Confused? Wave Function Direction Explained

[chemic_23]

Homework Statement

im quite confused of describing whether these wave functions y(x,t)= sin(kx-wt) ; y(x,t)=sin(kx+wt) ; y(x,t)=cos(kx-wt) ; y(x,t)=cos(kx+wt) travel to the right or to the left.

My prof told me that y(x,t)=sin(wt-kx) travels to the right (+x direction) but based on my other book, it's moving to the left (-x direction) pls can someone explain it to me? pls thank you...

 

[Dick]

Find out for yourself. Pick a fixed constant amplitude value on the wave, say c=sin(wt-kx) and see how it moves. The sin is constant if wt-kx is some constant, say b. So b=wt-kx. Now solve for x, so x=(wt-b)/k. I would say that means if t increases, then x increases (presuming w>0 and k>0). So I would say, 'right moving'.

 

[nlightner]

The direction of wave function depends on the sign of the wave number (k) and the angular frequency (w). In general, the wave function y(x,t)=Acos(kx-wt) or y(x,t)=Asin(kx-wt) will travel in the positive x direction if k>0 and w>0. This is because the wave is moving in the positive direction of the x-axis and the time variable t is also increasing, causing the wave to travel to the right.

On the other hand, if k<0 and w>0, the wave function will travel in the negative x direction, as the negative value of k indicates a wave moving in the negative direction of the x-axis. Similarly, if k>0 and w<0, the wave will travel in the negative x direction as the negative w value indicates a wave moving in the negative direction of the time variable.

In the case of y(x,t)=sin(wt-kx), the wave number is negative (k<0) and the angular frequency is positive (w>0), causing the wave to travel in the negative x direction. It is important to note that the direction of the wave function is always relative to the direction of the x-axis. So, while the wave may be moving in the negative x direction, it is actually traveling in the positive direction of the time variable.

I hope this helps to clarify the confusion. It is always important to check the signs of k and w to determine the direction of the wave function. Additionally, different sources may use different conventions, so it is always best to clarify with your professor for the specific convention being used in your class.