Wave model

A disturbance that carries **energy** from place to place **without** the medium itself travelling along with it.

The length of **one full wave** (e.g. crest to crest). Read it off a displacement-**distance** graph. Unit: metre (m).

The **maximum displacement** from the middle (rest) position — NOT crest to trough. Unit: metre (m).

The **time for one full wave** to pass a point. Read it off a displacement-**time** graph. Unit: second (s).

The **number of waves per second**. Unit: hertz (Hz), where 1 Hz = 1 per second.

$v = f\lambda$ — speed = frequency × wavelength. **Given** in the data booklet.

They are reciprocals: **f = 1/T** (and T = 1/f). Both are **given** in the data booklet.

$v = \dfrac{\lambda}{T}$ — since f = 1/T, speed = wavelength ÷ period.

Wavelength from a displacement-**distance** graph; period from a displacement-**time** graph. Always check the axis label.

v = f λ = 200 × 1.7 = 340 m s⁻¹.

v = λ ÷ T = 0.50 ÷ 0.0020 = 250 m s⁻¹.

Reading the wavelength off a **time** graph (or the period off a **distance** graph) — and forgetting to convert ms or kHz before substituting.

It **oscillates about its rest position**; it does not travel with the wave. Only the energy moves along.

**One wavelength λ**, which is why v = λ/T = fλ.

The **energy it transfers each second**: the energy in one wavelength passes a point every period.

A wave in which the particles vibrate **perpendicular** (at right angles) to the direction the wave travels. Example: light.

A wave in which the particles vibrate **parallel** (back and forth along the same line) to the direction the wave travels. Example: sound.

Transverse: **light** (and a wave on a rope). Longitudinal: **sound** (and a push-pull on a spring).

**Crests** (highest points) and **troughs** (lowest points).

**Compressions** (particles bunched together, high pressure) and **rarefactions** (particles spread apart, low pressure).

**No** — the particles vibrate on the spot about their rest position; only the **energy** moves along.

The **amplitude** (peak displacement) and the **period T** (the repeat time). Then f = 1/T.

The **amplitude** and the **wavelength λ** (one full repeat along the distance axis).

Check the **x-axis**: distance → snapshot → read the **wavelength**; time → one particle → read the **period**.

The point copies the displacement of the point just **behind** it (the side the wave came from). Wave moving right → look just to the **left**.

$v = f\lambda = \dfrac{\lambda}{T}$ — **given** in the data booklet.

About **four amplitudes** (rest → top → rest → bottom → rest), so average particle speed ≈ 4 × amplitude ÷ T.

Where the graph **crosses zero going down** (left to right): particles on both sides move towards it.

A **longitudinal mechanical wave**: compressions and rarefactions of pressure. It needs a **medium**; no sound in a vacuum.

The one at the **rest line** (zero displacement); particles at crests and troughs are momentarily still.

A **transverse** wave of vibrating electric and magnetic fields (light is one example). It needs **no medium** and travels through a vacuum.

They **all** travel at the same speed, **c = 3.00 × 10⁸ m s⁻¹** (the speed of light), whatever their region.

**Transverse** — the fields oscillate at right angles to the direction the wave travels.

**Radio → microwave → infrared → visible → ultraviolet → X-ray → gamma.** Wavelength falls, frequency and energy rise.

**Radio** — longest wavelength, lowest frequency, lowest energy. **Gamma** is the opposite end.

$c = f\lambda$ — speed of light = frequency × wavelength. Rearrange to $f = c/\lambda$ or $\lambda = c/f$. **Given** in the data booklet.

Sound **needs a medium** (it is mechanical); an EM wave **crosses a vacuum**. Also: sound is longitudinal, EM is transverse; EM is far faster.

EM wave: **electric and magnetic fields**. Sound wave: the **particles of the medium** (e.g. air molecules).

An **X-ray** (very short wavelength ⇒ very high frequency, about 10¹⁸ Hz).

Thinking different colours or regions travel at **different speeds** — in a vacuum they all travel at c.

The **speed of light c** — because $c = f\lambda$ rearranges to $f = c(1/\lambda)$, a straight line through the origin.

All **at right angles** to one another; E and B oscillate in phase.

About **10⁻⁶ – 10⁻⁴ m** (700 nm to 1 mm), so f ≈ 10¹² – 10¹⁴ Hz.

**Out of the page**: right hand, fingers along E, curl to B, thumb along the travel.

A line (or surface) joining all the points of a wave that are **in phase** — for example, all the crests.

A line showing the **direction in which the wave travels**, drawn at **right angles** to the wavefronts.

Two points are **in phase** if they are at the **same point in their cycle** at the same time (e.g. both at a crest).

The ray is always **perpendicular (90°)** to the wavefronts — the wave advances along the ray.

Exactly **one wavelength, λ** (crest to next crest).

Measure the gap between **two neighbouring wavefronts** — that distance is λ.

**Circles** (or spheres in 3D) spreading out from the source.

Straight, parallel lines — called **plane wavefronts**.

$v = f\lambda$ — wavelength λ (the spacing) × frequency f = wave speed v. **Given** in the data booklet.

λ = 0.50 m, f = 3.0 Hz, so v = fλ = 3.0 × 0.50 = 1.5 m s⁻¹.

Drawing it **along** a wavefront instead of **across** it — the ray must cross the wavefronts at 90°.

As **straight arrows pointing outwards** from the source, each crossing the circular wavefronts at 90°.

**Parallel** arrows, all at 90° to the straight wavefronts.

v = fλ = 20 × 0.030 = **0.60 m s⁻¹**.