🌊 Waves & Oscillations

Waves carry energy without carrying matter. This hub covers wave properties, sound, interference, standing waves, resonance and the Doppler effect.

What you will learn

Relate wave speed, frequency and wavelength with v = fλ
Distinguish transverse and longitudinal waves
Explain interference, standing waves and resonance
Apply the Doppler effect to moving sources

Study guide

High School · ~12 hours

📘 Waves Study Guide

The complete waves study guide: wave basics, sound, interference, Doppler effect, and oscillations — with formulas, checklists, and exam tactics.

High School concepts

Beat Phenomenon — When Two Close Frequencies Pulse Together

Two overlapping waves of nearly equal frequency make the loudness swell and fade in pulses. Learn the beat frequency formula, the superposition math behind…

Diffraction of Waves — Bending Around Corners, Simply Explained

Diffraction: why waves spread after passing edges and slits. When it's noticeable, single-slit minima, and everyday examples.

The Doppler Effect — Why Pitch Changes with Motion

The Doppler effect: how motion shifts observed frequency. Formula, the ambulance example, and uses from radar to astronomy.

Sound Intensity and Decibels — How Loud Is Loud?

Intensity is power per area in W/m²; the decibel scale compresses a trillion-fold range into 0–120 dB. Formulas, reference levels, and why +3 dB means double.

Standing Waves in Detail — Nodes, Antinodes and the Harmonic Series

How two identical waves traveling in opposite directions freeze into a pattern of still nodes and antinodes — the harmonic series f_n = nv/2L, with a worked…

Standing Waves and Resonance — Nodes, Antinodes and Harmonics

Standing waves: when waves interfere with their own reflections. Nodes, antinodes, harmonics, and resonance explained with examples.

Wave Interference — Constructive and Destructive Superposition

When waves meet: constructive and destructive interference, the superposition principle, phase, and real examples.

Wave Reflection — Phase Inversion, Fixed Ends and the Law of Reflection

What a wave does at a boundary: why fixed ends flip pulses upside down, free ends reflect them upright, why the angle of incidence equals the angle of…

Wave Speed, Frequency and Wavelength — v = fλ Explained

The wave equation v = fλ connects speed, frequency and wavelength. Definitions, units, and worked examples from sound to light.

Introductory College concepts

Resonance in Detail — Natural Frequency, Forced Vibration and Damping

Why systems vibrate hardest when driven at their natural frequency: forced oscillators, the resonance curve, damping, the Q factor, and a worked mass-spring…

Simple Harmonic Motion — Springs, Pendulums and x = A cos(ωt)

Simple harmonic motion: the mathematics of oscillation. Period formulas for springs and pendulums, energy, and real examples.

Beginner concepts

Sound Waves — How Sound Travels, Simply Explained

Sound is a longitudinal pressure wave. Speed of sound, pitch, loudness, echoes, and why there is no sound in space.

Transverse vs Longitudinal Waves — Definitions and Examples

Transverse waves oscillate perpendicular to travel; longitudinal waves oscillate parallel. Diagrams, examples, and key differences.

Formulas

Doppler Effect — Apparent Frequency Formula

Observed frequency equals emitted frequency times the ratio of wave speed adjusted for observer and source motion.

Wave Equation — v = fλ

Wave speed equals frequency times wavelength.

Calculators

🧮 Doppler Effect Calculator — f′ = fv/(v − vₛ)

🧮 Pendulum Period Calculator — T = 2π√(L/g)

🧮 Sound Intensity Calculator — I = P/A

🧮 Spring-Mass Period Calculator — T = 2π√(m/k)

🧮 Standing Wave Frequency Calculator — fₙ = nv/2L

🧮 Wave Equation Calculator (v = fλ)

🧮 Wave Period Calculator — T = 1/f

Simulations

Interactive

Doppler Effect Simulator

Drive a wave source toward and away from an observer: watch wavefronts bunch up ahead, stretch behind, and shift the heard pitch.