Waveform equations

[nstansbury]

Hi,

 

I am hoping someone can help me with these equations:

 

If two ping-pong balls were dropped simultaneously onto a completely flat surface of water, the waves from both balls would propagate radially outwards until they met, where their amplitudes would superimpose exerting a force of attraction on the two balls.

 

1. What equation/s would describe the force exerted on the two balls and allow me to discount any loss due to the viscosity of the fluid?
   
2. What equation/s would describe how the radius of the propagating wave would be proportional to its' amplitude?
   

 

Thanks.

 

In relation to: http://www.scienceforums.net/forum/showthread.php?t=33431

Edited June 12, 2008 by nstansbury
In 2) I originally said "wavelength" - meant "amplitude"

[Graviphoton]

Not sure about the first one, but have you considered using the inverse-square law for the second?

[nstansbury]

have you considered using the inverse-square law for the second?

 

What would my reciprocal be?

[iNow]

nstansbury,

 

He's been suspended from the site for a few days. You'll probably need to wait for a response from another member. Good luck.

[jedaisoul]

If two ping-pong balls were dropped simultaneously onto a completely flat surface of water, the waves from both balls would propagate radially outwards until they met, where their amplitudes would superimpose exerting a force of attraction on the two balls.

 

1. What equation/s would describe the force exerted on the two balls and allow me to discount any loss due to the viscosity of the fluid?
   
2. What equation/s would describe how the radius of the propagating wave would be proportional to its' wavelength?
   

I'm a little bemused:

1. Why would the superimposition of the radially propagated waves exert a force on the two balls (attraction or otherwise)?

2. How can there be an equation relating the radius of the propagating wave to its wavelength? The propagating wave is constantly moving, whilst its wavelength remains constant.

 

Perhaps you meant a standing wave rather than a propagating one?

[nstansbury]

Why would the superimposition of the radially propagated waves exert a force on the two balls (attraction or otherwise)?

 

There must be at least one force that pushes or pulls the wave surface back to its original flat position, otherwise we won't have waves! Though in the case of a surfer I would imagine it would be Gravity.

 

How can there be an equation relating the radius of the propagating wave to its wavelength? The propagating wave is constantly moving, whilst its wavelength remains constant.

 

Because as the wave propagates the circumference of the radial wave will progressively get larger thus the energy will be spread over a larger wave front, or something like that.

 

Perhaps you meant a standing wave rather than a propagating one?

 

No, because standing waves don't propagate

 

I need to describe waves radiating out from a single source.

 

What equation/s would describe how the radius of the propagating wave would be proportional to its' wavelength?

 

How can there be an equation relating the radius of the propagating wave to its wavelength? The propagating wave is constantly moving, whilst its wavelength remains constant.

 

Eeek - heinous error - I meant amplitude not wavelength - apologies jedaisoul

[jedaisoul]

There must be at least one force that pushes or pulls the wave surface back to its original flat position, otherwise we won't have waves! Though in the case of a surfer I would imagine it would be Gravity.

That does not explain why you expect the superimposition of the radially propagated waves exert a force on the two balls (attraction or otherwise). I would assume that the interaction takes place at a distance from the balls, at the point where the waves meet. How could that affect the balls?

 

Another point, when I was at school (many years ago) water waves were used as an example of transverse motion. I.e. The water just goes up and down whilst the wave moves laterally across the surface. Hence there should be no lateral movement of the water, or anything on it. However, nowadays I'm not sure that is accurate. Water is essentially incompressible, so cannot act like a vertical spring, just moving up and down. Logically, there has to be a transverse element in the motion. I.e. as the wave front falls, the water is squished out sideways, and as it rises, the water is sucked in. So the water molecules may oscillate laterally about a central point, rather than vertically. This gives rise to the "undertow" in front of the wave, and the outflow behind it. You only have to watch what happens when the wave reaches the shore to see this in action.

 

Trouble is, even in that case, there is still no sustained attractive force on the balls. They should each oscillate about a central position?

 

P.S. By the way, as you probably know, there is no such force as "suction". I used the term colloqually. What I meant was "...and as it rises, the water is pushed back by the air pressure". Just to save misunderstanding...

 

Eeek - heinous error - I meant amplitude not wavelength - apologies jedaisoul

Thanks for clarifying. I can't be difinitive about the amplitude problem, but it would seem to me to be proportional to the circumference 2 * pi * r (or pi * d). I.e. As the circumference grows, the amplitude should fall proportionately, but I'm no expert.

Edited June 16, 2008 by jedaisoul

[D H]

If two ping-pong balls were dropped simultaneously onto a completely flat surface of water, the waves from both balls would propagate radially outwards until they met, where their amplitudes would superimpose exerting a force of attraction on the two balls.

Assuming waves with equal energy and velocity, the two wavefronts will meet at the midpoint between the balls. What physical phenomenon makes you think that the mere superposition of the waves at the midpoint would exert a force of attraction on the two balls?

1. What equation/s would describe the force exerted on the two balls and allow me to discount any loss due to the viscosity of the fluid?
   
2. What equation/s would describe how the radius of the propagating wave would be proportional to its' amplitude?
   

1. None. See above.
   
2. The Navier-Stokes equations.
   You might also want to look into gravity-capillary waves or this water wave wiki.