IMAT Physics · Free notes

Oscillations and Waves: SHM, Sound and Light Waves

Oscillations and Waves has 6 past questions since 2011, and the ministry papers from 2023 on have asked 3 of them. So far almost all of them are about simple harmonic motion and pendulums, either as a short calculation or as a statement to judge true or false. Sound, the electromagnetic spectrum and interference are core syllabus that has barely been tested, and the newest question, on coherence, suggests that is changing. The hard part is precision about what stays fixed: where the speed is zero, what friction does, and which quantity keeps its value when a wave changes medium.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

6 formulas · 3 reference tables · 13 gotchas across all subtopics — the exam-eve cheat-sheet

Simple Harmonic Motion and Pendulums

Formulas (3)

Simple harmonic motion: displacement, velocity and acceleration · SHM from an end position $x = A\cos(\omega t) \qquad v = -A\omega\sin(\omega t) \qquad a = -\omega^2 x \qquad \omega = \frac{2\pi}{T}$
Energy in simple harmonic motion and damping · Energy of a mass on a spring $E = \tfrac{1}{2}kA^2 = \tfrac{1}{2}m v_{\max}^2$
The periods of a simple pendulum and a mass on a spring · Periods of the two standard oscillators $T_{\text{pendulum}} = 2\pi\sqrt{\frac{L}{g}} \qquad T_{\text{spring}} = 2\pi\sqrt{\frac{m}{k}}$

Watch out for (5)

Periodic is not the same as simple harmonic
→ Simple harmonic motion: displacement, velocity and acceleration
Velocity is zero at the ends, not at the centre
→ Simple harmonic motion: displacement, velocity and acceleration
Without friction an oscillator never stops
→ Energy in simple harmonic motion and damping
Passing the centre twice per period
→ The periods of a simple pendulum and a mass on a spring
A heavier bob does not change a pendulum's period
→ The periods of a simple pendulum and a mass on a spring

Waves, Sound and the Doppler Effect

Formulas (2)

Transverse and longitudinal waves, and v = fλ · Wave speed $v = f\lambda \qquad T = \frac{1}{f}$
Sound: speed, pitch, loudness and echoes · Distance from an echo $d = \frac{v\,t}{2}$

Reference tables (1)

The Doppler effect in words6 rows

Situation	Frequency heard or seen	Example
Source moving towards you	Higher than emitted	An ambulance siren as it approaches
Source moving away from you	Lower than emitted	The same siren after it has passed
You moving towards a still source	Higher: you meet the waves more often	Driving towards a ringing alarm
No relative motion	Same as emitted	Standing next to a parked car sounding its horn
Light from a galaxy moving away	Shifted to longer wavelengths (red shift)	Evidence that the universe is expanding
Ultrasound reflected from moving blood	Shifted by an amount that depends on the blood's speed	Doppler ultrasound scans of arteries and the fetal heart

Watch out for (4)

The frequency does not change in a new medium
→ Transverse and longitudinal waves, and v = fλ
An echo goes there and back
→ Sound: speed, pitch, loudness and echoes
Louder is not higher
→ Sound: speed, pitch, loudness and echoes
A moving source does not make sound travel faster
→ The Doppler effect in words

The Electromagnetic Spectrum, Diffraction and Interference

Formulas (1)

Superposition, coherence, interference and standing waves · Interference conditions and a string fixed at both ends $\Delta = n\lambda \ \text{(constructive)} \qquad \Delta = \left(n + \tfrac{1}{2}\right)\lambda \ \text{(destructive)} \qquad \lambda_n = \frac{2L}{n}$

Reference tables (2)

The electromagnetic spectrum: order, wavelengths and uses7 rows

Region	Typical wavelength	Use or source
Gamma rays	Below about $10^{-11}\ \text{m}$	Radiotherapy, sterilising medical equipment, radioactive decay
X-rays	About $10^{-11}$ to $10^{-8}\ \text{m}$	Imaging bones and teeth, CT scans
Ultraviolet	About 10 nm to 400 nm	Sterilising water, vitamin D in the skin, sunburn
Visible light	About 400 nm to 700 nm	Sight, optical fibres, photosynthesis
Infrared	About 700 nm to 1 mm	Heat radiation, remote controls, thermal cameras
Microwaves	About 1 mm to 30 cm	Microwave ovens, mobile phones, radar
Radio waves	Above about 30 cm	Radio and TV broadcasting, MRI scanners

Reflection, refraction, diffraction and polarisation of waves4 rows

Behaviour	What happens	What changes	Example
Reflection	The wave bounces off a boundary	Direction only	An echo; an image in a mirror
Refraction	The wave bends as it changes speed entering a new medium	Speed, wavelength and direction; not frequency	A straw looking bent in water
Diffraction	The wave spreads out after a gap or an edge	Direction spreads; speed, frequency and wavelength stay	Hearing a voice round a corner
Polarisation	Vibrations are limited to one plane	Plane of vibration	Polarising sunglasses cutting glare

Watch out for (4)

All electromagnetic waves have the same speed in a vacuum
→ The electromagnetic spectrum: order, wavelengths and uses
Diffraction does not change the wavelength
→ Reflection, refraction, diffraction and polarisation of waves
Coherence is about phase, not amplitude or brightness
→ Superposition, coherence, interference and standing waves
Nodes are half a wavelength apart, not a whole one
→ Superposition, coherence, interference and standing waves

PYQ weightage by concept

9 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

Simple Harmonic Motion and Pendulums0 PYQs · 0%

Concept	PYQs	Share
Simple harmonic motion: displacement, velocity and accelerationfoundation	—	—
Energy in simple harmonic motion and dampingfoundation	—	—
The periods of a simple pendulum and a mass on a springfoundation	—	—

Waves, Sound and the Doppler Effect0 PYQs · 0%

Concept	PYQs	Share
Transverse and longitudinal waves, and v = fλfoundation	—	—
Sound: speed, pitch, loudness and echoesfoundation	—	—
The Doppler effect in wordsfoundation	—	—

The Electromagnetic Spectrum, Diffraction and Interference0 PYQs · 0%

Concept	PYQs	Share
The electromagnetic spectrum: order, wavelengths and usesfoundation	—	—
Reflection, refraction, diffraction and polarisation of wavesfoundation	—	—
Superposition, coherence, interference and standing wavesfoundation	—	—