- #1
Gauss M.D.
- 153
- 1
Homework Statement
Find the combined elongation of the waves 7sin(wt) and 2sin(wt + pi/4). Express it both in real and complex form.
Homework Equations
A = sqrt(A12 + A22 + A1A2cos(Δθ)
The Attempt at a Solution
I was given the formula above, which I don't understand, but it does spit out the correct amplitude (8.53). But how do I find the phase shift of the new wave? I tried:
g(t) = 7sin(wt) + 2si(wt + pi/4)
g(0) = 2sin(pi/4) = √2
f(t) = 8.53sin(wt + θ)
f(0) = 8.53sin(θ)
But g(0) = f(0) since f(t) = g(t) so 8.53sinθ = √2
arcsin(√2/8.52) = θ = 0.167
Which is incorrect. How do I find the phase of the new wave?