What is the direction of propagation for a wave

[aaaa202]

for a wave of this type, for example:

f = cos(x+2y -vt)

What is then the definition of the direction of progation in the x-y plane? Because either way you go in the x-y plane the wave changes.

 

[CWatters]

If you plot f = cos(x) you get a nice sine wave that's not moving because it's independent of time. If you plot f = cox(x - vt) it appears to move in the x direction with time.

Think of it like this...

Pick a point on the x axis. Let's choose x=5 and note the value of f at that point at t=0. Then we want to know what the value of f will be at the same place (x=5) in the future. Let's define the future as t0+1. Let's also assume v=1 to make the sums simpler..

The new value of f at t0+1 will be cos(5-1) which equals Cos(4). In other words the value of f at x=4, t=0 moves to position x=5, t=1 Therefore the wave move towards increasing x (eg the right normally).

 

[aaaa202]

well I am with you on this. But only now we have that the wave is also dependent on x and y. And surely anywhere you move in the x-y plane will alter the look of the wave. What is it that makes the direction (2,1) so special? (note that the function was cos(2x+y-vt)

 

[CWatters]

Something like Cos(x+y) is a surface with waves in straight lines. The line x+y=0 corresponds to a crest for example. Same with Cos(2x+y). The line 2x+y=0 corresponds to a crest.

The vt part simply changes the phase so the waves appear to move perpendicularly to the crest but in reality none of the points on the wave move sideways at all. Each point is only ever going up and down in the vertical f axis.

You can actually see what the surface looks like using Excel. Create a table and fill it with data using =COS(2*B$1-$A2). Create a chart using the surface option..

Ignore all the numbers on this plot as I couldn't be bothered to tidy it up..