Is sine*sine a form of a standing wave?

[deadlytrogdor]

What kind of wave is Asin(kx)sin(wt)?

Using trig functions, I've rewritten it as

Bcos(kx-wt) - Bcos(kx+wt)

So it sort of looks like it's a standing wave in that it's a superposition of two waves traveling in opposite directions with equal amplitude and wavelength, yet I'm unsure since it seems like the two waves would be canceling each other out perfectly.

So what is it?

 

[Mindscrape]

You seem like you're on the right track. What do you mean they would be canceling each other out perfectly? You already saw that the equation could be written in terms of w(x,t)=Asin(kx)sin(wt), which is not 0. Also, I guess you're using a new factor B, but be sure to keep track of your factors of 2.

 

[deadlytrogdor]

Okay. I guess I just wasn't thinking about this correctly graphically--I was thrown off by the minus sign instead of the plus sign.

So, just to be perfectly clear, it is then a standing wave, based off of what I said originally, correct?

Was it necessary for me to get it into the cos-cos form to see that it is a superposition of two waves, or is there a way to tell from the sin*sin equation that it is a standing wave? If it was like sin(kx)cos(wt) or something like that, I would have recognized it, but the sin*sin throws me off a bit.

 

[Mindscrape]

Granted, standing waves are can be produced by interference, but I'd say the original equation describes it as a standing wave a bit better. You have a term that depends on frequency and time (wt), and you have a spatial term that will give nodes and antinodes. It's the spatial term that makes this a standing wave. It could be sin or cos.

sin(kx)cos(wt)=sin(kx)sin(wt+pi/2)=sin(2*pi/(lambda)*x)sin(wt+pi/2)

if x = lambda ± n*lambda/2 you have a node, I'll leave it to you to see how the antinodes would go

Maybe helpful
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

 

[deadlytrogdor]

excellent, thanks!