1. From signals in a wire to waves in space
In the earlier EE101 pages, we focused on what happens in circuits:
• Ohm’s Law gave us the basic V = I × R relationship.
• AC & Impedance showed how inductors and capacitors depend on frequency.
• Tuned Circuits introduced LC resonance and frequency selection.
All of that is closely tied to the idea of waves. Electrical engineering doesn’t stop at currents in a wire; those time-varying signals are part of larger electromagnetic waves that can travel through space.
• Ohm’s Law gave us the basic V = I × R relationship.
• AC & Impedance showed how inductors and capacitors depend on frequency.
• Tuned Circuits introduced LC resonance and frequency selection.
All of that is closely tied to the idea of waves. Electrical engineering doesn’t stop at currents in a wire; those time-varying signals are part of larger electromagnetic waves that can travel through space.
2. Basic wave vocabulary: f, λ, and v
A wave is a repeating pattern in space and time. It might be:
• A water wave on the surface of a lake.
• A sound wave in air.
• An electromagnetic wave (radio, microwave, visible light).
Three key quantities describe any simple wave:
• Frequency (f) – how many cycles per second the wave completes, measured in hertz (Hz).
• Wavelength (λ) – the distance between repeating features (e.g., crest to crest), measured in meters (m).
• Wave speed (v) – how fast the wave pattern moves through space, measured in meters per second (m/s).
These are tied together by a simple relationship:
• A water wave on the surface of a lake.
• A sound wave in air.
• An electromagnetic wave (radio, microwave, visible light).
Three key quantities describe any simple wave:
• Frequency (f) – how many cycles per second the wave completes, measured in hertz (Hz).
• Wavelength (λ) – the distance between repeating features (e.g., crest to crest), measured in meters (m).
• Wave speed (v) – how fast the wave pattern moves through space, measured in meters per second (m/s).
These are tied together by a simple relationship:
v = f × λ
If you know any two (frequency and speed, for example), you can calculate the third (wavelength).
3. The speed of light and electromagnetic waves
Electromagnetic (EM) waves include:
• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays and gamma rays
In a vacuum, all of these travel at the same fundamental speed:
For EM waves in free space, the relationship becomes:
• Low-frequency waves (small f) have long wavelengths (large λ).
• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays and gamma rays
In a vacuum, all of these travel at the same fundamental speed:
c ≈ 3 × 108 m/s
where c is the speed of light.
For EM waves in free space, the relationship becomes:
c = f × λ
• High-frequency waves (large f) have short wavelengths (small λ).• Low-frequency waves (small f) have long wavelengths (large λ).
4. A few frequency–wavelength examples
Using c ≈ 3 × 108 m/s:
1) Power-line frequency (60 Hz)
2) Mid-range AM radio (1 MHz = 1,000,000 Hz)
3) Visible light (e.g., 5 × 1014 Hz)
1) Power-line frequency (60 Hz)
f = 60 Hz
λ = c / f ≈ (3 × 108) / 60 ≈ 5 × 106 m
That’s a wavelength of about 5000 km — roughly the size of a continent.
λ = c / f ≈ (3 × 108) / 60 ≈ 5 × 106 m
2) Mid-range AM radio (1 MHz = 1,000,000 Hz)
f = 1 × 106 Hz
λ = c / f ≈ (3 × 108) / (1 × 106) = 300 m
A wavelength of about 300 meters — comparable to a few city blocks.
λ = c / f ≈ (3 × 108) / (1 × 106) = 300 m
3) Visible light (e.g., 5 × 1014 Hz)
f ≈ 5 × 1014 Hz
λ = c / f ≈ (3 × 108) / (5 × 1014) = 6 × 10-7 m
That’s about 600 nm (nanometers), in the red–orange part of the visible spectrum.
λ = c / f ≈ (3 × 108) / (5 × 1014) = 6 × 10-7 m
5. How this connects back to circuits
In low-frequency circuits (like 50/60 Hz power lines):
• The wavelength is so long that wires look electrically “short.”
