j-e_c
Apr19-10, 05:44 AM
My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency.
He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum:
y = y1 + y2.
y = Asin(\omegat - kx) + Asin(\omegat + kx). (1)
Where the plus and minus kx denotes their direction.
However, when (with a bit of trigonometric identity work) equation (1) is simplified it gives:
y = 2Asin(\omegat)cos(kx).
But how can this be? I mean, if x = 0, then the equation tells us that there is an antinode, which (for a string) isn't true.
I've seen the equation y = 2Acos(\omegat)sin(kx), which makes more sense when I consider a string for example.
To get to it you need the equation
y = Asin(kx - \omegat) + Asin(kx + \omegat) (2)
My question is, why would you use equation (2) and not equation (1)?
Thank you in advance for your help!
He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum:
y = y1 + y2.
y = Asin(\omegat - kx) + Asin(\omegat + kx). (1)
Where the plus and minus kx denotes their direction.
However, when (with a bit of trigonometric identity work) equation (1) is simplified it gives:
y = 2Asin(\omegat)cos(kx).
But how can this be? I mean, if x = 0, then the equation tells us that there is an antinode, which (for a string) isn't true.
I've seen the equation y = 2Acos(\omegat)sin(kx), which makes more sense when I consider a string for example.
To get to it you need the equation
y = Asin(kx - \omegat) + Asin(kx + \omegat) (2)
My question is, why would you use equation (2) and not equation (1)?
Thank you in advance for your help!