OCR GCSE Physics A: Wave properties, transverse and longitudinal waves (J249)

This guide teaches statements P5.1a, P5.1b, P5.1c, P5.1d, P5.1e, P5.1j and P5.1k of the OCR GCSE (9-1) Gateway Science Physics A specification (J249, Version 5.0, July 2026), within topic P5.1 Wave behaviour. The specification does not print any of them in bold, so Foundation and Higher Tier papers can both test them. Use the revision notes for quick recall and the practice set for questions. Course pages are at the OCR GCSE Physics hub and the printable checklist. If you are unsure where to start, try the free 10-minute diagnostics.

What you must be able to do

Statement	Outcome	Tier
P5.1a	Describe wave motion using amplitude, wavelength, frequency and period	Both tiers
P5.1b	Define wavelength and frequency	Both tiers
P5.1c	Describe and apply the relationship between wavelength, frequency and wave velocity	Both tiers
P5.1d	Apply formulae relating velocity, frequency and wavelength	Both tiers
P5.1e	Describe differences between transverse and longitudinal waves, in terms of direction of travel and direction of vibration	Both tiers
P5.1j	Describe how ripples on water model transverse waves and sound in air is longitudinal, and how the speed of each may be measured	Both tiers
P5.1k	Describe evidence that it is the wave that travels, not the water or the air	Both tiers

P5.1a and P5.1b: describing a wave

A wave transfers energy from one place to another. The material it passes through is the medium. Each part of the medium vibrates about a fixed rest position while the wave goes by.

Four quantities describe a wave.

• Amplitude is the maximum displacement of a point on the wave from its rest position. For a water ripple it is the height of a crest above the undisturbed surface. Measure it from the middle line, not from trough to crest. A larger amplitude means the wave carries more energy.
• Wavelength (symbol λ, measured in metres) is the length of one complete wave. Crest to crest is the usual choice. Trough to trough is equally good.
• Frequency (symbol f, measured in hertz, Hz) is the number of waves passing a point each second. It is also the number of vibrations each point of the medium makes in one second. 1 Hz is one wave per second.
• Period (symbol T, measured in seconds) is the time taken for one complete wave to pass a point. One complete vibration takes one period.

Period and frequency are linked. If 5 waves pass each second, each takes one fifth of a second:

T = 1 ÷ f and f = 1 ÷ T

For P5.1b, learn the definitions: wavelength is the length of one complete wave, measured between matching points such as neighbouring crests, and frequency is the number of waves passing a point per second.

Two graphs that look alike

The specification lists a common misconception: learners misread distance and displacement-time graphs of waves. Both show a smooth up-and-down curve, so check the horizontal axis.

Graph	Horizontal axis	What it shows	What you can read off
Displacement against distance	Distance along the wave	A snapshot of the whole wave at one moment	Wavelength (one full cycle along the axis), amplitude
Displacement against time	Time	The motion of one point as time passes	Period (one full cycle along the axis), amplitude

Amplitude is the same on both: the greatest height above the middle line. Wavelength appears only on the distance graph, and period only on the time graph. An oscilloscope trace of a sound is a displacement-time graph, so a gap between neighbouring peaks is a time, not a length. The specification suggests observing sound waves on an oscilloscope as a practical.

Worked example 1: a wave on a rope. A rope is flicked at 5.0 Hz. A photograph shows the crests are 0.36 m apart.

Wavelength: λ = 0.36 m (crest to crest)

Period: T = 1 ÷ 5.0 = 0.20 s

P5.1c and P5.1d: the wave speed equation

In one second, f waves pass a point and each is λ long. The wave therefore moves a distance of f × λ in each second. That distance per second is the wave speed (velocity):

v = f × λ

Here v is in m/s, f is in Hz and λ is in m.

The mathematical outcomes in the specification list this relationship as one to recall and apply. Rearranged:

f = v ÷ λ and λ = v ÷ f

For any calculation, write down what you are given, convert units (kHz × 1000 for Hz, cm ÷ 100 or mm ÷ 1000 for m, ms ÷ 1000 for s), then substitute and give a unit.

Worked example 2: wavelength from frequency. A sound has frequency 1.7 kHz. Take the speed of sound in air to be 340 m/s (data supplied).

f = 1.7 kHz = 1700 Hz

λ = v ÷ f = 340 ÷ 1700 = 0.20 m

Worked example 3: frequency from a trace. An oscilloscope trace of a note shows 5 complete waves across a time of 12.5 ms.

Time for one wave: T = 12.5 ms ÷ 5 = 2.5 ms = 0.0025 s

f = 1 ÷ T = 1 ÷ 0.0025 = 400 Hz

With sound travelling at 340 m/s: λ = 340 ÷ 400 = 0.85 m

Worked example 4: rearranging for frequency. Ripples on a pond move at 0.24 m/s and have wavelength 8.0 mm. Find the frequency.

λ = 8.0 mm = 0.0080 m

f = v ÷ λ = 0.24 ÷ 0.0080 = 30 Hz

If the speed stays the same, doubling the frequency halves the wavelength.

P5.1e: transverse and longitudinal waves

The specification says to include direction of travel and direction of vibration. Those two directions are what separate the two types.

