C.2 Wave model

UNIT SYLLABUS

SL/HL 3 hours

A wave is a disturbance that carries energy without carrying matter. This short unit builds the vocabulary everything else in Theme C depends on: wavelength, frequency, period and speed, tied together by $v = f\lambda$. The key classification is transverse (oscillation perpendicular to travel — light, water surface waves, waves on strings) versus longitudinal (oscillation parallel to travel — sound, with its compressions and rarefactions). Mechanical waves need a medium; electromagnetic waves are self-propagating oscillations of fields that cross empty space at $c$ — which is why you see the lightning before you hear the thunder.

Guiding Questions

? How do waves transfer energy from one place to another without a net transfer of matter?
? What properties distinguish mechanical waves from electromagnetic waves?

Anatomy of a transverse wave: the displacement–distance snapshot reveals wavelength and amplitude; particles move vertically as energy travels horizontally.

✓ What the IB expects you to master

Distinguish transverse from longitudinal travelling waves by the direction of particle oscillation relative to energy transfer.
Define and use wavelength $\lambda$ , frequency $f$ , period $T$ and wave speed $v$ , connected by $v = f\lambda = \lambda/T$ .
Describe sound as a longitudinal pressure wave: compressions and rarefactions, needing a medium.
Describe electromagnetic waves as transverse oscillations of electric and magnetic fields that require no medium and travel at $c$ in vacuum.
Contrast mechanical and electromagnetic waves: medium requirement, speeds, and what oscillates.
Read displacement–distance graphs (giving $\lambda$ ) and displacement–time graphs (giving $T$ ).

1 Key Formulas

Wave speed

v = f\lambda = \frac{\lambda}{T}

2 Exam Preparation & Topic Explanations

The two-graph trap

Wave questions love pairing a displacement–distance graph (a photo at one instant) with a displacement–time graph (one particle's history). Read wavelength ONLY from the distance graph and period ONLY from the time graph — mixing them up is the most common wave error in Paper 1.

Then $v = f\lambda$ finishes the job.

Pro Exam Strategy

Axis check first: distance → wavelength; time → period.
Frequency never changes at a boundary; speed and wavelength do.
For longitudinal waves, displacement graphs still look sinusoidal — compressions sit where displacement crosses zero going negative-to-positive (know how to locate them).
Estimate: sound ~340 m/s in air, light $3\times10^8$ m/s — million-fold difference explains lightning-then-thunder.

3 MCQ Practice

Q1. Sound of frequency 440 Hz travels at $340\ \text{m s}^{-1}$ in air. Its wavelength is approximately:

0.77 m
1.3 m
77 cm and 1.3 m are both wrong
0.13 m

Q2. A wave passes from one medium to another and its speed doubles. Its frequency:

Doubles
Halves
Stays the same, so the wavelength doubles
Stays the same, so the wavelength halves

Q3. Which is a correct difference between sound and light?

Sound is transverse; light is longitudinal
Sound requires a medium; light does not
Sound can be reflected; light cannot
Sound transfers energy; light does not

4 Short Answer Questions

PDF

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C.3 Wave phenomena

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