Vortex shedding:



Even though that's a cylinder, the principle is the same. Whether it causes the foil to hum depends on the natural frequency of the foil and the frequency of the vorticies. If one is a multiple of the other, the foil resonates = hum.

By making your trailing edge asymmetric, you change the frequency of the vorticies, hopefully to one that is not a multiple of the foil's natural frequency.

Here's another cool image of votex shedding caused by wind flowing past an island. These are called "Von Karmann Vortices":