Every object, substance, has a natural frequency at which it is "willing" to vibrate. When an external agent applies a forced vibration that matches this natural frequency, the object begins to vibrate with ever increasing amplitude, or resonate.
- For a swing, that natural frequency depends on its length, T = 2π√(L/g). If the swing is pushed at a frequency which either matches the swing's natural frequency or is a sub-multiple of that natural frequency, then the swing's amplitude builds, and we say that it is in resonance.
- When air is blown across the top of a soda bottle, standing waves are set up in the air column inside the bottle and the bottle "sings."
- When two identical tuning forks are placed side by side, the vibrations of one fork can force the second fork to begin to vibrate or resonate.
Open-Open Pipes
Pipes can either be open on both ends or on only one end. The open ends act as free-end reflectors (producing antinodes) and the closed ends act as fixed-end reflectors (producing nodes). Let's start our investigation with a pipe open at both ends, for example, a flute. Notice in the animation that both ends always remained open or "free" to move, that is they are antinodes. A summary of the first three harmonics for an open-open pipe are shown below.
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