# Diffraction occurs also for water waves or only for light and matter?

#### quasar987

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Does the phenomena of diffraction occurs also for water waves or only for light and matter?

I learned in one of Walter Lewin's lectures about the quantum mechanical explanation of diffraction for light and matter. Namely, when the wave-particle passes through the oppening, its position spread is sharply peaked, so according to Heisenberg, its momentum must be widely spread, which explains why it appears that the small opening acts as a point-source. It also justify considering the "large" opening as an infinity of point-sources. So that's very nice for light and matter, but what about water? Why does the Huygen's principle work for water? Or is it the same reason?

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#### Timbuqtu

Yes, diffraction does occur for water waves too. Hasn't your physics teacher ever demonstrated this? He should've...

The propagation of the quantum mechanical wave function of a particle, the electrodynamical wave of light and a classic water wave actually all obey the same equation, namely the wave-equation. So we expect similar phenomena.

#### Antiphon

All wave phenomena exhibit diffraction. This includes water, sound, radio, gravity (waves), seismic, etc.

#### dextercioby

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quasar987 said:
Does the phenomena of diffraction occurs also for water waves or only for light and matter?
In electrodynamics, we give a very nice mathematical proof of Huygens' principle. However, it's essential that the EM waves are, mathematically speaking, Fourier integral representations of the solutions to the d'Alembert equation. Unfortunately, the matter waves (thermal, seismic, string, membrane, viscous and ideal fluid,...) are not that simple to model, most of the waves equations are nonlinear, which means no superposition, and no validity of Huygens' principle.

Diffraction occurs for "gentle" waves, usually small perturbations to the continuum.

Daniel.

#### Antiphon

Huygen's principle is only an approximation to the phenomenon of EM diffraction.
It is typically a scalar formulation and even it's vector extensions do not produce
rigourously correct solutions. The d'Alembert equation contains does contain all the
phenomenology but can't be used to compute diffraction by complex materials. It's
best to stay with Maxwell's equations where boundary conditions can be easily applied
and all phenomenology is included.

In practice linearity is a very practical approximation tool as this paper on Seismic Diffraction illustrates.
http://www.eap.bgs.ac.uk/PUBLICATIONS/PAPERS/P1997/1997eliusc.pdf

#### marlon

diffraction occurs for any wave of which the wavelength is of the same magnitude or bigger then the opening it is passing through

marlon

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#### quasar987

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what is the reason for diffraction in the case of water waves?

#### Claude Bile

Diffraction occurs for any wave. It is one of the defining characteristics of wave behaviour. There are some exeptions for waves propagating in nonlinear media e.g. solitons, but by and large, with the exception of some isolated examples all waves have a tendancy to spread throughout whatever medium they are propagating in.

Claude.

#### quasar987

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Is there an explanation of diffraction of water waves in terms of newtonian mechanics ?

#### marlon

quasar987 said:
what is the reason for diffraction in the case of water waves?
The reason is the opening being of the same magnitude or smaller than the wavelength. Or you can also say that the reason is the Heisenberg uncertainty principle. The reason for this principle is the existence of non-commuting observables and the reason for this behaviour is...well...it is how mother nature intended it.

marlon

#### quasar987

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quasar987 said:
Is there an explanation of diffraction of water waves in terms of newtonian mechanics ?
That's not what I meant to ask, sorry. I meant to ask

"Is there an explanation of the apparent bending of waves around small obstacles and the spreading out of waves past small openings (Huygens principle) in terms of newtonian mechanics ?"

#### quasar987

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marlon said:
The reason is the opening being of the same magnitude or smaller than the wavelength. Or you can also say that the reason is the Heisenberg uncertainty principle.
I mentioned the uncertainty principle in my first post and how it is responsible for light and electron diffraction. Does the same thing exactly happens with water molecules ?!

Also, in the case of the apparent bending of waves around small obstacles, $\Delta x$ can be made arbitrarily large in the laboratory, so the momentum of the particles is extremely well determined, and there should be no bending.

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#### marlon

quasar987 said:
I mentioned the uncertainty principle in my first post and how it is responsible for light and electron diffraction. Does the same thing exactly happens with water molecules ?!

Also, in the case of the apparent bending of waves around small obstacles, $\Delta x$ can be made arbitrarily large in the laboratory, so the momentum of the particles is extremely well determined, and there should be no bending.
This bending of waves on small obstacles is the 'dual' variant of diffraction
http://ist-socrates.berkeley.edu/~phy7c/huygens.html [Broken]

and yes diffraction also happens to 'water waves'
Just look at what happens when you push on the end of a water hose...try not to get wet :)

marlon

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