Properties of Waves

Edexcel 4PH1 awards a mark for the correct unit alongside a numerical answer. For waves you will see:

• angle in degrees (°)
• frequency in hertz (Hz) — 1 Hz = 1 cycle per second
• wavelength / amplitude / displacement in metres (m)
• wave speed in metres per second (m/s)
• period in seconds (s)

Mark-scheme tip. Frequencies in real-life problems are often in kilohertz (kHz = 10³ Hz) or megahertz (MHz = 10⁶ Hz). Convert to Hz BEFORE using $v = f\lambda$ to avoid index errors.

Transverse wave. The particles oscillate at RIGHT ANGLES (perpendicular) to the direction in which the wave transfers energy.

• Examples: all electromagnetic waves (radio → gamma), water-surface ripples, waves on a string, S-waves in seismology.
• Diagram features: clear crests and troughs.

Longitudinal wave. The particles oscillate PARALLEL to (along) the direction of energy transfer.

• Examples: sound waves in any medium (air, water, metal), compressions on a slinky pushed end-on, P-waves in seismology.
• Diagram features: regions of compression (particles bunched) and rarefaction (particles spread out).

Spec 3.2 sentence to memorise. "In a transverse wave the oscillation is perpendicular to the direction of energy transfer; in a longitudinal wave the oscillation is parallel to it." Edexcel mark schemes accept either direction of energy transfer or direction the wave travels.

Edexcel uses five wave descriptors. Learn the exact definitions:

• Amplitude ($A$). Maximum displacement of a point on the wave from its rest position. Unit: m. Bigger amplitude = more energy.
• Wavefront. A line connecting points on a wave at the SAME stage of oscillation (e.g. all on the same crest). Adjacent wavefronts are one wavelength apart.
• Frequency ($f$). Number of complete oscillations per second past a fixed point. Unit: hertz (Hz).
• Wavelength ($\lambda$). Distance between two corresponding points on adjacent oscillations (crest-to-crest or trough-to-trough). Unit: m.
• Period ($T$). Time for one complete oscillation. Unit: s.

Reading a wave diagram.

• For amplitude: measure from the REST line (midpoint between crest and trough) UP to a crest.
• For wavelength: measure between any two equivalent points (peak to next peak).
• Period and frequency are NOT visible directly from a snapshot diagram — you need either an oscilloscope time-base or the wave equation.

Spec statement 3.4 is straightforward but easy to express badly under exam pressure. The mark scheme rewards two ideas:

1. A wave TRANSFERS ENERGY (and information) from source to receiver.
2. A wave does NOT TRANSFER MATTER. Each particle of the medium oscillates about a fixed equilibrium position.

Cork-on-water analogy. Drop a cork on a pond and create ripples. The cork bobs UP and DOWN as the wave passes, but it does NOT travel horizontally with the wave. The wave moves; the water (and the cork) stay put.

Sound analogy. When you talk to a friend, no air is actually delivered from your mouth to their ear. Air molecules oscillate back and forth locally; the pressure wave (disturbance) is what propagates.

Information transfer. Modern examples in spec 3.4 include radio (information encoded in EM waves) and optical fibres (digital data encoded in light pulses). Both transfer information at high rates without transferring any physical material.

The relationship. Wave speed = frequency × wavelength.

$v = f\lambda$

• $v$ = wave speed (m/s).
• $f$ = frequency (Hz).
• $\lambda$ = wavelength (m).

Why it works. In one period $T$, the wave moves one wavelength: $v = \lambda / T$. Since $f = 1/T$, $v = f\lambda$.

Both papers and all wave types (spec 3.7). The same equation applies to:

• Sound: e.g. $v_{\text{sound, air}} \approx 340\,\text{m/s}$, so a 1 kHz tone has $\lambda = 0.34\,\text{m}$.
• Light / EM: $v_{\text{EM, vacuum}} = c = 3 \times 10^{8}\,\text{m/s}$, so green light at 600 nm has $f = c/\lambda = 5 \times 10^{14}\,\text{Hz}$.
• Water ripples: typically a few m/s — depends on water depth.

Rearranging. Use these forms:

• $f = v / \lambda$ (frequency from speed and wavelength).
• $\lambda = v / f$ (wavelength from speed and frequency).

Mark scheme breakdown. A 3-mark calculation typically splits {formula} / {substitution} / {answer with unit}. ECF applies — if you state the formula, you can recover from arithmetic slips later.

Definition. Period $T$ = time for ONE complete oscillation. Frequency $f$ = number of complete oscillations PER SECOND.

Relationship.

$f = \dfrac{1}{T} \quad\Leftrightarrow\quad T = \dfrac{1}{f}$

• $T = 0.020\,\text{s} \Rightarrow f = 50\,\text{Hz}$ (UK mains supply).
• $f = 10^{6}\,\text{Hz} \Rightarrow T = 10^{-6}\,\text{s} = 1\,\mu\text{s}$.

Reading $T$ off an oscilloscope (spec 3.26P-3.27P, Paper 2). Measure the horizontal distance for one complete wave and multiply by the time-base setting (s/div). Then $f = 1/T$.

Pitfall. Standard-form arithmetic trips many candidates: $1/(2 \times 10^{-3}) = 500$, not 0.5 nor 5000. Practise reciprocal calculations.

What it is. When a wave SOURCE moves relative to an observer, the observed frequency (and wavelength) differs from the emitted frequency.

Approaching source. Wavefronts ahead of the source are bunched up → wavelength is SHORTER → observed frequency is HIGHER → sound has a HIGHER PITCH; light is BLUE-SHIFTED.

Receding source. Wavefronts behind the source are stretched out → wavelength is LONGER → observed frequency is LOWER → sound has a LOWER PITCH; light is RED-SHIFTED.

Wave speed unchanged. In a given medium, the wave speed is fixed (set by the medium, not the source). So if $\lambda$ shrinks, $f$ must rise to keep $v = f\lambda$ constant.

Edexcel scope. Spec 3.8 is QUALITATIVE only at 4PH1 — no Doppler formula required. Mark schemes reward:

1. Identifying wavefronts compressed (or stretched).
2. Stating $\lambda$ change.
3. Stating $f$ change.
4. Linking $f$ change to pitch (sound) or colour shift (light).

Cosmology link (Paper 2 only). In topic 8 the red-shift of light from distant galaxies is used as evidence for an expanding universe (spec 8.18P).

Spec 3.9 statement. All waves can be reflected and refracted.

• Reflection. A wave bounces off a barrier. Angle of incidence = angle of reflection (spec 3.15).
• Refraction. A wave changes direction (and wavelength) when it enters a new medium where its speed changes (spec 3.17 onwards).

This statement is the bridge to the next two subtopics — The Electromagnetic Spectrum (covers radio, micro, IR, visible, UV, X, gamma) and Light and Sound (laws of reflection, refraction, refractive index, critical angle, TIR).

Why mention it here? Spec 3.9 is sometimes assessed as a 1-mark "tick all that apply" item: which of the following waves can be reflected/refracted? Answer: ALL of them. Don't be tempted to say 'gamma doesn't refract' — every wave does to some extent.