Waves in Matter: Synthesis and Exam Skills

You have now met every part of Topic P5 — the two wave types, the wave equation, reflection and refraction, sound, ultrasound and seismic waves, and the electromagnetic spectrum with its uses and dangers. This final lesson pulls those threads together. The skill that earns the most marks in an exam is not knowing each fact in isolation but choosing the right equation, spotting hidden steps (like the there-and-back factor of two), and stringing several ideas into one answer. This lesson, part of Topic P5 (Waves in matter) of OCR Gateway Science A, gathers the key equations, recaps the required practicals, walks through a multi-step problem, and warns of the mistakes that lose marks most often.

By the end of this lesson you should be able to select and apply the P5 equations confidently, recall the required practical methods, avoid the most common exam errors, and tackle a multi-step waves problem from start to finish.

The P5 Equations at a Glance

Three relationships do almost all the calculating in P5. Knowing what each means, and when to reach for it, is half the battle.

Equation	What it finds	Watch out for
$v = f\lambda$	Wave speed from frequency and wavelength	Convert frequency to hertz ( $\text{kHz} \times 1000$ , $\text{MHz} \times 10^6$ )
$T = \dfrac{1}{f}$	Period from frequency (and back)	$f$ in $\text{Hz}$ , $T$ in $\text{s}$ ; check $f \times T = 1$
$\text{distance} = \text{speed} \times \text{time}$	Echo/ultrasound distances	The pulse goes there and back: use $2d = vt$ , so $d = \dfrac{vt}{2}$

Rearranged forms worth knowing:

$v = f\lambda \qquad f = \dfrac{v}{\lambda} \qquad \lambda = \dfrac{v}{f} \qquad T = \dfrac{1}{f} \qquad d = \dfrac{v\,t}{2}$

Two constants to remember: the speed of all EM waves in a vacuum is $3 \times 10^8 \text{ m/s}$ , and the speed of sound in air is about $340 \text{ m/s}$ .

Exam Tip: Before you calculate, write down what you know with units, then pick the equation that contains those quantities. If a time is an echo time, immediately ask whether the wave travelled there and back — if so, the distance is $2d$ .

Recap: The Required Practicals

P5 has one required practical area to know well — measuring the speed of waves — in three forms:

Water waves (ripple tank): find the frequency (from the motor or by counting waves per second) and the wavelength (measure across several waves and divide), then use $v = f\lambda$ .
Waves on a string (vibration generator): read the frequency from the signal generator; each loop is half a wavelength, so find $\lambda$ from the loops, then use $v = f\lambda$ .
Speed of sound (echo or two microphones): clap at a measured distance $d$ from a wall so claps match the echoes; the sound travels $2d$ between claps, so $v = \dfrac{2d}{t}$ . Or time a sound between two microphones a known distance apart.

The recurring good-practice points: measure across many wavelengths (or time many intervals) and divide, to reduce the percentage uncertainty, and repeat and take a mean to improve reliability.

Exam Tip: In any "measure the speed of a wave" question, the plan is nearly always find $f$ , find $\lambda$ , then $v = f\lambda$ — except the sound-echo method, which measures speed directly from $2d$ and $t$ . Always include one precision point (measure several wavelengths; use a large distance) for the final mark.

The Electromagnetic Spectrum at a Glance

It is worth fixing the order, properties and key uses/dangers in one place.

Order (low to high frequency): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Shared by all: transverse; transfer energy; travel at $3 \times 10^8 \text{ m/s}$ in a vacuum; can cross a vacuum.
Trend: from radio to gamma, frequency and energy increase, wavelength decreases.
Ionising (and most dangerous): ultraviolet, X-rays, gamma — damage cells, mutate DNA, cause cancer.

graph LR
  R[Radio] --> M[Microwave]
  M --> I[Infrared]
  I --> V[Visible]
  V --> U[Ultraviolet]
  U --> X[X-ray]
  X --> G[Gamma]

Reading left to right above, frequency and energy increase and wavelength decreases, with the ionising waves (ultraviolet, X-ray, gamma) at the right-hand end.

A Worked Multi-Step Problem

Exam questions often chain several P5 ideas together. Here is a worked example that uses the wave equation, the period, and the there-and-back echo idea in one go.

Worked Example — A boat, an echo and a wave

A boat floats on the sea. The waves passing it have a wavelength of $6 \text{ m}$ , and the boat rises and falls, completing one full bob every $3 \text{ s}$ .

(a) Calculate the frequency of the water waves. (b) Calculate the speed of the water waves. (c) The boat then uses sonar to find the depth of the sea. It sends an ultrasound pulse downwards and receives the echo $0.16 \text{ s}$ later. The speed of sound in seawater is $1500 \text{ m/s}$ . Calculate the depth of the sea.

Part (a) — frequency from the period:

Step 1 — the time for one full bob is the period: $T = 3 \text{ s}$ .

Step 2 — use $f = \dfrac{1}{T}$ : $f = \dfrac{1}{3} = 0.33 \text{ Hz}$ (to 2 significant figures).

Answer (a): the frequency is $0.33 \text{ Hz}$ .

Part (b) — speed from the wave equation:

Step 1 — use $v = f\lambda$ with $f = \dfrac{1}{3} \text{ Hz}$ and $\lambda = 6 \text{ m}$ .

Step 2 — substitute and calculate: $v = \dfrac{1}{3} \times 6 = 2 \text{ m/s}$ .

Answer (b): the water waves travel at $2 \text{ m/s}$ .

Part (c) — depth from the echo:

Step 1 — find the total distance the pulse travels: $\text{distance} = v \times t = 1500 \times 0.16 = 240 \text{ m}$ .

Step 2 — the pulse went to the sea bed and back, so halve it: $d = \dfrac{240}{2} = 120 \text{ m}$ .

Answer (c): the sea is $120 \text{ m}$ deep.

Notice how each part used a different P5 tool — the period link in (a), the wave equation in (b), and the there-and-back echo in (c) — and how part (c) would have given the wrong answer ( $240 \text{ m}$ ) without halving.

Exam Tip: In a multi-part question, an answer from one part often feeds into the next (here, the frequency from (a) is used in (b)). Carry the unrounded value forward where you can, and only round at the very end, to avoid rounding errors building up.

The Most Common P5 Exam Mistakes

Learning what trips students up is one of the fastest ways to gain marks. The biggest P5 errors are:

Waves in Matter: Synthesis and Exam Skills

Waves in Matter: Synthesis and Exam Skills

The P5 Equations at a Glance

Recap: The Required Practicals

The Electromagnetic Spectrum at a Glance

A Worked Multi-Step Problem

Worked Example — A boat, an echo and a wave

The Most Common P5 Exam Mistakes

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