- #1
fluidistic
Gold Member
- 3,924
- 261
Homework Statement
Show that the superposition of three waves with frequencies [tex]\omega _c[/tex], [tex]\omega _c + \omega _m[/tex] and [tex]\omega _c - \omega _ m[/tex] and same amplitude are equivalent to another wave of frequency [tex]\omega _c[/tex] which is modulated by a sinusoidal wave with frequency [tex]\omega _m, i.e. E=E_0 \left [ 1+a \cos (\omega _m t) \right ] \cos (\omega _c t)[/tex].
Homework Equations
Not sure, but I started with [tex]E_1=E_0 e^{i (\omega _c t + k_1 x)}[/tex], [tex]E_2=E_0 e^{i \left [ (\omega _c + \omega _m )t + k_2 x \right ]}[/tex] and [tex]E_3=E_0 e^{i \left [(\omega _c + \omega _m)t + k_1 x \right ]}[/tex].
The Attempt at a Solution
Using the equations in the Relevant part, I just summed them up and factorized by [tex]E_0[/tex]. I'm wondering if I started with the right equations. What do you think? I'm asking this question because I'm unsure and further I don't really see how to reach the answer from the equations I've put.