Forced Vibration

Vibrations are created when an object is struck, plucked or otherwise disturbed. We learned in the discussion about an object's natural frequency that the object will vibrate at one or more frequencies, depending on its physical properties. In the process of striking, plucking or otherwise disturbing the object, energy transfers into the object being disturbed. The object then responds to this additional frequency energy by vibrating. This vibrating energy emanating as sound waves from the object can actually energize other objects to vibrate.

The effect is rather amazing, as you are causing movement in another object without touching it.

It is possible, therefore, to transfer energy simply through frequency, in this case, a sound. So, just as surely as you can disturb an object by plucking or striking, you can also disturb it, or energize it, through sound.

We're sure most parents know exactly what we're talking about when they recall the last time their children played music too loudly. Disturbing?

The Standard Demonstration

You might recall the demonstration of this principal from your high school physics class. By striking one tuning fork, another similar tuning fork then began to vibrate and even continued to vibrate after the first tuning fork was stopped.

In this case, the sound energy was partially transferred from the first tuning fork to the second.

A Louder Example

If you take an object that is vibrating and place it in contact with a large, flat surface, sometimes referred to as a sounding board, the volume of the vibrations increases dramatically. When this happens, we are making a physical connection between the vibrating object and a large surface, forcing the surface to vibrate. The large surface acts as a drum. When the vibrating object is not touching anything, it is isolated. It is only able to make contact with a relatively few number of air particles and, therefore, makes relatively little sound. However, when the object is in contact with a large surface, like a table, drum or wall, it is able to affect many more air particles and thereby creates a much louder sound.

This is why a guitar, cello, violin and other string instruments are not simply constructed from the strings alone. If that were the case, the instrument would play much softer. The wooden sound box serves as a sounding board for the vibrating strings. The chamber vibrates at the same frequency as the strings. But because of its larger surface area, it forces more air particles into motion, thereby creating a louder sound.

It is also true that the vibrations will decay faster when in contact with the drum surface, since more of the energy is being converted into sonic energy.

The effects of Forced Vibrations at the Natural Frequency of High Q objects

High Q objects, when vibrated at their natural frequency, can actually be destroyed with a small energy input provided over a long period of time. Good examples of this would be a singer shattering a wineglass or the fate of the Tacoma Narrows Bridge which was torn apart by the wind causing its support cables to vibrate. In the case of the wineglass, the singer was able to sing and hold the wineglass's natural resonant frequency until failure resulted.

Although the Tacoma Narrows Bridge failure was not strictly due to resonance, it will provide a good visual example of forced vibrations leading to catastrophe of a High Q object. In this case, the wind was providing a small additional push of energy over a long period of time that kept increasing the amplitude of the vibration in the bridge. Eventually, the great oscillations of the bridge lead to a total collapse of the structure.

Click to see a video of the Tacoma Narrows bridge collapse.

Forced Vibrations are stunning when the vibrated object has a high Q, or ability to vibrate, and the vibrations are at the object's natural frequency. Otherwise, the effects of forced vibrations, which permeate our everyday experiences, are less than earth shattering.

What would have saved the Tacoma Narrows Bridge?

The simplistic solution is dampening. Dampening is the process of lowering a resonant objects Q value, usually by adding an appendage that absorbs energy.

Another concept that goes hand in hand with forced vibrations is the concept of entrainment where two vibrating objects experience mutual phase locking or synchronization.