15.3 Interference
Adding waves of different wavelengths and amplitudes results in complex waves. We can find some interesting effects if we consider what happens when two waves of the same wavelength overlap at a point. Two coherent waves, when meet in a region, they reinforce each other at some points and cancel out each other at some other points forming a pattern called interference. Again, we will use the principle of superposition to explain what we observe. Consider two loudspeakers producing sounds of same frequency and wavelength. Figure 15.3 shows how interference arises. The loudspeakers are emitting waves that are in phase because both are connected to the same source. At each point in front of the loudspeakers, waves are arriving from the two loudspeakers. At some points, the two waves arrive in phase (in step) with one another and with equal amplitude (Fig. 15.4-a). The principle of superposition predicts that the resultant wave has twice the amplitude of a single wave. We hear a louder sound.
(Fig. 15.3: Adding waves by the principle of superposition. Blue and green waves of the same amplitude may give a constructive or (b) destructive interference, according to the phase difference between them. (c) Waves of different amplitudes can also interfere constructively.)
The basic conditions for two waves to produce interference are
(i) Waves must be of same type i.e. sound waves can only produce interference with other sound waves.
(ii) Waves must be coherent (having a constant phase difference).
(iii) Waves must be moving in same or almost same direction.
Two waves can produce interference if amplitudes are different but this will decrease the contrast between different regions in interference pattern.