Coherent and Incoherent Addition of Waves

Introduction to coherent and incoherent addition of waves:
There are two types of sources of waves.  One is coherent source of waves and the other is incoherent source of waves. The sources and the waves are said to be coherent if they have the same frequencies, same wavelength, same speed, almost same amplitude and having no phase difference or a constant phase difference. If any of the property is lacking, the sources are said to be incoherent. The examples of the coherent sources and the waves are sound waves from two loud speakers driven by the same audio oscillator, electromagnetic waves from two microwaves horns driven by the same oscillator, light waves generated by Young have double slit experiment, light waves coming from a laser gun. To examine the coherent waves we have to observe the intensity pattern produced by the addition of two or more waves.
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Describing Coherent and Incoherent Waves:

Two waves produce the interference pattern only if they originate from coherent sources. The process of light emission from ordinary sources such as the sun, a candle, an electric bulb, is such that one to use special techniques to get the coherent sources. In order to obtain the fine interference pattern the path difference between the two waves originating from the sources should be very small. In practice the path difference should not be exceed a few centimetres to observe a good interference pattern. Is this topic formula for converting celsius to fahrenheit hard for you? Watch out for my coming posts.

Coherent and Incoherent Addition of Waves :
Consider the addition of two waves emitting from two sources of intensities I1 and I2. They two waves interfere each other so that the intensity of the resulting wave is I, which is given by the following relation. I = I1 + I2 + 2 (I1 I2 Cos q)1/2.Where q is the phase difference between two waves. For the constructive interference the value of q = 0°, so that the Cos q = 1 and for the destructive interference the value of  q = 90°, so that the Cos q = 0. In case of the incoherent sources or waves we can the intensity simply by algebraic method that means I = I1 + I2. Because of the incoherent sources the light emitted is not strictly monochromatic in nature.