If the amplitude of three intersecting waves is given by

\(y(r,t) = \frac{A}{r}e^{i(kr-wt)}[1-2cos(kdsin\theta)]\)

how can I then find the intensity at r = 200 m as a function of \(\theta\)?

I know that intensity is the square of the amplitude. Should I simply square y(r,t)? If I do, I get I as a function of t as well, because of the part \(e^{i(kr-wt)}\).

 

If the waves have the same frequency then ωt=θ

Transform the exponential term into a polar representation (cos(x)+jsin(x)) and then find the modulus (amplitude) of the resulting complex number.

 

If the waves have the same frequency then ωt=θ

Transform the exponential term into a polar representation (cos(x)+jsin(x)) and then find the modulus (amplitude) of the resulting complex number.

Analytic signals are SO much simpler to deal with, aren't they?


Eric