Superposition of 2 Waves: Equation

[jumbogala]

Homework Statement

What is the equation for the superposition of 2 waves?

Homework Equations

The Attempt at a Solution

Displacement of the first wave is D₁ = Asin(k₁x - ω₁t)

Displacement of second wave is D₂= Asin(k₂x - ω₂t)

Add together: D₁ + D₂ = 2Acos[(k₁-k₂)x/2 - (ω₁ - ω₂)t/2]*sin[(k₁ + k₂)x/2 - (ω₁ + ω₂)t/2]

But this isn't in terms of what the problem is asking! Help, can the form be changed somehow?

Is there a way to reduce the k1 and k2 so that it is in that form?

 

[ideasrule]

But it IS in terms of w1-w2 and w1+w2! Maybe the question meant that you could use y=Asin(w*t) instead of y=Asin(kx-wt), but otherwise, your work is correct.

 

[jumbogala]

Good point. But if the waves have different angular frequencies, wouldn't k be different? I don't see how you can just leave it out.

When a question asks for something in terms of w1 and w2, doesn't that mean I shouldn't have anything else in there?