As we know from our earlier discussion of waves, the defining feature of any wave or oscillation is its frequency, which is how often it repeats itself. We can set any object vibrating or oscillating back and forth at any frequency we like; take, for example, a yo-yo on an elastic string—we could bounce it back and forth fast or slow, and the faster it is, the higher the frequency, because it completes each round trip more “frequently.” Resonance happens due to the interplay of two quite different types of frequencies: one is called the driving frequency, and the other, the natural frequency. The driving frequency happens to be the one with no restrictions and has broader relevance in life as well as in nature. So let us talk about that first.
I bet even if you are not a scientist, you already know something about driving frequencies—because at some point in your life you most certainly have pushed someone riding a swing—perhaps one of your childhood friends or your own kid. The driving frequency here would be how frequently you push. Those pushes “drive” the motion of the swing, hence the name “driving” frequency. And it means exactly the same thing in any oscillatory system, mechanical or electronic, where an external force (like your push) drives the oscillations of the system (like the swing). The main difference is that in electronic systems, the oscillations would be invisible because they are oscillations of alternating current flow moving back and forth in a circuit. Simple as it sounds, the electronic driving frequencies propel all of our wireless technology where all sorts of electromagnetic waves propagating through the air (transmitted via towers and satellites to our TVs, radios, and cell phones) act as driving forces in the various electronic devices and give us the all-powerful “signal.”
. Unlike driving frequencies, which are external in origin, the natural frequencies are characteristic of the oscillating object itself and are restricted to certain specific values.
Resonance happens when we drive a system at one of its natural frequencies—meaning that the driving frequency matches a natural frequency of the system. The effect is quite dramatic: Since the driving frequency matches a natural frequency, the energy transfer from the driving force to the system is essentially perfect, because the system naturally wants to move at that frequency. The result is that the amplitude (or the size) of the oscillation increases with each push and can become extremely large, limited only by the damping or inherent resistance of the oscillating system. What is quite amazing is that we somehow seem to know about resonance by instinct even as a kid. When we had to get the swing to go higher and faster without help from anyone, we all got to know the trick that it works best if we pull in our legs and push them out in sync with the motion of the swing. In doing that, we are essentially matching the driving frequency of the pulling-in-and-pushing-out of our legs to the frequency of the motion of the swing. If we do it just right, we end up swinging high and fast with the least amount of effort.
), so when you tune your radio, you are adjusting the resonant frequency of the electronics inside to match the driving frequency of the station you would like to listen to. All the other signals floating out there around you get filtered out because they have very weak effect—only the resonant frequency gets amplified, allowing you to listen to the station of your choice. That is the same basic principle in all of wireless technology, but of course with layers and layers of engineering sophistication added on to improve, clarify, and enhance the signal.
and . Everyone has some elements of a violent streak in him or her. But for most people most of the time, no matter how mad we get, it is well within control. But, in a mob situation, or hanging out with the wrong crowd, with a lot of people feeling the same way, those hidden characteristics resonate, and by feeding off one another, they get amplified; then suddenly people are capable of doing crazy, violent things that they would never dream of doing by themselves. Because when we are alone, such tendencies are relatively weak and subdued. Mobs amplify those through resonant behavior. Mob behavior can therefore be viewed as a manifestation of collective resonant psychology.
Even in nonresonant situations, when we are egged on by people around us to do things that we would normally shy away from—when we feel peer pressure—we are being driven out of sync with our natural rhythms and tendencies. If those driving forces of peer pressure are strong enough, they can truly take over our behavior, and we find ourselves acting in ways unnatural to us.
The power of resonance can sometimes be very dangerous both in life and in nature. One famous incident happened in Tacoma Narrows in Washington state in 1940, when a large suspension bridge collapsed primarily due to resonance. The bridge had a tendency to vibrate and sway even in moderate winds of 10 to 20 miles per hour. One day, the wind happened to sway the bridge at one of its natural frequencies, and as a result, the bridge started swaying with higher and higher amplitude due to resonance, just like a swing as we discussed earlier. As the amplitude of the oscillations increased, it was too much for the tensile strength of the construction material, and the bridge eventually collapsed, even though the wind was only at about 40 mph.
, that the minimum distance or length over which the shape of a wave repeats is the wavelength of that wave.)
We will end the chapter by coming back to what we started with—how resonance allows an electron to tunnel through a barrier. In quantum mechanics, electrons can behave like a wave, and its speed is directly related to its wavelength (or equivalently its frequency)—the faster it moves, the shorter the wavelength of the electron wave. Now, if the electron moves at just the right speed so that its wavelength exactly matches the width of the barrier as shown in , then exact multiples of the wavelengths can “fit” within the width of the barrier, and then the electron-wave passes through the barrier as if it was not there. The frequency of the electron wave is its “natural” frequency, and the width of the barrier serves as the “driving” frequency (think of the two edges of the barrier “repeating” one edge after the other along the path of the electron). This is similar to the situation with the traffic lights—the distance (or “width”) between the lights determines the driving frequency of how often the lights change colors, and the frequency of the driver crossing traffic lights is the natural frequency. When the driving frequency differs from the natural frequency, it forces an alteration of behavior—the electron bounces back, the car stops at a light. But when the driving frequency resonates with the natural frequency, all barriers seem to vanish away.
Electric current is of two types: direct current (DC) or alternating current (AC). The current from a battery is DC; it always flows in one direction from the positive terminal to the negative (see ). The current from the power grid, that we use about the house, is AC, which as the name suggests “alternates” or changes direction forward and backward very rapidly, like water sloshing back and forth. The motivation for using AC is that there is a very little loss of power over long distances, unlike for DC. Of course, as we see here, the oscillatory nature of AC is also absolutely essential for wireless technology.
Frequency, for anything repeating in time, is measured in units of Hertz (in short, Hz), which correspond to a frequency or repetition of once per second, so when you tune your FM radio to, say, 97.5, it means 97.5 MHz or 97.5 Million Hertz, meaning the electromagnetic wave that contains the “signal” is oscillating 97.5 million times per second!
Recall from that the wavelength of a wave is the minimum distance over which it repeats itself.