Two standing waves forming a traveling wave

[fisico30]

Hello Forum,

it is well know that the sum of two identical sinusoidal waves propagating in opposite direction, with zero relative phase, create a standing wave:

Phi1(x,t)=sin(kx+wt+theta1)
Phi2(x,t)=sin(kx-wt+theta2)

with theta1=theta2, w1=w2 (same angular frequency).

Phi_tot=Phi1+Phi2=standing wave where the space and time part are separate:

Q1: what if the two wave don't have identical phase, i.e. theta1 not equal to theta2?

I read somewhere that it is possible to sum two standing waves and get a propagating wave...How? Do the two standing waves need to have different amplitudes or different relative phase?

thanks
fisico30

 

[AlephZero]

It doesn't matter if the phases are the same or different.

You should be aboe to can see this is true physically. You could measure the time starting at a different instant, when both phases were the same.

Or, do the math and expand out all the trig functions.

Q2. If the amplitudes are different, the resultant will be a traveling wave moving in the direction with the greatest amplitude. Again, the phases are not important.

 

[fisico30]

AlephZero,

thanks for the reply.
I am going to run a simulation, but as far as Q1, the two identical wave going in opposite direction, I feel like they must have the same phase because they must be always in phase opposition at certain points (the nodes) and in same phase at the antinodes...

By the way, what is a mixed wave, defined as part traveling part standing?

A pure traveling wave describes energy that moves.
A pure standing wave describes a wave that is stationary; energy is stored in place;

What does a mixed wave describe? What type of wave phenomenon?


thanks
fisico30