
and
S
2
meet at some point (say
P
). Then, according to principle of
superposition net displacement at
P
(from its mean position) at any time is given by
Here,
y
1
and
y
2
are the displacements of
P
due to two waves individually.
Resultant Amplitude And Intensity due to Coherent Sources
We have seen that the two waves from two sources S 1 and S 2 were meeting at point P. Suppose they meet at P in a phase difference ∆φ (or φ). If this phase difference remains constant with time, then sources are called coherent, otherwise incoherent. For sources to be coherent the frequencies ( f , ω or T ) of the two sources must be same. This can be explained by the following example. Suppose the phase difference is 0°. It means they are in same phase. Both reach their extremes (+ A or − A ), simultaneously. They cross their mean positions (in the same direction) simultaneously. Now, if we want their phase difference to remain constant or we want that the above situation is maintained all the time, then obviously their time periods (or frequencies) must be same.Intensity Factor In Interference
Since the intensity of a wave is proportional to the square of the amplitude, we have
This gives
and
Where
is called the amplitude ratio. If
and
are intensities of two interfering waves, then
If
, then
In this case
and
Interference In Physics FAQs
Q.1 : Define interference
Ans When two coherent waves of the same frequency moving in the same direction superpose, they give rise to variation of intensity in space – positions of maximum and minimum intensities appear alternately in the whole region of super Position.
Q.2 : What are two types of interference?
Ans. 1. Constructive interference
Destructive interference
Q.3 : State principle of superposition of waves
Ans When more than one wave occupies the same space at the same time, the displacements add at every point. This is the superposition principle. So, when the crest of one wave overlaps the crest of another, their individual effects add together to produce a wave of increased amplitude. This is called constructive interference. When the crest of one wave overlaps the trough of another, their individual effects are reduced. The high part of one wave simply fills in the low part of another. This is called destructive interference
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