I was sitting in a barber shop for kids the other day. Two children were being cut, and they were watching different cartoons on TVs in front of them. In the figure below, children A and B are at (0, 0.5) and (1, 0.5) and their TVs are at (0, 0) and (1, 0) respectively. I’m sitting at (2, 1).
Now, I heard TV A considerably louder, even though it was farther away from me than TV B. However, Kid B seemed to be content with the volume, i.e., apparently he heard TV B louder than TV A. It didn’t seem intuitive to me, so I started wondering (as I didn’t have much else to do) what is the shape of the area in which TV B is heard louder.
In more abstract terms: let’s have two sound sources A and B, which are d units apart. Let A be k times stronger. What is the shape of the area where B is heard louder?
The result is quite easy to derive (I was almost able to get it right in my head without pencil and paper) and — at least for me — a bit counter-intuitive, because V jnfa’g rkcrpgvat gur nern gb or svavgr.
If you don’t want to do the calculations yourself, here’s an interactive solution.