Waves Properties

Why This Matters

Waves 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'll need to connect wave characteristics (amplitude, frequency, wavelength) to wave behaviors (reflection, refraction, interference) and explain how these principles show up in real-world phenomena.

The key is understanding 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).

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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.

Amplitude

Amplitude is the maximum displacement from the rest (equilibrium) position. It measures how far the wave moves above or below that midpoint.

• Directly related to energy: doubling amplitude quadruples the energy carried by the wave
• Determines intensity in everyday experience. For sound, amplitude controls loudness. For light, it controls brightness.

Wavelength

Wavelength is the distance between two 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 visible light, wavelength determines color (red light has a wavelength around 700 nm, violet around 400 nm). In sound, wavelength relates to the physical size of the wave in the medium.

Frequency

Frequency is the number of complete cycles per second, measured in Hertz ($Hz$). One $Hz$ means one full wave cycle every second.

• Directly proportional to energy: higher frequency waves carry more energy
• Determines pitch in sound (higher frequency = higher pitch) and energy level in electromagnetic radiation (gamma rays have the highest frequency on the EM spectrum)

Period

Period is the 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 and predicting when the next crest or trough will arrive

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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

The fundamental wave equation is $v = f \lambda$ (velocity equals frequency times wavelength). This connects all three quantities and is the most-used formula in this unit.

• Medium-dependent: waves generally travel fastest in solids, slower in liquids, and slowest in gases. This is because particles in solids are packed more tightly, allowing vibrations to pass more quickly between them.
• Frequency remains constant when a wave changes mediums. Since speed changes but frequency doesn't, wavelength must adjust to compensate. You can see this directly from the equation: if $v$ changes and $f$ stays the same, $\lambda$ has to change.

Note: this "fastest in solids" rule applies well to sound and mechanical waves, but light actually behaves the opposite way. Light travels fastest in a vacuum and slows down in denser materials like glass or water. Keep track of which type of wave a question is asking about.

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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

Reflection occurs when a wave bounces back after hitting a barrier or boundary between mediums.

• The law of reflection states that the angle of incidence equals the angle of reflection (both measured from the normal, an imaginary line perpendicular to the surface)
• No change in speed or wavelength, because the wave stays in the same medium after bouncing
• Examples: mirrors, echoes, sonar

Refraction

Refraction is the bending of a wave as it enters a new medium, caused by a change in speed.

• Bending direction depends on the speed change: waves bend toward the normal when slowing down and away from the normal when speeding up
• This explains why a straw looks broken in a glass of water. Light changes speed as it passes from water to air, bending at the surface and shifting the apparent position of the submerged part of the straw.
• Lenses in eyeglasses and cameras work by using refraction to focus light

Diffraction

Diffraction is the spreading of a wave as it passes through an opening or around an obstacle.

• Most pronounced when the wavelength is close to the size of the opening. Long wavelengths diffract more noticeably than short ones.
• This is why you can hear someone talking around a corner but can't see them. Sound waves have wavelengths on the order of meters (similar to doorway sizes), so they diffract easily. Visible light has wavelengths around 400–700 nanometers, far too small relative to everyday openings to diffract noticeably.

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Wave Interactions and Energy Transfer

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

Interference

Interference occurs when two or more waves overlap in the same space at the same time. The resulting wave is the sum of the individual displacements at each point. This is called the superposition principle.

• Constructive interference: waves that are in phase (crests aligned with crests) combine to produce a larger amplitude. This means louder sound or brighter light.
• Destructive interference: waves that are out of phase (crests aligned with troughs) cancel each other, producing smaller or zero amplitude. Noise-canceling headphones work by generating a wave that's out of phase with incoming noise, canceling it out.

Resonance

Resonance is the dramatic increase in amplitude that occurs when a driving frequency matches the natural frequency of a system. Every object has a natural frequency at which it "wants" to vibrate.

• Energy transfers very efficiently at this frequency, causing amplitude to grow with each cycle
• Can be useful or dangerous. It makes musical instruments produce louder, richer sound. But it can also cause structural failure, as with the Tacoma Narrows Bridge collapse in 1940, where wind-driven oscillations matched the bridge's natural frequency and tore it apart.

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Quick Reference Table

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Self-Check Questions

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

2. A sound 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?