Adding y=A sin(kx+wt) and y=A sin(kx-wt) - Help Appreciated

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To add the equations y=A sin(kx+wt) and y=A sin(kx-wt), the goal is to demonstrate that they represent traveling waves that combine to form a standing wave. The resulting equation can be expressed as y=2a {sin(kx) sin(wt)}. This process involves applying the sine addition formula, sin(x+y)=cos(x)sin(y)+sin(x)cos(y), to both equations. By combining the similar terms, the standing wave can be derived effectively. Understanding this relationship is crucial for visualizing wave behavior in physics.
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I am stumped on how to add these together...

y=A sin(kx+wt)

and

y=A sin(kx-wt)

any help is greatly appreciated!
 
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It depends on what you are trying to do with them. Are you adding them in order to simplify them to a smaller equation or are you adding them in order to graph them?
 
I am actually trying to show that these are waves, and that the sum of these 2 traveling waves is the standing wave described by the equation

y=2a {sin(kx) sin(wt)}

The former equations are waves traveling to the right and left, respectively.

Thanks!
 
Remember that sin(x+y)=cos(x)sin(y)+sin(x)cos(y).

Use that on both of the different equations and add the similar figures. You should get your answer.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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