- #1
Rococo
- 67
- 9
Homework Statement
I need to show that the waves: sin((kx)+(θ/2)) and sin((kx)-(θ/2)), differing in phase by θ, add to give a resultant wave 2sin(kx)cos(θ).
But the answer I get is different so I'm not sure how to do this.
Homework Equations
sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)
The Attempt at a Solution
I tried adding the waves together and so:
A = ((kx)+(θ/2))
B = ((kx)-(θ/2))
(A+B) = ((kx) + (θ/2)) + ((kx)-(θ/2))
(A+B) = (kx) + (θ/2) + (kx) - (θ/2)
(A+B) = (kx) + (kx)
(A+B) = 2(kx)
(A-B) = ((kx)+(θ/2)) - ((kx)-(θ/2))
(A-B) = (kx) + (θ/2) - (kx) + (θ/2)
(A-B) = (θ/2) + (θ/2)
(A-B) = θ
sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)
sin((kx)+(θ/2)) + sin((kx)-(θ/2)) = 2sin((2kx)/2)cos((θ)/2)
sin((kx)+(θ/2)) + sin((kx)-(θ/2)) = 2sin(kx)cos(θ/2)
So I must have have gone wrong somewhere because my final answer is 2sin(kx)cos(θ/2), but it should be 2sin(kx)cos(θ).