Question

Two harmonic waves y1=a⋅sin⁡(kx−ωt) and y2=a⋅sin⁡(kx−ωt+ϕ) are moving in the same direction, if both the waves are superimposed then the initial phase angle of the resultant wave is:

• A. (A) ϕ
• B. (B) ϕ2
• C. (C) ϕ4
• D. (D) None of these

Answer 1

Answer: (B)

(B) ϕ2

Answer 2

Explanation:
Two harmonic waves are,y1=a⋅sin⁡(kx−ωt)y2=a⋅sin⁡(kx−ωt+ϕ)Where ϕ= phase difference between y1 and y2.By the principle of superposition, the net displacement is given by,y=2a⋅cos⁡ϕ2sin⁡(kx−ωt+ϕ2)⋯(1)By equation (1) it is clear that the initial phase angle of the resultant wave is ϕ2.Hence, the correct option is (B).