The superposition of two waves, [see attachment - it doesn't let me link the attachment because I'm new ;P] at the location x = 0 in space results in what kind of wave behavior? [As in, how often does it beat and what frequency is the sound?]
Wave equations are given, general form is: Acos(kx-wt).
k = 2pi/lamda; w = 2pi/T = 2pi*f
The Attempt at a Solution
This is troublesome because I'm not sure how to work with the different amplitudes. I can't think of a way to add them, because of the different amplitudes I can't factor and get a trig identity that is easy to work with.
Essentially I have: A cos(at) + B cos(bt)
But I can rewrite it as: A cos(at) + B cos(at-ct)
= A cos(at) + B ( cos(at)cos(ct) - sin(at)sin(ct) )
= cos(at)(A + B cos(ct)) - B sin(at)sin(ct)
...etc. It just gets uglier.
Any help on this would be greatly appreciated.. although, I'm going to sleep right now, I'll be up in a few hours.
5.5 KB Views: 494