When two rays of similar frequency, similar wavelength, and same speed moves in the similar direction, their superimposition gives result in the interference. Due to interference the last intensity of sound at that position is different from the addition of intensities due to each wave separately. This change of intensity due to superposition of two or more rays is known as interference.

Let at shown a point two waves reaches with phase difference and the relation of these waves is given by

y₁ = a₁ sinωt, y₂ = a₂ sin(ωt+Φ) (  then by the rule of superposition

   y = A sin(ωt+θ) 

Important points

(1) Constructive interference : Intensity will be maximum

when Φ = 0,2π,4π......2nπ ;  where n = 0,1,2 ........

when x = 0, λ, 2λ, ........... nλ;   where n  = 0, 1 .......

I_max = 

It seems the intensity will be maximized at that positions where path difference is an integral multiple of wavelength these points are known as points of constructive interference or interference maxima.

(2) Destructive interference : Intensity will be minimum

when Φ = π,3π,5π......(2n-1)π ;  where n= 1, 2, 3 ........

when x = λ/2, 3λ/2, ........... (2n-1)λ/2;           where n  = 1, 2, 3........

I_min = I₁+I₂ - 2 √I₁I₂  => I_min = (√I₁ -√I₂ )² ∝ (A₁-A₂)²

(3) All maxima are normally spaced and normally loud. Same is also true for minima. Also interference maxima  and minima are alternate as for maximum Δx = 0, λ, 2λ and for minimum Δx = λ/2, 3λ/2 etc .

(4)        

(5) If I₁=I₂=I_o then I_max = 4I_o and I_min = 0

Hence in interference power is neither prepared nor destroyed but is redistributed.

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