Resonance is forced motion at a frequency near the natural oscillation frequency of a system. It is a fundamental property of many, if not all, physical systems. Like pushing a child on a swing, it requires pushing the system in the right direction at the right time.
Most of us have seen a wine glass broken by the opera singer’s crystal trill or have tried to carry a tray with water in it. Although the connection may not be clear, these are but two of many examples of resonance.
Resonance is one of the most spectacular effects of physics. It allows small inputs in energy to amplify, just as pushing the swing in resonance will cause it to go higher with each small push.
All musical instruments depend either upon resonance of a vibrating string under tension or vibrating air inside a tube. Playing any musical instrument involves nothing more than changing the length of a string or of a tube full of air, skill notwithstanding.
The same effects happen with air between the walls of the shower. Shower stalls and bathtubs happen to be of proper size to resonate in the lower frequencies of men’s voices, which may partly explain why men sing in the shower more often than women.
A trained vocalist learns to change the size and shape of a resonant cavity in the throat and chest to maintain timbre over a wide range of frequencies as an announcer learns to lend rich tones to modulated broadcast voices.
Engineers and architects must design auditoriums and concert halls to prevent certain frequencies in the music from resonating and muddying the sound of a symphony, a choir or a rock band.
In music, both timbre and harmony are affected by resonance.
Timbre is the difference in sound produced by two different instruments playing the same note, of the fundamental frequency. Each instrument has a unique sound that is determined by its pattern of overtones, which are multiples of the fundamental frequency. Harmony arises because the waves of the two or more tones combine to form new waveforms that also sound pleasant.
Other phenomena that involve resonance are many and in unexpected places.
Objects have color because of which wavelengths of light are either reflected or absorbed. When white light strikes a piece of dyed cloth, the different dye molecules resonate at certain unique frequencies. The result is that the resonant frequencies are amplified and re-emit the light. The others do not and so they are absorbed.
Resonance structures in chemistry allow electron wave functions to fill double bond sites in ring molecules like benzene and in other organic molecules where a carbon atom with a double bond sits angled to a carbon atom with a single bond.
A tray full of water is impossible to carry because the frequency of water sloshing back and forth is very close to the frequency of walking steps. Certain oceanic tides have resonant components, such as the Bay of Fundy where the tidal sloshing frequency is the same as tidal frequency and daily tidal range is nearly 50 feet at the northern end of the bay. Resonance also influences tides in the Gulf of Mexico and to a lesser extent the North Atlantic Ocean.
On the scale of the solar system are the resonances of planetary orbits. An orbital resonance occurs when orbiting bodies exert a periodic gravitational influence on each other — Earth and Venus, the Galilean moons of Jupiter. The most visible effects of gravitational resonance are the rings of Saturn and the gaps between them.
Richard Brill is a professor of science at Honolulu Community College. His column runs of the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.
