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## Homework Statement

Hello everyone,

I am stuck with a basic concept.How do we can recognize if a given equation is wave or not?For example we know that the standing waves equation is y=2Acos(kx)sin(ωt). In my text book there is a problem which says that two waves having only different amplitudes are traveling on opposite directions on x-axis. They have asked if the waves form standing waves.

## Homework Equations

## The Attempt at a Solution

First of all i wrote the following equations.

y

_{1}=A

_{1}sin(kx-ωt) ; y

_{1}=A

_{2}sin(kx+ωt)

i added them and got

y

_{1}+y

_{2}= (A

_{2}+A

_{1})sin(kx)cos(ωt)+(A

_{2}-A

_{1})coskxsinωt

how do i recognize if this equation represents a standing wave or not??