5.12 Resonance
137
5.12 Resonance
An important phenomenon in nature is the transfer of energy from one oscillatory
system to another near a natural vibratory frequency of the receiving system. At this
frequency, the energy transfer is greatest.
The phenomenon is called ‘resonance’. To imagine resonance behavior, think of
pushing a swing with a rhythmic shove. If your intent is to make the swing gain
amplitude, your rhythm should match the swing’s natural frequency. Over many
cycles of the swing, when you push with the natural frequency, it takes only a little
effort on each cycle of the swing to cause a build up in the energy stored in the
swinging motion.
Alexander Graham Bell liked to demonstrate sound resonance by singing into a
piano, thereby causing only those strings to respond which matched the frequencies
in his singing voice. Singing certain notes in the bathroom can cause the air in the
room to resonate as standing waves are set up between the rigid walls.
Here are some other important examples:
• Your radio, television, and cell phone use resonance circuits to tune to stations or
channels (frequencies), while speaker cones are made to NOT resonate, in order
to have a ‘flat’ response to various sound signal frequencies.
• Light arriving at your retina is resonantly absorbed by rhodopsin and other
pigments in the rod and cone cells within the retina.
• Light energy is utilized by plants through resonant excitation of chlorophylls and
accessory pigment molecules.
• In a process called ‘auscultation’, a doctor listens for resonant echoes when he
thumps on your chest to cause an internal organ or cavity to vibrate. Organs
such as the lung, the heart, soft and hard regions of the digestive tract all have
particular resonant frequencies which can be heard on the skin as particular and
identifiable sounds.
• The colors of your clothes result from light scattering by organic dyes which
resonantly absorb the complementary colors.
• Biochemists use resonance in analyzing organic compounds by performing an
infrared spectroscopy of the material. Light in the infrared band can resonantly
excite the vibrational modes of atoms with particular bonds in a molecule.
Detecting the frequencies of these excitations forms a signature of a particular
kind of molecule.
Resonance can occur in the forced vibration of a material. For a small segment
of mass m of the material experiencing a force from an external wave, Newton’s
second law lead to
¨
ξ + 2πβ ˙
ξ + 4π
2 f
2
0 ξ = (F o /m) cos (2πf t) .
(5.44)
Here, the first term on the left-hand side of the equation is the acceleration of the
mass (whose position measured from equilibrium is called ξ ). The second term on
137
5.12 Resonance
An important phenomenon in nature is the transfer of energy from one oscillatory
system to another near a natural vibratory frequency of the receiving system. At this
frequency, the energy transfer is greatest.
The phenomenon is called ‘resonance’. To imagine resonance behavior, think of
pushing a swing with a rhythmic shove. If your intent is to make the swing gain
amplitude, your rhythm should match the swing’s natural frequency. Over many
cycles of the swing, when you push with the natural frequency, it takes only a little
effort on each cycle of the swing to cause a build up in the energy stored in the
swinging motion.
Alexander Graham Bell liked to demonstrate sound resonance by singing into a
piano, thereby causing only those strings to respond which matched the frequencies
in his singing voice. Singing certain notes in the bathroom can cause the air in the
room to resonate as standing waves are set up between the rigid walls.
Here are some other important examples:
• Your radio, television, and cell phone use resonance circuits to tune to stations or
channels (frequencies), while speaker cones are made to NOT resonate, in order
to have a ‘flat’ response to various sound signal frequencies.
• Light arriving at your retina is resonantly absorbed by rhodopsin and other
pigments in the rod and cone cells within the retina.
• Light energy is utilized by plants through resonant excitation of chlorophylls and
accessory pigment molecules.
• In a process called ‘auscultation’, a doctor listens for resonant echoes when he
thumps on your chest to cause an internal organ or cavity to vibrate. Organs
such as the lung, the heart, soft and hard regions of the digestive tract all have
particular resonant frequencies which can be heard on the skin as particular and
identifiable sounds.
• The colors of your clothes result from light scattering by organic dyes which
resonantly absorb the complementary colors.
• Biochemists use resonance in analyzing organic compounds by performing an
infrared spectroscopy of the material. Light in the infrared band can resonantly
excite the vibrational modes of atoms with particular bonds in a molecule.
Detecting the frequencies of these excitations forms a signature of a particular
kind of molecule.
Resonance can occur in the forced vibration of a material. For a small segment
of mass m of the material experiencing a force from an external wave, Newton’s
second law lead to
¨
ξ + 2πβ ˙
ξ + 4π
2 f
2
0 ξ = (F o /m) cos (2πf t) .
(5.44)
Here, the first term on the left-hand side of the equation is the acceleration of the
mass (whose position measured from equilibrium is called ξ ). The second term on