Consider two sinusoidal waves: fi = A1 cos (kz – wt + 01) and f2 = A2 cos (kz – wt + 02). We can write their complex forms as =Aje(kz-wt+61) = áei(kz-wt) f2 =Aze"(kz-wt+62) = Ãze¨(kz-wt) where the complex amplitudes á = A¡eiø1 and Ã2 Now suppose we want to combine the two: f3 = fi + f2 = Ãze*(k3z-w3t) Azeios ei(k3z=wzt) Find expressions for A3, o3, k3, and wz.
Consider two sinusoidal waves: fi = A1 cos (kz – wt + 01) and f2 = A2 cos (kz – wt + 02). We can write their complex forms as =Aje(kz-wt+61) = áei(kz-wt) f2 =Aze"(kz-wt+62) = Ãze¨(kz-wt) where the complex amplitudes á = A¡eiø1 and Ã2 Now suppose we want to combine the two: f3 = fi + f2 = Ãze*(k3z-w3t) Azeios ei(k3z=wzt) Find expressions for A3, o3, k3, and wz.
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Transcribed Image Text:Consider two sinusoidal waves: fi = A1 cos (kz – wt + ø1) and f2 = A2 cos (kz – wt + 02).
We can write their complex forms as
fi =Aje(kz-wt+61) = áeï(kz-wt)
f2 =Aze(kz-wt+62) = Ãze³(kz-wt)
where the complex amplitudes Ã1 = Ajeø1 and Ã, = Azeió2
Now suppose we want to combine the two:
fs = fi + f2 = Ãze(k3:-w3t) = Azeiøs ei(kzz=wzt)
Find expressions for A3, $3, k3, and w3.
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