Types of Waves

Why This Matters

Waves are the universe's way of moving energy from one place to another, and understanding them unlocks everything from how you hear music to how earthquakes reveal Earth's hidden interior. In College Physics, you're being tested on your ability to classify waves by what they need to travel, how their particles move, and how waves interact with each other. These distinctions show up repeatedly in multiple-choice questions and form the backbone of FRQs on wave behavior.

Don't just memorize that sound is a longitudinal wave—know why particle motion matters, how standing waves differ from traveling waves, and what physical principles connect seemingly different phenomena like guitar strings and earthquake detection. When you understand the underlying mechanisms, you can tackle any wave problem the exam throws at you.

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Waves Classified by Medium Requirements

The most fundamental distinction in wave physics is whether a wave needs matter to propagate. This determines where the wave can travel and what physical interactions govern its behavior.

Mechanical Waves

• Require a medium (solid, liquid, or gas)—no particles, no wave propagation
• Energy transfers through particle interactions—the medium's particles oscillate but don't permanently displace
• Classification branches into longitudinal and transverse—based on how those particles move relative to wave direction

Electromagnetic Waves

• No medium required—can propagate through the vacuum of space at $c = 3 \times 10^8 \text{ m/s}$
• Oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation—self-sustaining field disturbances
• Spans the entire EM spectrum—from radio waves ($\lambda \sim$ meters) to gamma rays ($\lambda \sim 10^{-12}$ m), all traveling at the same speed in vacuum

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Waves Classified by Particle Motion

Once you know a wave is mechanical, the next question is: how do the medium's particles move relative to the wave's direction? This determines the wave's structure and what physical quantities describe it.

Longitudinal Waves

• Particle motion parallel to wave propagation—particles oscillate back and forth along the same axis the wave travels
• Compressions and rarefactions define the wave structure—regions of high and low particle density, respectively
• Sound waves are the classic example—pressure variations traveling through air, liquids, or solids

Transverse Waves

• Particle motion perpendicular to wave propagation—particles oscillate up-down or side-to-side while the wave moves forward
• Crests and troughs define the wave structure—maximum displacements above and below equilibrium
• Light waves and waves on strings are key examples—note that light is transverse even though it's not mechanical

Surface Waves

• Travel along the interface between two media—boundary phenomena like the air-water interface
• Combine longitudinal and transverse motion—particles trace circular or elliptical paths as the wave passes
• Water waves are the primary example—the complexity of particle motion explains why water wave physics gets tricky

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Waves Classified by Behavior

Beyond medium and particle motion, waves are classified by what they do—whether they transport energy through space or create stationary patterns through interference.

Traveling Waves

• Transport energy from source to destination—the wave profile moves through space at the wave speed $v = f\lambda$
• Can be longitudinal or transverse—classification by behavior is independent of classification by particle motion
• Described by wavelength $\lambda$, frequency $f$, and amplitude $A$—these parameters fully characterize the wave's spatial and temporal structure

Standing Waves

• Formed by interference of two traveling waves moving in opposite directions—superposition creates a stationary pattern
• Nodes and antinodes are the defining features—nodes show zero displacement, antinodes show maximum displacement
• Essential for understanding musical instruments—vibrating strings, air columns, and drumheads all produce standing waves with quantized frequencies

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Real-World Wave Applications

These wave types aren't abstract—they show up in phenomena you experience daily and in technologies that shape modern life. Connecting wave physics to applications is prime FRQ territory.

Sound Waves

• Longitudinal mechanical waves traveling through air (or other media)—pressure oscillations your ear detects
• Frequency determines pitch, amplitude determines loudness—the physics behind every musical note and spoken word
• Speed depends on medium properties—$v = \sqrt{\frac{B}{\rho}}$ in fluids, faster in denser media like water or steel

Water Waves

• Surface waves at the air-water interface—particles undergo circular motion that decreases with depth
• Influenced by wind, gravity, and boundaries—wave behavior changes dramatically in shallow water near shorelines
• Demonstrate dispersion—different wavelengths travel at different speeds, causing wave packets to spread out

Seismic Waves

• Generated by earthquakes and explosions—carry information about geological events and Earth's interior
• P-waves (primary) are longitudinal—faster, arrive first, travel through solids and liquids
• S-waves (secondary) are transverse—slower, arrive second, blocked by Earth's liquid outer core

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Quick Reference Table

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Self-Check Questions

1. Both sound waves and P-waves are longitudinal—what shared property allows them both to travel through liquids, and why can't S-waves do the same?

2. A guitar string vibrates in its third harmonic. How many nodes and antinodes are present, and what equation relates the string length to wavelength?

3. Compare electromagnetic waves and mechanical waves: if both transfer energy, what fundamental difference explains why only one can reach Earth from the Sun?

4. Water waves exhibit circular particle motion. Explain how this represents a combination of longitudinal and transverse behavior, and predict what happens to this motion as depth increases.

5. An FRQ describes two identical waves traveling in opposite directions on a string. What type of wave results, and how would you identify the locations of maximum and minimum displacement?