Diffraction of Sound Waves Through Slit

[gex]

Hi there,

I have a scenario in which different frequencies will be played behind a curtain with a 2m opening. I would like to calculate the angle of diffraction for different frequencies played by the piano. One equation that I came across through research is Fraunhofer's Single Slit equation. (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html) I am just curious as to whether I can apply this to sound even though it was developed for light waves.

-Thank you in advance.

 

[BvU]

Formulas apply, yes. Notes:
the curtain probably isn't a 100% barrier...
the waves at the 2 m opening will probably not be all that plane waves
echos and other acoustics will smear out the results

 

[gex]

Thank you for your response BvU, so to clarify, even though a certain frequency might not diffract far enough to reach a certain point on the concert hall, its reflections off of walls will cause it to eventually reach that point?

 

[BvU]

Yes. In agreement with practical experience, I would say. It takes an effort to achieve minima with sound waves: best bet is two speakers and a sine wave. A curtain with an opening is far from ideal. And a piano is a complicated source. But: experiment ! Who knows.

 

[gex]

Cool! Thanks a lot for your help BvU, but if you don't mind I have one more question. Is it possible to quantify the loss in sound intensity as it travels to the back of the concert hall and gets reflected back?

 

[BvU]

My estimate is you have to turn to numerical simulations rather soon. Don't think the usual 1/r^2 dependence of spherically expanding waves (i.e. from a point source) is practically useful.
Note that the section on acoustics doesn't even mention diffraction... (but the encompassing sound section does...)

 

[gex]

Perfect, thanks a lot for all your help BvU!