A simple construction of the Rijke tube is as shown below :

A wire mesh is inserted into the tube, at a position around 1/4th its length. It is held vertically(preferably using a stand). The burner is introduced into the tube, in order to heat the gauze. After heating for a while, the burner is removed. A howling sound is heard.

The sound comes from a standing wave set up in the tube due to a convection current. The hot gauze causes the air around it to expand and therefore rise up out of the tube. This will in turn suck cold air up the bottom of the tube, keeping the convection current going. This process sets up a standing wave in the tube.