# Wave Sets

1. Jan 17, 2008

### Don Carnage

Hi.

As it can be seen at the ocean waves arrange in sets. Typical a set of 5 to 7 waves
where the middle ones are the biggest. What I don't understand is how this can happen.
Is it really possible for waves to exchange energy with each other..?? I though that
linear plane waves could "interact" in forms of constructive/destructive interference
but not that wave in the middle of a wave set could somehow suck energy from the others..
Maybe its because I am comparing EM waves with mechanical longitudinal waves or what..?

2. Jan 17, 2008

### jdg812

Even linear waves can be arranged in such sets. Because they are not 'monochromatic'. Combination of two waves with approximately the same frequencies produces beating of waves, which you saw.

If wave is nonlinear, then there are many other mechanisms of sets formation, for example modulational instability.

3. Jan 17, 2008

### Don Carnage

But if the waves are not-monochromatic (of different wavelengths) but linear they must travel with different speeds because their wave speed is v = omega / k, where k is a function of lambda (the wavelength)..
and if they have different speeds sets wont exist.. but they do !?

Last edited by a moderator: Jan 17, 2008
4. Jan 17, 2008

### Don Carnage

Furthermore waves sets suck energy from its surroundings which can be seen when a set hits the shore because there will be a moment of totally calm right after....

5. Jan 17, 2008

### jdg812

A wave in sea consists of many crests, from shore to horison
Another wave consists of many crests as well.
They have slightly different speeds, but they overlap all the time, so sets exists.

In popular English WAVE means ONE crest.
In physics, wave means a whole thing, from Florida to Africa.

6. Jan 17, 2008

### Don Carnage

hehe i still dont get it :P

7. Jan 17, 2008

### Don Carnage

or well.. I understand what you are telling me but how this makes them arrange in sets..

8. Jan 17, 2008

### Don Carnage

When waves arrange in sets is it then an intrinsic sort of property contained in the waves or is it due to external forces.?

9. Jan 17, 2008

### Don Carnage

I mean if it was some kind of intrinsic property i must be rather simple to write a program which show how the arrange in sets :D

10. Jan 17, 2008

### jdg812

If you just make an animation of the couple of linear waves

A*sin (W1*t -K1*x) + B*sin (W2*t -K2*x)

(use K2 = 1.05*K1, and t as parameter of the animation, K1*x changes from 0 to 100, not from 0 to 2*Pi only)

you would see not only your sets, but change of the amplitude of the largest crest. Then next crest would become the largest one.

In this example everything is linear and intrinsic

11. Jan 17, 2008

### Don Carnage

Ok -I will give it a look tomorrow.. thx a lot..

Peter

12. Jan 18, 2008

### Don Carnage

Ok now I have written a program that generates 50 *.dat files in gFortran.
I can open them in gnuplot one at the time but it simply doesn't illustrate it.
Does anybody know an animation tool for Linux that can read datefiles..?

13. Jan 18, 2008

### jdg812

Last edited: Jan 18, 2008
14. Jan 18, 2008

### Don Carnage

very nice.. are these just *.gif animations. What program has been used to make the plots?
Doesn't look like Gnu plot.. maybe Matlab..?

15. Jan 18, 2008

### Don Carnage

So will a superpositioning of two linear waves with different ang. frq.'s and wavevector's always result in these sets.. damn I have to get my animation working.. its just so exiting and non-intuitive.. wonder what happens when I superposition a lot of waves.

Well on the other hand I know from quantum theory that the most located quantum particles are the ones of huge Fourier Sums there trough containing A LOT of superpositioned waves. One thing is to read it - another is to actually see it :P

16. Jan 18, 2008

### jdg812

I prefer Maple or Mathematica

If frqs are about equal, yes
If not, still yes, but beating too quick and not easy to observe...

Actually you dont need animation or numerical simulations...
Sum of a couple of trig functions is product of trig with arguments
(a + b)/2 and (a - b)/2
The second one is beating term...

Last edited: Jan 19, 2008
17. Jan 18, 2008

### Don Carnage

I don't understand what you mean..

18. Jan 18, 2008

### jdg812

cos a + cos b = 2 cos((a + b)/2) * cos((a - b)/2)
a = W1*t - K1*x
b = W2*t - K2*x

19. Jan 19, 2008

### esalihm

Linear Mechanical waves can't suck energy from each other. They go through each other and form temporary and compound waves by constructive and destructive interference.
I havent heard of those waves of 5 and7. Is that just a practical observation?
Because I can't see any reason why one cant create a wave of 10 or 20 peaks with a wide enough pool or with spring too...

Last edited: Jan 19, 2008
20. Jan 19, 2008

### jdg812

Linear waves can't, but nonlinear can.