Question

derive an expression for the resultant wave produced due to superposition of wave​

Answer 1

Explanation:

Superposition of Sinusoidal Waves that Differ by a Phase Shift. When these two waves exist in the same medium, the resultant wave resulting from the superposition of the two individual waves is the sum of the two individual

Answer 2

Expression for the consequent wave produced because of superposition of wave​

Explanation:

When those  waves exist withinside the equal medium, the consequent wave due to the superposition of the 2 individual waves is the sum of the 2 individual waves:

yR(x,t)=y1(x,t)+y2(x,t)=Asin(kx−ωt+ϕ)+Asin(kx−ωt).

Consider 2 waves = equal frequency

                                  Different amplitude A₁ & Aₓ

Phase difference → ∅

y₁ = A₁ sin mt

y₂ = A₂ Sin( wt + ∅)

Resultant  displacement y = y₁ + y₂

y = A₁ Sin wt + A₂ Cos (wt + ∅) + A₂ Cos wt Sin ∅

Let A₁ + A₂ cos∅ = A cos θ    (1)

A Sin ∅ = A sin θ                     (2)

y = A cos θ  sin wt + A sin θ  cos wt

y = A sin ( wt +  θ)

Answer →  y = A sin ( wt +  θ)