What is the direction of propagation for a wave

In summary, the wave has a direction, it changes depending on where you are in the x-y plane, and it looks like a surface with waves in straight lines.
  • #1
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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.
 
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  • #2
If you plot f = cos(x) you get a nice sine wave that's not moving because it's independant 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).
 
  • #3
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)
 
  • #4
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..
 

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  • #5


The direction of propagation for a wave is the direction in which the wave travels. In the example given, the wave is described by the function f = cos(x+2y-vt), which means that the wave is propagating in the x-y plane. The direction of propagation in this plane is determined by the coefficients of x and y, which are 1 and 2, respectively. This means that the wave is propagating at an angle of tan^-1(2/1) = 63.4 degrees with respect to the x-axis. This direction remains constant as the wave travels, regardless of the position in the x-y plane. So, while the wave may change in amplitude and phase as you move in the x-y plane, the direction of propagation remains the same.
 

What is the direction of propagation for a wave?

The direction of propagation for a wave is the direction in which the wave travels. This can be described as the direction in which the energy of the wave is moving.

How is the direction of propagation determined?

The direction of propagation for a wave is determined by the direction of the wave's oscillations or vibrations. In most cases, the wave will travel in the same direction as its oscillations.

Can a wave travel in multiple directions?

Yes, in some cases, a wave can travel in multiple directions. This is known as wave interference, where two or more waves combine and form a new wave with a different direction of propagation.

What factors affect the direction of propagation?

The direction of propagation for a wave can be affected by several factors, including the medium through which the wave is traveling, the frequency of the wave, and any external forces acting on the wave.

Is the direction of propagation always perpendicular to the wave's direction of motion?

No, the direction of propagation is not always perpendicular to the wave's direction of motion. In some cases, the two directions may be parallel, such as in the case of a longitudinal wave, where the wave's motion is in the same direction as its propagation.

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