7.02 Properties of Waves- Key Concepts and Examples

What You Need to Know About Wave Properties

Waves are everywhere. Sound, light, ocean swells, radio signals — all waves. Understanding their properties isn't optional if you're studying physics. It's the foundation.

This guide cuts through the fluff and gives you the actual concepts you need to master wave mechanics. No motivational nonsense. Just the facts.

The Core Properties of Waves

Amplitude

Amplitude is the maximum displacement of a wave from its rest position. Think of it as the height of a wave — how far up or down it goes from the middle line.

In sound waves, amplitude determines loudness. In light waves, it relates to brightness. Bigger amplitude means more energy.

Key point: Amplitude measures energy, not speed or distance traveled.

Wavelength (λ)

Wavelength is the distance between two consecutive points in phase on a wave. Usually measured from crest to crest or trough to trough.

It's a distance, so it uses meters. Radio waves have wavelengths of meters to kilometers. X-rays have wavelengths smaller than atoms.

Frequency (f)

Frequency tells you how many wave cycles pass a fixed point per second. The unit is Hertz (Hz) — one Hz equals one cycle per second.

High frequency means short wavelength. Low frequency means long wavelength. They're inversely related.

Your WiFi operates at 2.4 GHz or 5 GHz. That's billions of cycles per second.

Period (T)

The period is the time for one complete wave cycle. It's just the inverse of frequency:

T = 1/f

If a wave has a frequency of 100 Hz, its period is 0.01 seconds. One cycle takes that long.

Wave Speed (v)

The fundamental wave equation:

v = f × λ

Wave speed equals frequency times wavelength. This works for all waves — sound, light, water, whatever.

Sound travels at about 340 m/s in air. Light travels at 3 × 10⁸ m/s. The difference is staggering.

Types of Waves

Transverse Waves

The displacement is perpendicular to the direction of propagation. The medium moves side-to-side while the wave moves forward.

Examples: light waves, waves on a string, water waves (mostly).

Longitudinal Waves

The displacement is parallel to the direction of propagation. The medium compresses and expands in the same direction the wave travels.

Examples: sound waves, seismic P-waves.

Longitudinal waves have compressions (squeezed together) and rarefactions (spread apart).

Surface Waves

Ocean waves are a mix. Particles move in circular paths, combining transverse and longitudinal motion. That's why they're complicated to model.

Wave Behavior: Reflection, Refraction, Diffraction, Interference

These four phenomena explain how waves interact with boundaries and each other.

Reflection

Waves bounce off surfaces. The angle of incidence equals the angle of reflection. This is how mirrors work — light reflects off surfaces and into your eyes.

Echoes are sound reflecting off distant walls. Sonar uses reflection to detect underwater objects.

Refraction

Waves change direction when they enter a different medium. This happens because wave speed changes.

Light bends when it goes from air into water. A straw looks bent in a glass of water. That's refraction.

The degree of bending depends on the media and the wavelength. Shorter wavelengths bend more.

Diffraction

Waves spread out when they pass through an opening or around an obstacle. The amount of spreading depends on wavelength relative to the opening size.

You can hear around corners because sound waves diffract. AM radio signals diffract around buildings better than FM signals because AM has longer wavelengths.

Interference

When two waves meet, they add together. This is superposition.

Constructive interference: Peaks line up with peaks. The result is a bigger wave. Energy increases locally.

Destructive interference: Peaks line up with troughs. They cancel out. Noise-canceling headphones work this way.

Interference proves waves are real physical phenomena, not just mathematical constructs.

Wave Equation Practice

Most wave problems use the same equation. Memorize it:

v = f × λ

Given two values, solve for the third. That's it.

Example: A wave has wavelength 2 m and frequency 50 Hz. What's its speed?

v = 50 × 2 = 100 m/s

Example: Sound travels at 340 m/s. A sound wave has frequency 440 Hz. What's its wavelength?

λ = v/f = 340/440 = 0.77 m

These calculations are straightforward once you know which variables you're solving for.

Quick Reference: Wave Properties at a Glance

Real-World Examples

• Earthquakes: P-waves are longitudinal, S-waves are transverse. Their different speeds help scientists locate the epicenter.
• Medical imaging: Ultrasound uses high-frequency sound waves. The echoes build a picture of internal organs.
• 5G networks: Higher frequencies mean faster data but worse penetration through walls. That's why 5G needs more cell towers.
• Musical instruments: Different frequencies produce different notes. A guitar string's thickness and tension determine its resonant frequency.

Common Mistakes to Avoid

• Confusing wavelength with amplitude. Wavelength is horizontal distance; amplitude is vertical displacement.
• Forgetting that wave speed depends on the medium. Light slows down in water. Sound speeds up.
• Mixing up frequency and period. They're reciprocals, not the same thing.
• Ignoring units. Always check that your answer uses the correct measurement system.

The Bottom Line

Wave properties aren't complicated once you separate them. Amplitude is energy. Wavelength is size. Frequency is speed of cycles. Period is time per cycle. Wave speed connects everything.

The wave equation v = fλ solves most problems you'll encounter. Practice identifying which variables you have and which you need to find.

That covers the essentials. No summary paragraph needed — you either get it now or you go practice more problems.