Oscillations & waves

The big picture

A point on a string moves locally while the disturbance travels along the string. Tracking one material point and tracking a crest answer different questions. Learn to switch between those pictures without confusing particle speed with wave speed.

Oscillations introduce phase, energy exchange and restoring forces. Standing waves add boundary conditions; damping and driving add energy loss and input. Each new model should retain a clear link to the simpler one it extends.

What to read, and why

Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.

1. STAGE 1

   Follow one oscillator

   Relate displacement, velocity, acceleration and energy through a cycle; then add damping and a periodic drive.

   Oscillations: restoring forces, phase and energy →Build spring and pendulum models from equilibrium, then connect their motion to energy and initial conditions.7 worked examples · 9 checks · Complete free chapterDamping, driving and the meaning of resonance →Follow the energy, impose the initial conditions, and say which response is being measured.7 worked examples · 6 checks · Open explanation · member practice

2. STAGE 2

   Follow a travelling pattern

   Read the signs and units in a wave equation and locate the nodes allowed by the boundaries.

   Travelling waves, superposition and energy →Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.8 worked examples · 10 checks · Open explanation · member practiceStanding waves, pipe modes and resonance measurements →Use boundary conditions to find nodes, harmonics and the information hidden in resonance spacings.5 worked examples · 8 checks · Open explanation · member practice

3. STAGE 3

   Change the observation

   Distinguish source motion from observer motion and identify the frame in which wave speed is defined.

   Sound: Doppler shifts, beats and intensity levels →Count arriving wavefronts, track a changing phase difference and use decibels as logarithmic ratios.9 worked examples · 7 checks · Open explanation · member practice

Choose a method before an equation

Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.

Try a complete free problem

These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.