B Diffraction of Sound Waves Through Slit

1. May 7, 2017

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.

2. May 7, 2017

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

3. May 7, 2017

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?

4. May 7, 2017

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.

5. May 7, 2017

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?

6. May 7, 2017

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...)

7. May 7, 2017

gex

Perfect, thanks a lot for all your help BvU!