Oscillations and resonance in nature

IT is said that Tansen, the legendary composer of Indian classical music and one of the nine jewels of the Mughal Kingw Akbar, shattered most of the glasses in the court with the recital of Deepak raga. On July 1, 1949, the Tacoma Narrows Bridge in Washington, USA started to sway vertically and subsequently collapsed. The high tide in the Bay of Fundy in Canada averages 11 meters. What is the feature common to all these phenomena? It is physics in action, resonance oscillation in particular.

When an object is displaced from its equilibrium position and released, it oscillates back and forth about the equilibrium position. One of the most recognizable characteristics of oscillatory motion is that the motion repeats itself at regular time interval called period. As the motion is repetitive, we call it "periodic motion." The other characteristic of such motions is frequency (inverse of the period) – the number of oscillations per second.

Most of the things in nature oscillate (vibrate) at a characteristic (natural) frequency or frequencies. Some familiar examples are the motions of the pendulum of a clock and playground swing, up and down motion of small boats, ocean waves, and motion of the string or reeds on musical instruments. A healthy heart beats in periodic motion.

In all oscillatory motions, energy is dissipated because of the presence of some kind of damping force. The amplitude (maximum displacement from the equilibrium position during a single period of oscillation) of a damped oscillator will decrease and motion will ultimately die. To maintain the oscillations, energy has to be fed into the system. We then say that the motion is forced or driven. Children on swings pumping their feet or pendulum in clocks driven by coiled springs are examples of forced oscillation.

When an oscillator is driven at a frequency corresponding to a particular natural frequency, the oscillation is said to be in resonance. Energy is most efficiently supplied to an oscillator when the external driver acts at the resonance frequency.

Resonance phenomena play an important role in many practical situations. As an example, a child pumping a swing at the frequency equal to the natural frequency of the swing will attain maximum height. Similarly, people trying to push a car stuck in snow or mud are most successful when they allow the car to rock back and forth and time their pushes appropriately.

Tansen could shatter glasses because when the frequency of sound from a singer's voice matches the natural frequency of a glass, there will be resonance with maximum transfer of energy to the glass. This transfer of energy can cause vibrations large enough to shatter a glass.

The power of resonance is not confined to shattering glasses only. A spectacular example of resonance oscillation is the collapse of the Tacoma Bridge caused by 65-80 kilometers per hour wind. In layman's terms, the wind induced resonance and produced vertical vibrations of the span with peak-to-peak motions of 1.5 meter. About an hour after the bridge started oscillating, the violent large-amplitude motion led to its collapse into the waters of Puget Sound.

This is one of the reasons why soldiers crossing bridges do not walk in unison. They break step so that the frequency of their footsteps does not match the natural frequency of the bridge. Otherwise, they may set the bridge vibrating at resonance and perhaps cause its ultimate destruction.

Another interesting example of resonance can be witnessed in the enormous tides in Canada's Bay of Fundy in Nova Scotia. The time between successive high tides at the head of the bay is about 12.4 hours and the normal tidal surge averages 0.3 meter. But the period of oscillation of water waves as it sloshes back and forth in the bay is about 13 hours. Since the two periods, and hence the frequencies are nearly equal, large resonant amplitude occurs giving rise to 11-meter high tides.

In all these examples, there are both dissipative forces that reduce vibrations and external forces that supply energy. If there is a balance of these two energies, the amplitude of the motion will remain constant. If energy enters the system faster than it is dissipated, there will be disaster, as with glasses and Tacoma Narrows Bridge. If the energy does not enter the system at very nearly the right frequency, little or no vibrations occur, since the energy supplied is immediately dissipated.

The writer is a Professor in the Department of Physics & Engineering Physics, Fordham University, New York