Yes, I know. I had already taken the derivatives of the two individual waves and found they satisfy two different wave equations with velocities v and 2v. I understand now why mathematically the sum wouldn't satisfy the wave equation. I still don't know why the resulting wave from summing the...
The second wave has velocity 2v, so the wave equation is of the form d2y/dx2 = 1/v2 d2y/dt2 and the wave equation is satisfied only when v = 2v as the factor of 4v2 on the RHS will cancel.
I thought the wave speed was related to the frequency through v = f/lambda, so if the second wave has...
I put the two separate waves into Desmos with a t slide and it seems like I get temporal beats that appear and disappear rather than travel. So is it safe to assume that since the sum of the waves with different speeds v and 2v do not satisfy the wave equation and the physical result is beats...
So the wave of the form y = Asin(x-vt) + Asin(x+2vt) produces a beat? Does anyone know if beats satisfy the wave equation? I can't seem to find a definite answer online.
The solution that I posted is substituting the actual form I was given (y = Asin(x-vt) + Asin(x+2vt)) into the wave equation, which doesn't satisfy it. But individually, y = Asin(x-vt) and y = Asin(x+2vt) satisfy the wave equation, so I'm not sure why their sum doesn't.
Hello,
I have a wave of the form
y = Asin(x-vt) + Asin(x+2vt)
which I substituted into the wave equation to find out if it satisfies it. It didn't because of the speed of the left traveling wave being equal to 2v. What I got was:
A[-sin(x-vt)-sin(x-2vt)] = 1/v2 * A[-v2sin(x-vt) -...
Yes hello, I like physics and I'm studying physics. yay. I have a question but I didn't want to bother my tutors or lecturers with emails since we're on break at the moment so I joined. It said in the introductory email that I can't ask about that here though. Okay cool so hi. I like Dark Souls...