Wireless 101
M02 · L01
Module 2

Anatomy of a Sine Wave

Every signal in wireless communications starts with one fundamental building block — the sine wave. Master it, and you hold the key to understanding all of wireless.

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Wireless 101
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Foundations

What is a Signal?

A signal is any quantity that varies over time and carries information. Sound waves, voltage in a wire, light from a laser — all signals.

  • Sound — air pressure changing over time
  • Radio — electromagnetic field oscillating
  • Digital — voltage switching between high and low
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Wireless 101
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The Building Block

The Sine Wave

The sine wave is the purest signal possible — a single frequency, perfectly smooth. Every other signal is built from combinations of sine waves.

The Sine Wave Equation
y(t) = A \cdot \sin(2\pi f t + \varphi)
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Parameter 1

Amplitude

Amplitude is the height of the wave — how far it swings from zero. In sound, amplitude is loudness. In radio, it’s signal strength. Higher amplitude means more energy.

A
Symbol
Volts
Unit (Radio)
dB
Measured In
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Interactive
Try It

Drag to change Amplitude

A0.60
y(t) = 0.60 · sin(2πt)
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Wireless 101
M02 · L01
Parameter 2

Frequency

Frequency is how many cycles per second the wave completes, measured in Hertz (Hz). A 440 Hz sine wave is the musical note A. A 2.4 GHz wave is your WiFi signal.

  • Low frequency — long, slow waves (bass sounds, AM radio)
  • High frequency — short, fast waves (treble sounds, 5G)
  • 1 Hz = one complete cycle per second
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Wireless 101
Interactive
Try It

Drag to change Frequency

f1.0 Hz
y(t) = sin(2π · 1.0 · t)
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Parameter 3

Phase

Phase is the starting position of the wave — how far it’s shifted in time. Two waves at the same frequency but different phases can either reinforce or cancel each other.

φ
Symbol
Radians
Unit
0–2π
Full Cycle
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Wireless 101
Interactive
Try It

Drag to change Phase

φ0.00
y(t) = sin(2πt + 0.00)
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Wireless 101
Interactive
Full Control

Your Sine Wave

A0.70
f2.0
φ0.00
y(t) = 0.70 · sin(2π · 2.0 · t + 0.00)
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Wireless 101
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Related Quantities

Period & Wavelength

Period (T) is the time for one complete cycle. Wavelength (λ) is the physical length of one cycle. They’re intimately connected to frequency.

Period & Wavelength
T = \frac{1}{f} \qquad \lambda = \frac{c}{f}
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Wireless 101
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Everywhere

Sine Waves in the Real World

The sine wave isn’t just a math concept — it’s the shape of nature.

  • AC power — 50/60 Hz sine wave in every wall outlet
  • Radio carriers — pure sine waves carrying information
  • Sound — tuning forks produce near-perfect sine waves
  • Pendulums — position traces a sine wave over time
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Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

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Wireless 101
Key Takeaways
Summary

Key Takeaways

3
Parameters
A,f,φ
Controls
  • The sine wave is the fundamental building block of all signals
  • Amplitude = how strong, Frequency = how fast, Phase = when it starts
  • Period T = 1/f, Wavelength λ = c/f
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Wireless 101
Up Next
Next Lesson

Time Domain vs. Frequency Domain

Now that you understand the sine wave, it’s time to discover the two ways to look at any signal — and the powerful transform that connects them.

Coming Up
Fourier’s Gift to Engineering →
All lessons Read article
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