Why are leaves green?

Why is the sky blue?

Why do some materials absorb certain colors of light but not others?

The answer begins with a simple observation:

Every physical system has its own natural frequency.

When a driving force matches that frequency, something remarkable happens.

The system responds dramatically.

This phenomenon is called resonance, and it lies at the heart of optics, acoustics, chemistry, and even the stability of bridges and buildings.

The First Experiment — One Oscillator

A colored bouncing ball was suspended from a horizontal rod.

Holding the rod, the support was moved back and forth horizontally.

The frequency of the hand motion was then changed gradually.

The response of the ball changed in three surprising ways.

Low Driving Frequency

When the hand moved very slowly, the ball simply followed.

The motion of the ball and the hand occurred almost together.

They were nearly in phase.

The ball faithfully copied the motion of its support.

Near Resonance

As the frequency increased, the oscillations became larger and larger.

The ball swung with much greater amplitude.

It almost appeared to fly away.

Something else changed as well.

The hand and the ball no longer moved together.

When the hand moved one way, the ball tended to move the other.

A significant phase shift had developed.

The system was passing through its resonance.

High Driving Frequency

The experiment was repeated at much higher frequencies.

Now something completely unexpected happened.

The hand moved rapidly.

The support oscillated vigorously.

Yet the ball hardly moved at all.

It seemed almost unaware that the support was oscillating.

The driving motion had become too fast for the pendulum to respond effectively.

What Did We Learn?

Every oscillator responds differently depending on the driving frequency.

Three distinct regimes appear:

The experiment also reveals that the phase between the driving force and the response changes continuously as resonance is crossed.

This change in phase is just as important as the change in amplitude.

A Second Experiment — Two Oscillators

Now two pendulums were suspended from the same support.

One pendulum had a fixed length.

The second could be adjusted by changing its length.

Initially, the pendulums had different natural frequencies.

When one pendulum was set into motion, very little energy was transferred to the other.

Then the length of the second pendulum was adjusted until both had the same natural frequency.

A remarkable transformation occurred.

Energy passed efficiently from one pendulum to the other.

The second pendulum began to oscillate .

Matching frequencies allowed the two systems to exchange energy efficiently.

The Connection to Light

This is exactly how matter interacts with light.

Light is not a single frequency.

It contains a spectrum of frequencies.

Atoms, molecules, and solids possess characteristic natural frequencies associated with their electrons and vibrations.

When light of the appropriate frequency encounters a material, the material responds strongly.

Frequencies far from resonance produce much weaker responses.

This simple pendulum experiment is a mechanical model for optical resonance.

Why Different Materials Have Different Colors

Different materials have different natural frequencies.

As white light falls on a material:

• Some frequencies are absorbed efficiently.
• Others are reflected or transmitted.

The reflected frequencies determine the color we see.

The colors of the world arise because different materials respond differently to different frequencies of light.

A Deeper Realization

Although the experiment uses a bouncing ball and pendulums, the principle is universal.

The same physics explains:

• A child pumping a swing
• Musical instruments
• Wine glasses shattering
• Radio tuning
• Molecular vibrations
• Laser operation
• Optical absorption
• Chemical spectroscopy

Resonance is one of the unifying ideas of physics.

 

Continue the Investigation

The experiment you've just explored is only the beginning. Our hands-on investigation sets are designed to help you recreate, extend, and deepen these ideas through observation and experimentation.

Every investigation has the potential to lead to a new question. If you discover something interesting, improve the experiment, or develop a new variation, share it with the Geometers community. Your work may inspire others and could even be featured here.

Keep experimenting. Keep questioning. Keep discovering.