# Resonance

### energy frequency oscillation motion

There are many instances in which we want to add energy to the motion of an object which is oscillating. In order for this transfer to be efficient, the oscillation and the source of new energy have to be "matched" in a very specific way. When this match occurs, we say that the oscillation and source are in resonance.

A simple example of an oscillation that we have all seen is that of a child on a playground swing. The motion starts when someone pulls the swing to a position away from the point of stable equilibrium and lets go. The child then moves back and forth, but gradually slows down as the energy of the motion is lost due to friction in the joint where the rope or chain of the swing attaches to its support. Of course, the child wants to continue moving, usually higher and faster, and this requires the addition of more energy. It is easy to accomplish this by pushing the swing, but we all know from experience that the timing is critical. Even a small push can add energy efficiently if it occurs just at the instant when the swing has moved to its highest position and begins to move back to the point of stable equilibrium. If the push occurs a little too late, not all of the energy of the push is added (inefficient). Even worse, if the push occurs too soon, the result will be to slow down the swing (removing energy instead of adding it). Also, it obviously does no good to push at other times when the swing has moved away (it looks strange and anyway, there is zero efficiency since no energy is transferred into the motion). The trick is to push at the "right" instant during every repetition of the swinging motion. When this occurs, the adult's push (the energy source in this case) and the oscillation are in resonance.

The feature of the motion that must be matched in resonance is the frequency. For any oscillation, the motion takes a specific amount of time to repeat itself (its period for one cycle). Therefore, a certain number of cycles occurs during each second (the frequency). The frequency tells us how often the object returns to its position of maximum displacement, and as we know for the swing, that is the best location at which to add energy. Resonance occurs when the rhythm of the energy source matches the natural, characteristic frequency of the oscillation. For this reason, the latter is often called the resonant frequency. It is common to say that the source of energy provides a driving force, as in the case where a push is needed to add energy to the motion of a swing.

In a way, resonance is just a new name for a familiar situation. However, resonance is also important in other instances which are less obvious, like lasers and electronic circuits. A particularly interesting example is the microwave oven, which cooks food without external heat. Even if an object like a book (or a steak) appears to be stationary, it is composed of microscopic atoms which are oscillating around positions of stable equilibrium. Those motions are too small to see, but we can feel them since the temperature of an object is related to their amplitudes—the larger the amplitudes, the hotter the object. This is very similar to the motion of the child on the swing in which a larger amplitude means more energy. If we can add energy to the motion of a swing by a driving force in resonance, then we should be able to add energy (heat) to a steak very efficiently. Conventional ovens cook food from the outside, for example by heating air molecules that bump into atoms at the surface of the food. However, the microwave oven uses resonance to cook from the inside.

The water molecule is made of one oxygen atom and two hydrogen atoms which are held together, not in a straight line, but in a "V" shape. The oxygen atom is located at the bottom of the "V" and the hydrogen atoms are at ends of the arms. It should not be too surprising to learn that water molecules and even the oxygen and hydrogen atoms within them can oscillate. However, experiments discovered a specific oscillation (really a rotation of the entire molecule) that is particularly important. The characteristic frequency of that oscillation falls within the same range as the microwave type of electro-magnetic radiation. Microwaves are commonly used in radar, so a large amount of work had already been done to develop dependable, relatively compact devices to produce them. The breakthrough was in realizing that a good steak (even a bad one) contains a large amount of water. If we place a steak within a microwave oven and turn it on, microwaves are produced within the interior of the oven at the resonant frequency of the water molecule. The microwaves act as the driving force to add energy by making the molecules oscillate with greater amplitude. This heats the steak, cooking it from within.

There are many other situations when resonance is important. For example, a rock guitarist must be careful when playing in front of a powerful speaker. When a string vibrates (oscillates) after being struck, an electro-magnetic pick-up converts that motion into an electrical pulse which is then sent to an amplifier and on to the speaker. If the sound vibration from the speaker (same frequency as that of the string oscillation) happens to match a resonant frequency of the guitar body, feedback can occur. Actually, this is an example of positive feedback. The sound adds energy to the guitar body, which also vibrates; this adds energy to the string to produce a larger electrical signal, and even more sound. This pattern can repeat until the volume at this resonant frequency grows to drown out other notes, and the rest of the band. Similarly, resonance can have destructive consequences. A famous case is that of the Tacoma Narrows Bridge in Washington State, where winds managed to act as a driving force to make the bridge sway wildly until it collapsed by adding energy to an oscillation at the resonant frequency.

See also Oscillations.

## Resources

### Books

Clark, J. Matter and Energy: Physics in Action. New York: Oxford University Press, 1994.

Ehrlich, R. Turning the World Inside Out, and 174 Other Simple Physics Demonstrations. Princeton, NJ: Princeton University Press, 1990.

Epstein, L.C. Thinking Physics: Practical Lessons in Critical Thinking. 2nd ed. San Francisco: Insight Press, 1994.

James J. Carroll

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Cycle

—One repetition of an oscillation as an object travels from any point (in a certain direction) back to the same point and begins to move again in the original direction.

Frequency

—The number of cycles of an oscillating motion which occur per second. One cycle per second is called a Hertz, abbreviated as Hz.

Positive feedback

—This occurs when an oscillation "feeds back" to continually increase its amplitude. The added energy comes from some external source, like a guitar amplifier, which produces a driving force at the same frequency as that of the original oscillation.

Resonant frequency

—A particular frequency that is characteristic of an oscillation. A driving force can efficiently add energy to an oscillation when tuned to the resonant frequency.

## User Comments

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over 9 years ago

Point of Order: 22.235GHz is considerably closer to NINE (9) times (< 2% error) the operating frequency of the typical microwave oven than it is to "ten times" said frequency...

over 9 years ago

Just to clarify: The microwave frequency is exactly 1/10th that of the resonant frequency, so the molecule gets "kicked" once every ten rotations, which is still more than enough to make the oven very efficient relative to other means of heating.

over 11 years ago

I could be way off base here - I also have no source to site for my info, so please correct me if im wrong but...

I think you will find that by dividing the frequency in half - you are still working with the same fundamental frequency - just with less energy. You can keep doubling or dividing the frequency infinitely - but its always working from the same fundamental (lowest - depending on your perspective) frequency. If you made the wave longer, it wouldnt resonate as quickly (so-to-speak) - but you could raise the amplitude of the longer wave to make up for the loss of being able to reproduce the shorter (higher-energy) wave (excluding any feedback variables or rotating trays), and cook your steak just fine - though it may take a little longer. =P

The math should work the same for all molecules dependant on their fundamental resonant frequency. Of course this also depends on how much 'space' exists within (between) whatever it is that you intend to 'excite' (irradiate). That will alter the math from a simple 'multiply or divide by 2' into a logarithm of sorts - but im really bad with math - so I can only guess that the resonance should still be predictable as long as you also use the volume of the 'space' as a variable. How you measure that? I dont know, I suppose it would be easiest to 'fill it' with something smaller than your molecule or atom - but thats a whole other topic I think. =) Plus thats only really important if you are aiming for a precise measurement and not important to what I believe is the purpose of this article.

over 11 years ago

You stated that the microwave oven
operates at the resonant frequency
of water. I think if you check around,
you will find that this in incorrect.

The lowest resonance of the water
molecule is 22.235 GHz. This frequency
is almost 10 times higher than the
operating frequency of the microwave
oven (2.45 GHz).