planar waves

[el`Ol]

Hello all!

I have a theoretical question about wave propagation:
Is the wavefront an uncurved planar generates for wavelengths far smaller than its diameter really more planar (less wavefront curving) than for wavelengths much larger, or is it just more limited in dispersion?


Thanks,
Oliver

 

[JinMTVT]

also very intereted in this matter..

if anyone could make or link some videos or sketches
of how all this works...

nice question!

 

[p3142]

Q:Is the wavefront of an uncurved planar for smaller wavelengths really more planar than for larger wavelengths ?

Disregard effects occuring at the suspension for a moment.
Then only the planar membrane will emit sound and the sound is emitted from the limited area of the membrane.
Next, assume that all points of the planar membrane are in phase.

We thus get a simple first order approximation.

What you have now is exactly comparable to light diffraction of a single slit illuminated from behind by a planar light wave. This is a standard optics problem.
Google for pictures of diffraction at a single slit.

Hope that helps,

Regards,
Peter

 

[Few]

The wave front immediately in front of the membrane will look quite planar, except near the edges where diffraction will create curved wave fronts. Very far from the source, at a distance that's large compared to the width of the membrane, the wave will appeared to have emanated from a narrow slit and so will exhibit curvature.

You make your own simulations, and modify the width of the source, here. Under setup choose "single slit", and choose "Mouse = Edit Walls." You can then use the mouse to make the slit wider and watch what happens. Make the slit narrow if you want to see the curvature that shows up many slit-widths away from the source.
Few

 

[el`Ol]

Thanks for the link.
I believe to see that the favefront indeed becomes flatter with increasing source frequency.

 

[JinMTVT]

that is correct only if the "slit" is less large than the borders

if you make the slit half the screen in the simu
and then draw walls like in a room with the complete front wall as a piston, the waves stay planar for most of the travel