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The ABC's of
Resonance
Resonance causes an object to move back and forth or up and down.
This motion is generally called oscillation. Sometimes the
oscillation is easy to see such as the motion of a swing on a
playground or the vibration in a guitar string. In other cases the
oscillation is impossible to see without measuring instruments. For
example, electrons in an electrical circuit can oscillate but it
happens on a molecular level.
In resonance the oscillation occurs at a specific frequency. These
oscillations build up rapidly to very high levels. Ultimately some
of the energy in the oscillations has to be removed from the object
or the size of the oscillations get so large that the object breaks.
Resonance requires 3 basic conditions:
-
An Object With a Natural
Frequency:
The object can be a mechanical
device or an electronic circuit. An object's natural frequency
is the frequency it tends to oscillate at when disturbed. The
oscillation can be a mechanical vibration as is the case when
the string of a guitar is strummed. In an electronic circuit the
oscillation is a variable voltage or current. An object can have
more than one natural frequency. These are called harmonics. A
guitar string sounds musical because it vibrates with several
harmonics when it is strummed.
-
A Forcing Function at the Same
Frequency as the Natural Frequency:
In mechanical systems the forcing
function is a variable force. In electronic circuits it arises
from a variable electric field. In either case the forcing
function does work on the object it is applied to. Since work is
a form of energy transfer it causes energy to build up in the
object.
-
A Lack of Damping or Energy Loss:
For an object to resonate,
mechanical or electrical energy has to build up in the object.
Anything which removes these forms of energy tends to interfere
with resonance. Damping is a means of removing electrical or
mechanical energy by converting it to heat. The term damping
should not be confused with the term dampening which means to
make something slightly wet.
Friction, air resistance, and
viscous drag can all provide damping in mechanical systems.
Electrical resistance performs the same function in electronic
circuits. Other forms of energy loss can include sound (musical
instruments) or light emissions (lasers).
When the forcing function's frequency
matches the natural frequency of an object it will begin to
resonate. The forcing function adds energy at just the right moment
during the oscillation cycle so that the oscillation is reinforced.
This makes the oscillation's amplitude grow larger and larger.
These oscillations would eventually
become infinitely large. However, as mentioned earlier, long before
the oscillations reach infinity one of three things happens:
-
the object's dynamics change
so that the resonant frequency and forcing functions no
longer match
-
the energy lost as heat,
sound, or light becomes equal to the energy input
-
the object breaks (see The
Dark Side of Resonance)
The Dark Side of
Resonance
The Tacoma-Narrows Bridge
Every powerful phenomenon in nature has its dark side and resonance
is no exception. It's best experienced in moderation. Taken to an
extreme, resonance causes things to break catastrophically. For
example, when an opera singer with a very loud voice hits the right
frequency she can cause a champagne glass to resonate and break.
On the morning of November 7, 1940, the four month old Tacoma
Narrows Bridge began to oscillate dangerously up and down. A
reporter drove out on the bridge with his cocker spaniel in the car.
The bridge was heaving so violently that he had to abandon his car
and crawl back to safety on his hands and knees.
At about 11:00 the bridge tore itself apart and collapsed. It had
been designed for winds of 120 mph and yet a wind of only 42 mph
caused it to collapse. How could this happen? No one knows exactly
why. However, the experts do agree that somehow the wind caused the
bridge to resonate. It was a shocking calamity although the only
loss of life was the cocker spaniel.
View
NOVA videos of the collapse.
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