Question

If the ratio of amplitude of two waves is 3:1 then the ratio of maximum to minimum intensities is

Answer 1

Step-by-step explanation:

given  

If the ratio of amplitude of two waves is 3:1 then the ratio of maximum to minimum intensities is

• Now Intensity is proportional to (amplitude)^2
• Intensity resultant will be I 1 + I 2 + 2 [I 1 I 2 cos φ]
• For maximum intensity φ = 0 and for minimum intensity φ = π/2
• Now I max = (√I 1 + √I 2)^2 and I min = (√I 1 - √I2)^2
•   So I max / I min = (√I 1 + I 2)^2 / (√I1 – I 2)^2
• Now dividing by √I 2 we get  
•                                   = (√I 1 / I 2 + 1) ^2 / (√I 1 / I 2 – 1)^2
•                                     = (a1 / a2 + 1)^2 / (a1 / a2 – 1)^2 (by putting amplitude)
•                                      = (3 / 1 + 1)^2 / (3 / 1   - 1)^2
•                                        = 4^2 / 2^2
•                                         = 16 / 4  

          I max / I min = 4 : 1

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https://brainly.in/question/7877897