Radiation of a point source into a semi-infinite space

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