The mixture of two or more signals (concurring at the same time in the same point of the space) is known as superimposition. When we are interested only in one of the signals, the rest are supposed to contaminate it. The contaminating signals can be considered generically as 'noise' if they do not carry any information or as interference signals if they carry any similar information to the one we are interested in and from which it is difficult to separate.
From the physical view, interference is the phenomenon of redistribution of energy on account of superimposition of waves from two sources.
When the interference is due to waves of similar frequency there are points where resultant intensity is maximum, in which case interference is said to be constructive, and there are points where the resultant intensity is minimum, and interference is said to be destructive.
When the interfacing signals occupy different frequency bands than the desired signal, appropriate filtering can remove interference.
The mechanism of the interference (and supersimposition in general) is similar in mechanical and electromagnetic waves. However, when they carry sound information (can be mechanical or electromagnetic, for example radio waves), the shape of the complex wave (its evolution in the time) is the main important characteristic, and the interference is studied in terms of how it changes that shape. While the approach to the study the interference is different with waves which most important characteristic is its intensity or (light, noise, etc.)
Interference of sound waves can be demonstrated using Quincke's tube. It consists of two U-tubes ABCDE and FGH, whose limbs can be inserted telescopically into each other. The tube ABCDE is provided with two side tubes at B and D. The side tube at D is fitted with a rubber tube. A tuning fork of high frequency (about 1000Hz) is sounded near the opening at B. Initially, the path lengths BCD and BGD are made equal. The rubber tube is held against the ear. The waves arriving at D along the two paths will be in phase. Hence, a loud sound is heard. Now, the tube FGH is gradually pulled out. When the path difference between the waves becomes l/2, the waves reaching D via the paths BCD and BGD will be 180o out of phase and cancel each other. The compression due to one wave will overlap with the rarefaction due to the other wave. On increasing the path difference, a loud sound is heard again, when the path difference i.e., BGD-BCD is l. This experiment, besides illustrating interference, provides a good laboratory method of measuring the velocity of sound in air. Initially, the path lengths are adjusted to be equal. The outer tube is pulled out till the sound intensity becomes minimum. The distance through which the tube has been slided will be l/4, since the path difference is l/2. By measuring this distance using a scale, l can be calculated. Assuming the frequency of the tuning fork to be f, the velocity of sound can be calculated using the relation v = f l.
Let two similar waves of amplitudes A1 and A2 having same frequency and wavelength travel past a point in a medium, producing individual displacements y1 and y2.
Then,
,
Where f is the phase difference between the waves at the point under consideration. Then, according to the principle of superposition,
y = y1 + y2
Expanding the 2nd term in the above expression using the formula
sin (A + B) = sin A cos B + cos A sin B, we get,
The above equation represents a simple harmonic wave of wavelength l, velocity v and amplitude R. It differs in phase with respect to the first wave by an angle q, which can be found by referring to figure.
In this figure,
In the same figure, applying Pythagoras theorem,
Case (i) When f = 0
When the two waves are in phase, the resultant amplitude is given by
The maximum value of cos q is 1.
Thus, R will be maximum when f = 0
Two waves are said to interfere constructively or reinforce each other, if the resultant amplitude is maximum. The condition for constructive interference is that the phase difference
A phase difference of 2p corresponds to a path difference l.
Let the phase difference f correspond to a path difference d.
Thus, two waves will undergo constructive interference at all points at which the path difference is an even multiple of half a wavelength.
Two waves are said to interfere destructively, if the resultant amplitude is minimum. This happens if
Thus, the condition for destructive interference is that the path difference should be an odd multiple of half a wavelength.
See Cancellation
When two or more wave motions traveling through a medium superimpose one another, a new wave is formed whose resultant displacement
at any instant is equal to the vector sum of the displacement due to individual waves
at that instant
The two short lined waves traveling in opposite direction first add up (center) to form a resultant wave and then move off as if nothing happened to them.
(It is important to note that each wave preserves its individual characteristic of wave motion)
This shows that when an up-wave (crest) meets a down-wave and are identical, then the resultant is a straight line.
When two down waves superimpose one another, a new wave is formed but in a downward direction (the amplitude of the resultant wave is the sum of the amplitudes of two waves).
The above picture shows what happens when a wave meets another. It is even more surprising to know that such things happen with light. Two light waves produce brightness as well as darkness! This phenomenon where there is redistribution of light intensity, when two or more light waves superimpose, is called interference. The experiment to observe such a phenomenon was first done by a doctor, Thomas young.
Thomas YoungThe above phenomenon was difficult to observe as the two waves had to be coherent i.e., the two waves should have a constant phase difference with respect to time at a particular place where they meet. This is clear from the following diagram.
Notice that a, d, e, f, the phase (if on meeting) relation between the two sets of waves is constant. Such waves can be produced by a single light source and then made to pass through two slits as described later. Two separate light sources can never produce waves whose phase relation is constant at a particular place where they meet i.e., their phase relation keeps changing and as a result, a uniform illumination is obtained on the screen.
Notice a, b, c, the phase relation between wave trains from the two lamps keeps changing randomly.