If you move your finger up and down slowly, the ball will follow along without bouncing much on its own. At first you hold your finger steady, and the ball bounces up and down with a small amount of damping.

Most of us have played with toys where an object bobs up and down on an elastic band, something like the paddle ball suspended from a finger in Figure 14.18. The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance, and a system being driven at its natural frequency is said to resonate. The natural frequency is the frequency at which a system would oscillate if there were no driving and no damping force. Over time the energy dissipates, and the amplitude gradually reduces to zero- this is called damping. This is a good example of the fact that objects-in this case, piano strings-can be forced to oscillate but oscillate best at their natural frequency.Ī driving force (such as your voice in the example) puts energy into a system at a certain frequency, which is not necessarily the same as the natural frequency of the system. It will sing the same note back at you-the strings that have the same frequencies as your voice, are resonating in response to the forces from the sound waves that you sent to them.

Sit in front of a piano sometime and sing a loud brief note at it while pushing down on the sustain pedal. Before the start of this section, it would be useful to review the properties of sound waves and how they are related to each other, standing waves, superposition and interference of waves.

Frequency of tuning fork formula