Radiation of a point source into a semi-infinite space

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Hello,

I'm trying to make a simple model of an acoustic point source radiating into a semi-infinite space.

I have built the model by defining a monopole point source in the origin of a sphere. The sphere is surrounded by a PML. After this, I removed half of the geometry using the 'difference' boolean, to create a hemisphere. The source is now located in the center pf the flat side of the hemisphere, which is a hard surface.

When I calculate the SPL on the boundary of the (hemi)sphere for both versions of the model, I find that the SPL for the hemisphere is 6 dB higher than that of the sphere. However, I only expected a 3 dB difference, since halving the volume would double the squared pressure.

Did I make a mistake in my model, or did I get my theory wrong?

Thanks in advance,

Thijs Hekman



2 Replies Last Post 2018年5月17日 GMT-0400上午6:52
Elin Svensson COMSOL Employee

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Posted: 5 months ago 2018年5月16日 GMT-0400上午4:12

Hello Thijs,

It is the pressure that will be doubled. You can consider it as the sum of the pressure from the source emitted into the half-space you are studying and the pressure emitted into the other half-space (which is then reflected at the boundary). This is also the limiting case of a source placed in a half-space (with a sound hard boundary) which is moved closer and closer to the boundary. The solution is the sum of the free-space pressure field from the source and its image source.

Kind regards, Elin

Hello Thijs, It is the pressure that will be doubled. You can consider it as the sum of the pressure from the source emitted into the half-space you are studying and the pressure emitted into the other half-space (which is then reflected at the boundary). This is also the limiting case of a source placed in a half-space (with a sound hard boundary) which is moved closer and closer to the boundary. The solution is the sum of the free-space pressure field from the source and its image source. Kind regards, Elin

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Posted: 5 months ago 2018年5月17日 GMT-0400上午6:52

Hi Elin,

Thank you for your reply. I wasn't sure, if the it was the pressure, or the intensity that would be doubled and I coulnd't really find any clear answers elsewhere.

Now I do have a remaining question regarding my actual COMSOL application. I am modeling the outlet of a ventilation duct. I have enclosed a diagram of the model. The model is 3D, but this top down view should be clear enough.

The black part is the actual duct, while the grey area represents the open space to which the sound radiates. This space is surrounded by a PML. I am interested in the far-field pressure in the room. From the application library manual, I learned that calculating the far-field pressure of a source radiating into a semi-infinite space can be done by using the 'symmetry in the x,y,z=0 plane' option in the far-field calculation.

I'm wondering whether I can consider my model a plane source emitting into a semi-infinite space and should therefore use the 'symmetry in the x,y,z=0 plane' option to calculate the correct far-field pressure field.

Kind regards,

Thijs

Hi Elin, Thank you for your reply. I wasn't sure, if the it was the pressure, or the intensity that would be doubled and I coulnd't really find any clear answers elsewhere. Now I do have a remaining question regarding my actual COMSOL application. I am modeling the outlet of a ventilation duct. I have enclosed a diagram of the model. The model is 3D, but this top down view should be clear enough. The black part is the actual duct, while the grey area represents the open space to which the sound radiates. This space is surrounded by a PML. I am interested in the far-field pressure in the room. From the application library manual, I learned that calculating the far-field pressure of a source radiating into a semi-infinite space can be done by using the 'symmetry in the x,y,z=0 plane' option in the far-field calculation. I'm wondering whether I can consider my model a plane source emitting into a semi-infinite space and should therefore use the 'symmetry in the x,y,z=0 plane' option to calculate the correct far-field pressure field. Kind regards, Thijs

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