14.4 Electromagnetic Waves

Electromagnetic waves are made of oscillating electric and magnetic fields that are perpendicular to each other and to the direction the wave travels. They do not need a medium, so they move through vacuum at the speed of light, $c = 3.00 \times 10^8 \text{ m/s}$, and they are sorted into the electromagnetic spectrum by wavelength from radio waves down to gamma rays.

Why This Matters for the AP Physics 2 Exam

This topic builds the core picture of light as a wave, which connects to almost everything else in Unit 14, including diffraction, interference, and thin-film effects. On the AP Physics 2 exam, you can expect to work with models and representations of waves, sketch or interpret diagrams of the electric and magnetic fields, and use the wavelength-frequency-speed relationship in calculations. Knowing how to read and build these representations supports both the multiple-choice section and the free-response questions that ask you to translate between a description, a diagram, and an equation.

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Key Takeaways

• Electromagnetic waves are transverse waves made of oscillating electric and magnetic fields that are mutually perpendicular and perpendicular to the direction of propagation.
• Electromagnetic waves do not need a medium, so they travel through vacuum, all at the same speed $c = 3.00 \times 10^8 \text{ m/s}$.
• The spectrum is ordered by wavelength: radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays (longest to shortest).
• Visible light by decreasing wavelength is red, orange, yellow, green, blue, violet. Red is longest, violet is shortest.
• Use $c = \lambda f$ to connect wavelength and frequency. Longer wavelength means lower frequency.
• You should know the order of the spectrum, but you will not be asked to memorize exact wavelength ranges for each category.

Properties of Electromagnetic Waves

Oscillating Electric and Magnetic Fields

Electromagnetic waves consist of oscillating electric and magnetic fields that work together to carry energy through space.

• The electric field and magnetic field oscillate perpendicular to each other and to the direction the wave travels.
• This perpendicular arrangement is what makes electromagnetic waves transverse waves.
• As the wave travels, the changing electric field is paired with a changing magnetic field, and that mutual relationship lets the wave keep going.
• Electromagnetic waves are commonly modeled as plane waves, which have flat, planar wave fronts where all points share the same phase.

Propagation Without a Medium

Unlike mechanical waves such as sound, electromagnetic waves can travel through empty space.

• Electromagnetic waves do not need particles to transfer energy from one place to another.
• This is why light from distant stars and galaxies can reach us across the vacuum of space.
• The speed of all electromagnetic waves in a vacuum is the same universal constant:

$c = 3.00 \times 10^8 \text{ m/s}$

Categories by Wavelength

The electromagnetic spectrum covers a huge range of wavelengths, from kilometers down to picometers. In order of decreasing wavelength:

• Radio waves (longest wavelengths)
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays (shortest wavelengths)

Visible light is a small slice of the full spectrum. By decreasing wavelength, the colors are:

• Red (longest visible wavelength)
• Orange
• Yellow
• Green
• Blue
• Violet (shortest visible wavelength)

Visible electromagnetic waves are also called light, and sometimes electromagnetic waves of all wavelengths are referred to as light or electromagnetic radiation.

The relationship between wavelength ($\lambda$), frequency ($f$), and speed ($c$) for all electromagnetic waves is:

$c = \lambda f$

How to Use This on the AP Physics 2 Exam

Problem Solving

When you see a frequency or wavelength for an electromagnetic wave, start with $c = \lambda f$. Since $c$ is fixed in vacuum, wavelength and frequency are inversely related, so doubling the frequency cuts the wavelength in half. Keep units consistent and convert to meters before plugging in.

Free Response

If a question asks you to describe or sketch an electromagnetic wave, show the electric field and magnetic field oscillating perpendicular to each other and perpendicular to the direction of travel. Be ready to explain why electromagnetic waves are transverse and why they do not need a medium, using the idea that the oscillating fields sustain each other.

Common Trap

The exam will not ask you for exact wavelength numbers for each band, so focus on the correct order of the spectrum and visible colors instead of memorizing boundary values.

Practice Problem 1: Wave Propagation

Solution

Use the relationship between speed, wavelength, and frequency:

$c = \lambda f$

Where:

• $c = 3.00 \times 10^8 \text{ m/s}$ (speed of light in vacuum)
• $f = 5.0 \times 10^{14} \text{ Hz}$ (given frequency)
• $\lambda$ is the wavelength we need to find

Rearranging to solve for wavelength:

$\lambda = \frac{c}{f} = \frac{3.00 \times 10^8 \text{ m/s}}{5.0 \times 10^{14} \text{ Hz}} = 6.0 \times 10^{-7} \text{ m} = 600 \text{ nm}$

This wavelength (600 nm) falls within the visible light portion of the electromagnetic spectrum, in the orange-yellow region.

Practice Problem 2: Electromagnetic Wave Structure

Solution

Electromagnetic waves and sound waves propagate in fundamentally different ways.

Electromagnetic waves:

1. Consist of oscillating electric and magnetic fields that sustain each other.
2. The changing electric field is paired with a changing magnetic field, and that mutual relationship continues as the wave travels.
3. This self-sustaining cycle lets electromagnetic waves propagate without a medium.
4. The fields themselves carry the energy through space.

Sound waves:

1. Are mechanical waves that require a medium (solid, liquid, or gas).
2. Propagate through compressions and rarefactions of particles in the medium.
3. Transfer energy through particle interactions.
4. Without particles to compress and expand, sound cannot travel.

This is why we can see light from distant stars across the vacuum of space, but sound cannot travel through that same vacuum.

Common Misconceptions

• Electromagnetic waves do not need a medium. Only mechanical waves like sound require particles to travel through.
• The electric and magnetic fields are not parallel. They oscillate perpendicular to each other and both are perpendicular to the direction of propagation.
• Not all electromagnetic waves have the same wavelength or frequency, but in a vacuum they all travel at the same speed $c$.
• Higher frequency means shorter wavelength, not longer. Because $c$ is fixed, $\lambda$ and $f$ move in opposite directions.
• Visible light is only a small part of the full spectrum, not the whole thing. Radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays are all electromagnetic waves too.
• Red light has the longest visible wavelength and violet has the shortest, so violet has the higher frequency.

Related AP Physics 2 Guides

• 14.2 Periodic Waves
• 14.3 Boundary Behavior of Waves and Polarization
• 14.6 Wave Interference and Standing Waves
• 14.7 Diffraction
• 14.1 Properties of Wave Pulses and Waves
• 14.5 The Doppler Effect