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)
where ![1019_Interference of sound waves1.png](https://www.expertsmind.com/../CMSImages/1019_Interference of sound waves1.png)
and tanΦ =a2sinΦ/a1+a2cosΦ
and since Intensity ∝ A2 .
![353_Interference of sound waves2.png](https://www.expertsmind.com/../CMSImages/353_Interference of sound waves2.png)
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![434_Interference of sound waves.png](https://www.expertsmind.com/../CMSImages/434_Interference of sound waves.png)
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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 .......
Imax = ![86_Interference of sound waves3.png](https://www.expertsmind.com/../CMSImages/86_Interference of sound waves3.png)
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........
Imin = I1+I2 - 2 √I1I2 => Imin = (√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) ![1463_Interference of sound waves4.png](https://www.expertsmind.com/../CMSImages/1463_Interference of sound waves4.png)
(5) If I1=I2=Io then Imax = 4Io and Imin = 0
(6) In interference the intensity in maximum (√I1 +√I2 )2 exceeds the addition of individual intensities (I1 + I2) by an amount 2 √I1I2 while in minima (√I1 -√I2 )2 lacks (I1 + I2) by the same amount 2 √I1I2 .
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![1101_Interference of sound waves5.png](https://www.expertsmind.com/CMSImages/1101_Interference%20of%20sound%20waves5.png)
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Hence in interference power is neither prepared nor destroyed but is redistributed.
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