The shaking board sets the dowel vibrating. If the next shake is timed just right to reinforce the next vibration of the dowel, the vibration in the dowel builds up. This process of using a series of small inputs to create a large motion is known as resonance . The longer the dowel, the more slowly it tends to vibrate - the lower its natural frequency. Thus, the long dowel will resonate at lower frequencies than the short dowel.
Stiffer dowels have higher resonant frequencies.
Each dowel may have more than one resonant frequency. Just as each dowel has its natural frequencies of vibration where resonance occurs, so most objects tend to vibrate at certain frequencies. You may have noticed that parts of your car rattle at a certain speed or that certain objects vibrate and buzz in response to a particular note from your stereo. These are everyday examples of resonance. Resonance has also been responsible for some spectacular destruction.