Superposition of Harmonic Waves

[azolotor]

Homework Statement

Find the resultant of the superpostion of two harmonic waves in the form

E=Ecos(α-ωt)

with amplitudes of 3 and 4 and phases of π/6 and π/2 respectively. Both waves have a period of 1s.

Homework Equations

ω=2πf = 2π/t

The Attempt at a Solution

I first plugged everything in so you get:

E=3cos(π/6-2πt)
E=4cos(π/2-2πt)

then I used the formula

tanα = [3sin(π/6-2πt) + 4sin(π/2-2πt)]/[3cos(π/6-2πt) + 4cos(π/2-2πt)] to get the angle. I am unsure of what to do. I understand the formula in the book conceptually for adding the two waves of different phases but I am unsure of how to use it. Thanks in advance

 

[haruspex]

tanα = [3sin(π/6-2πt) + 4sin(π/2-2πt)]/[3cos(π/6-2πt) + 4cos(π/2-2πt)] to get the angle. I am unsure of what to do. I understand the formula in the book conceptually for adding the two waves of different phases but I am unsure of how to use it. Thanks in advance

But you didn't post any such formula as a relevant equation. Or do you mean the tan α formula above? If so, what is α defined to mean in that equation?

 

[rude man]

Expand Ecos(wt - ψ) in terms of sin and cos. Do this for both your given waves.

Stipulate a resultant E'cos(wt - ψ'). Determine E' and ψ' by equating coefficients of the above-mentioned sines and cosines.