PRACTICE COLLECTION / 25 PROBLEMS
Oscillations & waves
Follow a cycle, compare phases and find patterns. Each problem includes progressive hints, guided reasoning and a question to test the idea again. Problems marked “Free sample” are complete for everyone; membership opens the rest.
LEARN BEFORE YOU PRACTISE
Build the reasoning first.
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 →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 →Standing 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 →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 →Interference: phase, brightness and contrast
Predict what a detector reads by connecting path, phase and field addition.
6 worked examples · 5 checks →Damping, 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 →CONCEPTS IN THIS COLLECTION
PRACTISE AT YOUR PACE
Problems in this collection
25 problems · Showing 12
Oscillations & waves
What changes when gravity becomes weaker?
What is its new period?
Compare casesOscillations & waves
Phase opposition is not the only interference case
What is the resultant displacement amplitude?
Compare casesOscillations & waves
Adjacent resonances reveal the fundamental
How many displacement antinodes are present in the 480 Hz mode?
Read graphs & measurementsOscillations & waves
A pressure disturbance has a bulk elastic response
What is the speed of a small-amplitude sound wave?
Connect conceptsOscillations & waves
A swinging rod is not a point bob
Use inertia about the pivot and weight acting at the center of mass.
Connect conceptsOscillations & waves
Add intensities before decibels
Find the level when both operate together.
Compare casesOscillations & waves
Combine amplitudes with phase
Find the amplitude of their sum.
Apply a principleOscillations & waves
Trade amplitude against frequency
Find the ratio of new average power to old average power.
Compare casesOscillations & waves
How fast is an oscillator halfway to an end?
What is its speed as a fraction of the maximum speed?
Apply a principleOscillations & waves
Fit the longest standing wave on a string.
What is the fundamental frequency?
Connect conceptsOscillations & waves
How quickly does the spring cycle?
The ratio of stiffness to inertia determines angular frequency squared.
Apply a principleOscillations & waves
Speed through equilibrium
Find its maximum speed.
Apply a principle12 of 25 shown