Does Sound Rise and Sink like heat?
Simple answer to Does Sound Rise? is no.
The advanced answer to Does Sound Rise? is it can but not how you may have thought. The best example is in a thermal inversion and refraction. Let's setup an example to answer Does Sound Rise?
It's the morning of a clear sky in the middle of summer over a lake. The lake water has been cooled down a lot overnight because of the clear sky, strong winds and no sun.
Now when the sun comes out it will eventually warm the lake.
Firstly though, it will heat the air above the lake because the particles are separated from each other they warm quicker because they haven't gotten as cold as the lake over night. As this happens the cooler water is transferring its cold to the air just above it.
So now you have cooler air over the lake and hotter air above. So imagine a dome of cool air and then hotter air around it. In the terrible drawing below you can see the shaded part above the water represents the dome. The arrows represent 2 men talking.
Now 2 guys over opposite sides of the lake can talk to each other easier because the sound is amplified by the warmer sound speeding over the dome slightly faster than the sound within the dome. This causes some of the speech sound waves to combine and increase in amplitude.
Does Sound Rise?
No. Sound bends in a similar way to light hitting a glass window or splitting when it hits a glass prism.