Waves Common Exam Traps

Overview

This page is a fast revision warning sheet for Waves.

Focus on avoiding:

• misconceptions
• graph-reading mistakes
• phase errors
• formula misuse
• wrong wave classification
• careless interpretation errors

This is not a full lesson note. Use it for quick exam revision.

Why It Matters

Wave questions are often lost through misreading graphs, mixing up definitions, or using correct formulas on the wrong quantities. A short traps page is useful because these mistakes are common, repetitive, and easy to fix once made explicit.

Definition

This page is a revision support note collecting common misconceptions and quick corrections for foundational wave ideas, especially graph interpretation, phase, wave classification, and the physical meaning of standard relations.

Key Representations

Core forms to keep straight:

$$v=f\lambda$$ $$f=\frac{1}{T}$$ $$\Delta \varphi =\frac{2\pi \Delta x}{\lambda }$$ $$\Delta \varphi =\frac{2\pi \Delta t}{T}$$ $$I=\frac{P}{S}$$

Trap 1: Confusing Particle Motion with Wave Propagation

Wrong idea: Particles move forward with the wave.

Correct: In most mechanical waves, particles oscillate about equilibrium while the disturbance travels.

Example:

• sound wave travels forward
• air molecules mainly vibrate back and forth

Reminder: Energy moves; matter does not move overall.

Trap 2: Mixing Up Displacement-Distance and Displacement-Time Graphs

Wrong idea: Both graphs show the same thing.

Correct:

Displacement-Distance Graph

• snapshot of many particles at one instant
• use to find wavelength

Displacement-Time Graph

• motion of one particle over time
• use to find period and frequency

$$f=\frac{1}{T}$$

Reminder: Space graph gives $\lambda$, time graph gives $T$.

Trap 3: Confusing Amplitude with Wavelength

Wrong idea: Amplitude and wavelength are both “wave size”.

Correct:

• amplitude = maximum displacement from equilibrium
• wavelength = distance between adjacent in-phase points

Reminder: Vertical scale often gives amplitude; horizontal spacing often gives wavelength.

Trap 4: Misusing $v=f\lambda$

Wrong idea: Increasing frequency always increases speed.

Correct: In a given medium, wave speed is usually fixed.

$$v=f\lambda$$

So if $f$ increases in same medium, $\lambda$ decreases.

Reminder: Frequency is set by source; speed depends on medium.

Trap 5: Getting Phase Difference Wrong

Wrong idea: Any two peaks are always $\pi$ out of phase.

Correct:

• one full cycle = $2\pi$
• half cycle = $\pi$
• quarter cycle = $\frac{\pi }{2}$

By distance:

$$\Delta \varphi =\frac{2\pi \Delta x}{\lambda }$$

By time:

$$\Delta \varphi =\frac{2\pi \Delta t}{T}$$

Reminder: In phase means the same complete oscillatory state, modulo $2\pi$—the same displacement alone is insufficient if the directions of motion differ.

Trap 6: Thinking All Waves Need a Medium

Wrong idea: Every wave requires particles.

Correct:

Mechanical Waves

Need medium:

• sound
• water waves

Electromagnetic Waves

Do not need medium:

• light
• radio
• X-rays

Reminder: Light travels through vacuum.

Trap 7: Saying Sound Is Transverse

Wrong idea: Sound has crests and troughs like water waves.

Correct: Sound in air is longitudinal.

It consists of:

• compressions
• rarefactions

Particle oscillation is parallel to wave travel.

Trap 8: Forgetting Only Transverse Waves Can Be Polarised

Wrong idea: Any wave can be polarised.

Correct: Only transverse waves can be polarised.

Therefore:

• light can be polarised
• sound in air cannot

Reminder: Polarisation is strong evidence of transverse nature.

Trap 9: Confusing Intensity with Amplitude

Wrong idea: Intensity and amplitude are the same quantity.

