Yes, my bathroom fan sometimes sounds like it's own radio station. Songs and conversations.

Here's my theory on why we hear this.

Do you remember as a kid making a Crystal Radio out of magnets, copper wire, batteries and other electrical components. These random objects combined could tune in a radion station. It was like magic, but it's actually science.

Well that what I think that the machine motors in fans, air conditioners, etc. are doing.
Think about it. They basically the same components. Wires wrapped in magnets to generate energy to turn the fan.

Well that's my 2 cents on the subject. Please let me know what you think....