• We can often treat components as lumped elements (all in one spot).
At higher frequencies (radio, microwave, etc.):
• Wavelengths become comparable to the physical size of circuits, cables, antennas, and enclosures.
• Wires act like transmission lines rather than ideal connections.
• Impedance, reflections, and matching become crucial — waves can bounce, interfere, and set up standing patterns.
This is where:
• The impedance of lines and loads must be matched (for efficient power transfer).
• Tuned circuits (from Resonance) become powerful tools for selecting frequency bands.
• Concepts from wave physics and electromagnetics merge directly with circuit design.
• The wavelength is so long that wires look electrically “short.”
• We can often treat components as lumped elements (all in one spot).
At higher frequencies (radio, microwave, etc.):
• Wavelengths become comparable to the physical size of circuits, cables, antennas, and enclosures.
• Wires act like transmission lines rather than ideal connections.
• Impedance, reflections, and matching become crucial — waves can bounce, interfere, and set up standing patterns.
This is where:
• The impedance of lines and loads must be matched (for efficient power transfer).
• Tuned circuits (from Resonance) become powerful tools for selecting frequency bands.
• Concepts from wave physics and electromagnetics merge directly with circuit design.
6. Frequency vs. what we “hear” or “use”
Frequency shows up in very practical ways:
• Audio: – Low frequencies (e.g., 100 Hz) → bass notes. – High frequencies (e.g., 10 kHz) → treble, “brightness”.
• Radio: – AM, FM, shortwave, and Wi-Fi are all just different frequency bands of EM waves. – Tuning a radio literally means selecting which frequency (and thus which λ) your circuit responds to.
• Digital signals: – Faster data rates (GHz clocks, high-speed serial links) push circuits into regimes where wave behavior and transmission line design are essential. – Edges of digital pulses contain very high-frequency components, even if the base clock rate is lower.
• Audio: – Low frequencies (e.g., 100 Hz) → bass notes. – High frequencies (e.g., 10 kHz) → treble, “brightness”.
• Radio: – AM, FM, shortwave, and Wi-Fi are all just different frequency bands of EM waves. – Tuning a radio literally means selecting which frequency (and thus which λ) your circuit responds to.
• Digital signals: – Faster data rates (GHz clocks, high-speed serial links) push circuits into regimes where wave behavior and transmission line design are essential. – Edges of digital pulses contain very high-frequency components, even if the base clock rate is lower.
7. A simple mental picture to keep
You can think of the EE chain like this:
1) Ohm’s Law – How voltage, current, and resistance relate in the simplest case.
2) Impedance – How resistors, inductors, and capacitors respond when signals vary with time.
3) Resonance – How L and C together can prefer one frequency and ignore others.
4) Waves – How those time-varying signals tie into frequency (f), wavelength (λ), and speed (v or c), especially for EM waves.
The same basic ideas show up from:
• A 60 Hz power transformer.
• A radio tuner.
• A fiber-optic link carrying light.
• A satellite antenna talking to Earth.
Only the frequency and the physical scale change.
1) Ohm’s Law – How voltage, current, and resistance relate in the simplest case.
2) Impedance – How resistors, inductors, and capacitors respond when signals vary with time.
3) Resonance – How L and C together can prefer one frequency and ignore others.
4) Waves – How those time-varying signals tie into frequency (f), wavelength (λ), and speed (v or c), especially for EM waves.
The same basic ideas show up from:
• A 60 Hz power transformer.
• A radio tuner.
• A fiber-optic link carrying light.
• A satellite antenna talking to Earth.
Only the frequency and the physical scale change.
Summary: Waves are how signals extend into space. Frequency (f), wavelength (λ), and speed (v) are tied by v = f × λ.
For light and radio in free space, c = f × λ. As frequency rises, wavelength shrinks, and circuit design gradually turns into wave and field engineering.