Correct:

Intensity is power per unit area:

$$I=\frac{P}{S}$$

For comparable sinusoidal waves of the same frequency in the same medium:

$$I\propto A^2$$

where $A$ means amplitude and $S$ means area.

Reminder: Double amplitude gives four times intensity.

Trap 10: Misreading the Inverse-Square Relationship

Wrong idea: Double distance gives half intensity.

Correct:

For point-source spreading:

$$I\propto \frac{1}{r^2}$$

So doubling distance gives:

$$\frac{1}{4}$$

of original intensity.

Tripling distance gives:

$$\frac{1}{9}$$

of the original intensity. This result requires a lossless isotropic point source with spherical spreading. Do not apply it automatically to directional sources, strong absorption or guided waves.

Trap 11: Mixing Frequency and Period

Wrong idea: Frequency increases when period increases.

Correct:

$$f=\frac{1}{T}$$

So larger period means lower frequency.

Reminder: Slow oscillation = long $T$ = small $f$.

Trap 12: Treating a longitudinal-wave curve as a particle path

Wrong idea: Air particles move along the sinusoidal pressure or displacement curve.

Correct: Air particles oscillate parallel to propagation. A curve of particle displacement or pressure variation against position is a graph of a quantity, not a route through space. At a compression centre, pressure variation is maximum while particle displacement is zero.

Trap 13: Misreading an oscilloscope trace

Wrong idea: The vertical axis of a microphone–oscilloscope trace is air-particle displacement.

Correct: The oscilloscope displays microphone output voltage against time. Convert the horizontal span of several cycles using the calibrated time base, divide by the number of cycles to find $T$, then use $f=1/T$.

Trap 14: Confusing stationary-sound spacing

Wrong idea: The distance between successive pressure-signal maxima is one wavelength.

Correct: Successive same-kind pressure-amplitude maxima, or successive same-kind minima, are separated by $\lambda /2$. If $N$ intervals occupy length $L$, then $\lambda =2L/N$.

Trap 15: Applying Malus’ law to the wrong input

Wrong idea: For unpolarised light incident on the first polariser, the output is immediately $I_{\mathrm{u}}{\cos }^2\theta$.

Correct: An ideal first polariser transmits $I_{\mathrm{u}}/2$. Malus’ law, $I=I_0{\cos }^2\theta$, then applies to plane-polarised light incident on a subsequent analyser, with $I_0$ measured immediately before it.

Trap 16: Letting Later Topics Replace The Foundation

Wrong idea: Every Topic 10 waves question is really an interference, diffraction, or stationary-wave question.

Correct: First identify the foundation: graph type, wavelength, period, phase difference, wave type, or intensity relationship. Later superposition ideas build on these definitions.

Quick Checklist

Before submitting answers, ask:

• Is this graph in space or in time?
• Did I confuse amplitude with wavelength?
• Is speed determined by source or medium?
• Is this wave transverse or longitudinal?
• Can it be polarised?
• Did I use $\Delta \varphi$ correctly?
• Did I apply inverse-square law properly?
• Did I mix frequency and period?
• Did I distinguish pressure variation from particle displacement?
• Did I identify what the oscilloscope axes actually represent?
• Is $I_0$ in Malus’ law the intensity immediately before the analyser?

Quick Exam Wording

For a progressive wave, say that energy is transferred by the travelling disturbance, while particles of a mechanical medium oscillate about equilibrium with no overall matter transfer. For polarisation, say that only transverse waves can be polarised.

Links

• Main topic: Waves
• Related concept: Wave Basics
• Related concept: Wave Displacement and Phase
• Later topic: Superposition of Waves
• Prerequisite: Oscillations and Simple Harmonic Motion

Final Memory Line

Most wave mistakes come from confusing:

• particle motion vs wave travel
• space graph vs time graph
• amplitude vs wavelength
• frequency vs speed
• wave type vs wave behaviour