Q117 / 150 · MHT CET 2017 · Physics

If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by

  • A
    π
  • B
    Zero
  • C
    π/3
  • Correct answer
    D
    2π/3

Solution

Let the equation of two waves are
y1=asin⁡ωt-kx                    …i
And y2=asin⁡ωt-kx+ϕ …ii
When they superpose, the resultant wave is
y=y1+y2
=asin⁡ωt-kx+sin⁡ωt-kx+ϕ
=a2sin⁡ωt-kx+ϕ2cos⁡-ϕ2
=2asin⁡ωt-kx+ϕ2cos⁡ϕ2
=2acos⁡ϕ2sin⁡ωt-kx+ϕ2 …iii
Comparing Eq. (iii) with (i) or (ii), we get
a=2acos⁡ϕ2⟹cos⁡ϕ2=12
⟹ cos⁡ϕ2=cos⁡π3  
∴  cos⁡ϕ2=cos⁡π3  
∴  ϕ2=π3
or       ϕ=2π3

Hence, the correct answer is option: 'D'.

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