How Do You Derive the Resultant Wave Using Superposition?

[heycoa]

Homework Statement

Using expansion of sin and cos functions, show that the resultant of adding the following two waves:
a) E₁ = E₀₁*sin(wt-k(x+Δx))
b) E₂ = E₀₁*sin(wt-kx)

Gives: E = 2E₀₁*cos((1/2)kΔx)*sin[wt-k(x+Δx/2)]

Homework Equations

N/A

The Attempt at a Solution

I don't know how to sum the two waves using superposition. I don't understand how to get to the final solution. Please help.

 

[TSny]

To sum the waves using superposition, you just add the mathematical expressions for E1 and E2. See if one of these trig identities will help: http://en.wikipedia.org/wiki/List_o...#Product-to-sum_and_sum-to-product_identities

 

[heycoa]

yes that worked! thank you very much

 

[TSny]

Good work!