When a tuning fork vibrates over an open pipe and the air in the pipe starts to vibrate, the vibrations in the tube are caused by

The vibrations in the tube are caused by resonance. When the tuning fork vibrates over the pipe, its vibrations causes the air molecules in the pipe to vibrate as well, with a resonant frequency. The external vibration by tuning fork causes the air particles to vibrate with an ever increasing amplitude at resonant frequency.