Huygens principle consequence of isotropy

[jd12345]

IS huygens principle a consequence of isotropy of space? According to wikipedia http://en.wikipedia.org/wiki/Huygens–Fresnel_principle it is

I don't really understand this : let's say a sound wave , a vibrator pushes the air molecule does this mean that molecule vibrates in all directions? Ofcourse the air molecule's backward vibrations will be canceled by the vibrators forward vibration but will the molecules vibrate in other directions too?

 

[harrylin]

IS huygens principle a consequence of isotropy of space? According to wikipedia http://en.wikipedia.org/wiki/Huygens–Fresnel_principle it is

Not really: the Huygens principle can equally well be used for anisotropic space. The principle is that every point can be regarded as a source of secondary waves.

I don't really understand this : let's say a sound wave , a vibrator pushes the air molecule does this mean that molecule vibrates in all directions? Ofcourse the air molecule's backward vibrations will be canceled by the vibrators forward vibration but will the molecules vibrate in other directions too?

Good point; it depends on the wavelength if the resulting pressure wave spreads out strongly or not, thus qualitatively similar to light. Note that Huygens primarily modeled light (I think), which is modeled as a transverse wave (oscillating perpendicular to the propagation). Thus your issue doesn't arise with light, but it could be interesting to discuss how much longitudinal waves behave differently.

 

[jd12345]

ok actually my initial doubt was: IS there a proof to huygens principle that every point is regarded as a source of secondary waves? I thought the isotropy of space could explain it but as you say its not necessary
So is there a proof for huygens principle?

 

[harrylin]

ok actually my initial doubt was: IS there a proof to huygens principle that every point is regarded as a source of secondary waves? I thought the isotropy of space could explain it but as you say its not necessary
So is there a proof for huygens principle?

It's a successfully working model. And on top of that, it makes sense. What more can you ask for?

 

[PJC01]

Yes, Huygens principle is a consequence of isotropy of space. Isotropy means that the properties of space are the same in all directions. In the case of sound waves, this means that the air molecules will vibrate in all directions, not just back and forth. This is because the air molecules are free to move in any direction, and the vibrations caused by the sound wave will propagate equally in all directions. This is why we can hear sound from any direction, not just from the direction of the source. Huygens principle states that every point on a wavefront can be considered as a source of secondary wavelets, and these secondary wavelets combine to form a new wavefront. This principle is based on the assumption of isotropy, as it allows for the propagation of waves in all directions.