If I have three different waves each with difference amplitude and phase angle how would i find the combined phase angle shift?
wave 1: A=5 phi=0
wave 2: A=5 phi=pi/4
wave 3: A=9 phi=pi/2
phi'=arctan(a2sin(phi)/(a1+a2cos(phi)), where phi in this case is the difference between the phase angles of two waves.
The Attempt at a Solution
My first strategy was to add wave 1 and 2 and then add their sum to wave three. this gave me the correct combined amplitude of 15.29. I then applied the same thinking to the phase angles but the answer i got was incorrect so i tried vector addition and using the law of cosines and I got a nonsensical answer - arcos(-1.41). Needless to say i need a nudge in the right direction. Thanks for the help