	Transverse wave	Longitudinal wave
Vibration direction	At right angles (90 degrees) to the direction of travel	Parallel to the direction of travel (back and forth along it)
Pattern	Crests and troughs	Compressions (particles close together) and rarefactions (particles spread out)
Wavelength measured	Crest to crest	Compression to compression
Examples	Ripples on water, a wave on a rope, light	Sound in air, a push-pull pulse along a slinky

The specification suggests using a slinky spring to model waves. Stretch it along a bench. Move one end sideways and a transverse pulse runs along it. Push the end in and out along the spring and a longitudinal pulse runs along it, with bunched coils (compressions) and stretched coils (rarefactions) moving along.

In both cases the coils themselves end up where they started. Tie a ribbon to one coil: it shifts sideways or forward and back, and then returns.

P5.1j: ripples, sound and measuring their speeds

Ripples model transverse waves

Water ripples are a convenient way to see a wave. When ripples spread, the water surface moves up and down while the ripples travel outwards across it. The vibration (up and down) is at right angles to the travel (outwards), so ripples are transverse. That makes them a useful model for other transverse waves.

Sound in air is different. A loudspeaker cone moves in and out. It pushes on the air next to it, and each layer of air then pushes the next. The air vibrates back and forth along the direction the sound travels, so sound is longitudinal. You cannot see sound, which is why ripples help as a model.

Measuring the speed of ripples

Method 1: use v = f λ.

1. In a ripple tank, a motor-driven dipper makes waves at a known frequency. Read f from the motor setting or count the ripples passing a mark for a measured time (for example 9 ripples in 3.0 s gives 3.0 Hz).
2. Light the tank from above so the crests show on a sheet below. Measure the distance across several wavelengths with a ruler, then divide by the number of wavelengths. This reduces the error from reading one small distance.
3. Calculate v = f λ.

Method 2: use speed = distance ÷ time, timing one crest between two marks a measured distance apart.

Worked example 5. Six wavelengths of ripples span 0.21 m on the screen. Nine ripples pass a mark in 3.0 s.

λ = 0.21 ÷ 6 = 0.035 m

f = 9 ÷ 3.0 = 3.0 Hz

v = f λ = 3.0 × 0.035 = 0.105 m/s, or 0.11 m/s to 2 significant figures

Measuring the speed of sound in air

Sound is fast, so the times are short. Three approaches work.

• Echo method. Stand a measured distance d from a large wall. Make a sharp sound and time how long it takes the echo to come back. The sound travels there and back, so the distance is 2d: speed = 2d ÷ t. Repeat and average, as hand timing is poor over short intervals.
• Two microphones and a timer. Place two microphones a measured distance apart in a line from a source. A timer records the time between the pulse reaching one microphone and the other. Speed = distance ÷ time. Electronic timing removes human reaction time.
• Oscilloscope and wavelength. A signal generator drives a loudspeaker at a known frequency. A microphone connected to an oscilloscope is moved away from the speaker until its trace shifts by one whole wave. The distance moved is one wavelength, so v = f λ.

Worked example 6: echo. A pupil stands 51 m from a wall. The echo returns 0.30 s after a clap.

Distance travelled = 2 × 51 = 102 m

v = 102 ÷ 0.30 = 340 m/s

Worked example 7: timing gates. Two microphones are 1.50 m apart. The timer shows 4.4 ms between them.

t = 4.4 ms = 0.0044 s

v = 1.50 ÷ 0.0044 = 340.9 m/s, so 340 m/s to 2 significant figures

P5.1k: the wave travels, the medium does not

The specification asks for evidence that it is the wave that travels and not the water or the air.

Ripples. Float a cork or a small piece of polystyrene on the water in a ripple tank. When ripples pass, the cork bobs up and down, and also sways slightly, but stays in about the same place. If the water itself flowed outwards, the cork would be swept to the edge. Instead the ripples cross the tank while the water at each place only vibrates. A Mexican wave in a stadium is a good picture: the wave runs round the ground while each person only stands up and sits down in the same seat.

Sound in air. If the air itself travelled from a loudspeaker to you, you would feel a steady wind, and smoke or light dust would be blown towards you. Instead you hear the sound while the air at your ear is no windier, and smoke near a speaker just shakes back and forth about its position. The air particles vibrate to and fro and pass the vibration on. The slinky shows the same thing: a compression runs the length of the spring, but each coil only moves a short distance and returns.

What does travel is the disturbance, which carries energy. This is why a wave is described as a way of transferring energy without transferring matter.

Common errors

• Measuring amplitude from trough to crest. It is the height from the middle line to a crest (or trough).
• Reading a wavelength from a displacement-time graph, or a period from a displacement-distance graph.
• Forgetting to convert kHz, cm or ms before substituting into v = f λ.
• Calling a longitudinal wave “up and down”. It vibrates along the direction of travel.
• Using the distance to the wall instead of twice that distance in an echo calculation.
• Writing that the water or air “travels with the wave”. Say that it vibrates about a fixed position.

Official syllabus

OCR, GCSE (9-1) Gateway Science Physics A (J249). Specification Version 5.0, July 2026; first assessment 2018. Topic P5.1 Wave behaviour, statements P5.1a to P5.1e, P5.1j and P5.1k.