I have taught it to A-level students and to undergraduate engineers. Electrical engineers, in particular, need to be thoroughly familiar with the phenomenon and yet, I could see that its significance eluded them. There are few, if any, good visible examples in real life. The Tacoma Narrows Bridge is one famous example, where strong winds set the bridge oscillating. Eventually it hit its resonant frequency and collapsed.
The Millennium Bridge in London was quickly renamed the "Wobbly Bridge" as engineers had failed to take into account that pedestrians tended to walk in step. This social coherence created an input frequency acting on the bridge which then started to oscillate. To avoid a repeat of the Tacoma experience, it was quickly closed down until dampening systems were put in place.
Everything has a natural frequency: complex objects with many components will also have different natural frequencies for each part. Bridges are large objects and have low natural frequencies that we can actually see - although the constructors would rather we didn't! But most of the time we experience frequencies that we can not actually see. Bang a drum and it will vibrate at its natural frequency. Tighten its drumhead and it will vibrate at a slightly higher frequency. We can hear these frequencies but we can't normally see them.
However, here's an experiment that illustrates what's actually happening at the drumhead. Instead of striking the drum and letting it vibrate naturally, here the input is from an oscillator that makes the surface vibrate. The drumhead is a square metal plate and the input frequencies come from a speaker under the plate. Salt is sprinkled on the surface so that we can see how the plate vibrates and how it changes its behaviour as the input frequency is increased.
These beautiful patterns are the ways in which the metal plate oscillates in response to the input frequencies from the speaker. But what happens if the input frequency starts to get close to the plate's natural frequency? This is easier to show if we switch materials again, this time from metal to glass. The video below has been slowed down so we can see how the glass reacts to an input frequency that is slowly increased.
As the input frequency comes close to the resonant frequency of the glass the amplitude of the oscillations increases - that is, the glass is not just reacting to the input but also amplifies it up to the point at which it shakes so violently that it breaks. The problem with the bridges at the top is not that they were vibrating in reaction to an input but that those vibrations had a very high amplitude. But that is precisely what happens at resonant frequencies: an object will "over react" to an input when it is at or very near its own natural frequency. A low amplitude input thereby creates a high amplitude output if the right frequency is chosen.
This resonance effect may be destructive or useful. Tuning into an analogue radio or TV signal works in the same way. Each radio station emits at a particular frequency, so in this case the input frequency is fixed and we alter the natural frequency of the receiver until it matches the station we want. Other stations that are being transmitted on other frequencies are effectively ignored because the receiver is now tuned to one station and its output is naturally amplified. It is even possible to hear a radio station through an ear-piece without extra amplification.
Small inputs can thereby create large outputs. Whether such resonance phenomena are good or bad depends largely on whether they are useful or not, or whether intentional or accidental.
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