Waves Properties

Why This Matters

Waves are the universe's delivery system—they transport energy across space and through matter without moving material from one place to another. Whether you're listening to music, seeing colors, or feeling the warmth of sunlight, you're experiencing wave behavior. On your Physical Science exam, you're being tested on your ability to connect wave characteristics (amplitude, frequency, wavelength) to wave behaviors (reflection, refraction, interference) and explain how these principles show up in real-world phenomena.

Don't just memorize definitions—understand what each property tells you about a wave's energy, speed, and interaction with its environment. The strongest exam answers connect mathematical relationships (like $v = f \lambda$) to observable effects (like why a straw looks bent in water). Master the "why" behind wave properties, and you'll be ready for any question they throw at you.

---

Fundamental Wave Measurements

These four properties describe what a wave looks like and how it behaves over time. Together, they define a wave's identity—change one, and you change the wave's energy, appearance, or behavior.

Amplitude

• Maximum displacement from rest position—measures how far the wave moves from its equilibrium point
• Directly related to energy; doubling amplitude quadruples the energy carried by the wave
• Determines intensity—in sound, amplitude controls loudness; in light, it controls brightness

Wavelength

• Distance between consecutive identical points on a wave (crest to crest or trough to trough), measured in meters
• Inversely related to frequency—shorter wavelengths mean higher frequencies for waves traveling at the same speed
• Determines wave type—in light, wavelength determines color; in sound, it influences the physical size of the wave

Frequency

• Number of complete cycles per second, measured in Hertz ($Hz$)
• Directly proportional to energy—higher frequency waves carry more energy
• Determines pitch in sound and energy level in electromagnetic radiation (gamma rays have the highest frequency)

Period

• Time for one complete wave cycle, measured in seconds
• Inversely related to frequency: $T = \frac{1}{f}$—if frequency doubles, period is cut in half
• Useful for timing wave events—helps predict when the next crest or trough will arrive

---

Wave Speed and Medium Interactions

Wave speed isn't just about the wave itself—it depends on what the wave is traveling through. The medium determines the speed; the wave's frequency stays constant when entering a new medium.

Wave Speed

• Calculated using $v = f \lambda$ (velocity equals frequency times wavelength)
• Medium-dependent—waves travel fastest in solids, slower in liquids, slowest in gases
• Frequency remains constant when waves change mediums; wavelength adjusts to accommodate the new speed

---

Wave Behaviors at Boundaries

When waves encounter obstacles, boundaries, or openings, they exhibit predictable behaviors. These interactions explain everything from echoes to rainbows to the colors on a soap bubble.

Reflection

• Wave bounces back when it hits a barrier or boundary between mediums
• Angle of incidence equals angle of reflection—this law governs mirrors, echoes, and sonar
• No change in speed or wavelength—the wave stays in the same medium after bouncing

Refraction

• Wave bends when entering a new medium due to a change in speed
• Bending direction depends on speed change—waves bend toward the normal when slowing down, away when speeding up
• Explains lenses and optical illusions—why a straw looks broken in water, how eyeglasses focus light

Diffraction

• Wave spreads out when passing through an opening or around an obstacle
• More pronounced when wavelength is similar to opening size—long wavelengths diffract more noticeably
• Explains why you can hear around corners—sound waves diffract easily; light waves (short wavelength) do not

---

Wave Interactions and Energy Transfer

When waves meet each other or interact with systems, energy can combine, cancel, or amplify. These phenomena explain sound quality, light patterns, and even structural failures.

Interference

• Occurs when two or more waves overlap in the same space at the same time
• Constructive interference: waves in phase combine to produce larger amplitude (louder sound, brighter light)
• Destructive interference: waves out of phase cancel to produce smaller or zero amplitude (noise-canceling headphones use this)

Resonance

• Amplification occurs when driving frequency matches natural frequency of a system
• Energy transfers efficiently, causing amplitude to increase dramatically over time
• Can be useful or dangerous—makes musical instruments louder, but can collapse bridges (Tacoma Narrows, 1940)

---

Quick Reference Table

---

Self-Check Questions

1. Which two wave properties are inversely related, and what equation connects them to wave speed?

2. A wave passes from air into water. Its speed increases—what happens to its wavelength, and why does its frequency stay the same?

3. Compare constructive and destructive interference: what conditions produce each, and give one real-world example of destructive interference being useful.

4. Why can you hear someone talking around a corner but not see them? Which wave behavior explains this, and what property of sound vs. light makes the difference?

5. A bridge begins to sway violently when soldiers march across it in rhythm. Which wave phenomenon is responsible, and what would you recommend to prevent structural damage?