Stationary Waves: Explaining Amplitude of Wave

[arvindsharma]

Dear All,
when two waves y=Asin(wt-kx) and y=A(sinwt+kx) superpose the stationary wave is formed with equation y = 2Asinkxcoswt.in my textbook they take 2Asinkx as amplitude of wave.why didn't they take 2Acoswt as amplitude of stationary wave.please explain me in detail.

I will be thankful to you all.

Arvind

 

[jtbell]

Imagine a string that is stretched horizontally and vibrating vertically in a standing wave (stationary wave). There are two ways of looking at it:

1. A point on the string at a fixed horizontal position x oscillates vertically with amplitude 2A sin (kx). All points on the string oscillate with the same frequency, but with different amplitudes that vary with x.

2. On the other hand, if you use a camera to take a snapshot of the vibrating string at a fixed time t, then the "frozen" string has the form of a wave with amplitude 2A cos (ωt).

So it depends on what you mean by "amplitude" and what you want to use it for. Normally, we use view #1, but depending on the circumstances we might use view #2 sometimes.