# Stationary waves equations

Stationary waves....

## Homework Statement

Which of the following equations can form stationary waves....
1. y=Asin(wt-kx)
2. y=Acos(wt-kx)
3. y=Asin(wt+kx)
4. y=Acos(wt+kx)

## The Attempt at a Solution

Answer is 1,3 and 2,4 which is obviously correct...But why cant other combinations be possible as long as they are travelling in opposite directions (like 2 and 3)?
And ya can standing waves be formed by waves of different amplitudes?

2 & 3 are travelling in the same direction :)

No..... they are opposite..... 2 is in the +ve x direction and 3 is in the -ve x direction....

Why do you think so? (your explanation)
Hint: The functions are not same....one is sine and the other is cosine The direction of wave is determined by the sign of the quantity (coefficient of w/coefficient of x) it its is positive then the wave is travelling in -ve x direction and vice versa.....That is my explanation.....

the wave is travelling in -ve x direction and vice versa.....

As long as the function defining wave remains the same!
You can write 2. y=cos(wt-kx) as y=sin(π/2-wt+kx)=sin(w't+kx)

As long as the function defining wave remains the same!
You can write 2. y=cos(wt-kx) as y=sin(π/2-wt+kx)=sin(w't+kx)

But how can one write it as sin(w't+kx)......w has to remain same and has to be positive...
And ya....how does it explain why 2 and 3 can not form a standing wave?

But how can one write it as sin(w't+kx)......w has to remain same and has to be positive...

My mistake.
Its y=sin(π/2-wt+kx)=sin(Φ-wt+kx). Compare this with y=sin(kx+wt).

And ya....how does it explain why 2 and 3 can not form a standing wave?

2. and 3. are travelling in the same direction. They can't produce a standing wave.

I am still not clear..how are they travelling in the same direction? if the velocities have opposite sign....

So to avoid the confusion, there is a fundamental method. If f(x,t) is the function representing a wave, then df/dt=0 (if wave shape remains constant, which is usually the case). Find out the sign of dx/dt from each equation and compare 