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Drop a pebble into a still pond and rings of ripples spread out across the surface. A leaf floating there bobs up and down as each ripple passes, but it does not travel across the pond with the wave — it finishes roughly where it started. That single observation captures the most important idea in this whole topic: a wave transfers energy from one place to another without transferring matter. The ripple carries energy across the water, yet the water itself (and the leaf riding on it) stays put, simply moving up and down as the disturbance goes by. This lesson opens Topic P4 (Waves and radioactivity) of OCR Gateway Combined Science A by sorting waves into two great families — transverse and longitudinal — defining the quantities used to describe every wave, and treating sound as our everyday example of a longitudinal wave.
By the end of this lesson you should be able to describe the difference between transverse and longitudinal waves, give examples of each (including sound), define amplitude, wavelength, frequency, period and wavefront, explain that waves transfer energy and not matter, and use the relationship T=f1 to connect period and frequency.
This lesson is mostly AO1 recall and understanding of wave types and terms, with AO2 application when you use T=f1 to connect period and frequency in a calculation.
A wave is a disturbance that travels through a material (or through space), carrying energy from one place to another. The key point — the one examiners return to again and again — is that a wave moves energy along, not matter. The particles of the material (the water, the air, the rope) oscillate (vibrate back and forth) about a fixed position as the wave passes, but they are not carried along with it.
Picture again the leaf on the pond, or a duck sitting on the sea: as waves roll past, the duck rises and falls but is not swept out to sea. The water particles move up and down about their resting places; the wave pattern travels forward, but the water stays where it is. Energy has crossed the surface, yet no water has been transported.
Exam Tip: If you remember only one fact about waves, make it this: waves transfer energy, not matter. The particles of the material oscillate about a fixed point; they do not travel with the wave. This one sentence answers a surprising number of P4 questions.
In a transverse wave, the oscillations (vibrations) are perpendicular — at right angles, 90° — to the direction in which the wave transfers energy. In other words, the parts of the material move up and down (or side to side) while the wave itself travels along at right angles to that movement.
Imagine shaking one end of a long rope up and down: a wave travels along the rope from your hand outwards, but each part of the rope moves up and down, across the direction of travel. The high points of the wave are called crests (peaks) and the low points are called troughs.
Examples of transverse waves:
In a longitudinal wave, the oscillations are parallel to — along the same line as — the direction in which the wave transfers energy. The parts of the material move backwards and forwards along the same direction that the wave is travelling.
The classic model is a slinky spring pushed and pulled along its length. As you push the end in and out, regions where the coils are squashed together travel along the spring, separated by regions where the coils are stretched apart. The squashed-together regions are called compressions (the particles are close together and the pressure is high); the stretched-apart regions are called rarefactions (the particles are spread out and the pressure is low). A longitudinal wave is therefore a travelling pattern of compressions and rarefactions.
Examples of longitudinal waves:
Exam Tip: Get the two definitions word-perfect. Transverse: oscillations perpendicular to the direction of energy transfer. Longitudinal: oscillations parallel to the direction of energy transfer. Many students lose marks with a vague "up and down" — always name the direction of energy transfer as well.
The diagram below shows a transverse wave (top) with its crests and troughs, and a longitudinal wave (bottom) with its compressions and rarefactions. In both, the wave transfers energy to the right, but the direction of the oscillations is different.
| Feature | Transverse wave | Longitudinal wave |
|---|---|---|
| Direction of oscillation | Perpendicular to energy transfer | Parallel to energy transfer |
| Wave shape | Crests and troughs | Compressions and rarefactions |
| Examples | Water, all EM waves | Sound |
| Can travel through a vacuum? | EM waves can; water waves need a medium | No — always needs a medium |
Exam Tip: A longitudinal wave cannot travel through a vacuum because it needs particles to compress and rarefy. Electromagnetic waves, which are transverse, can travel through a vacuum — that is how light and radio reach us from the Sun and from satellites.
Whatever family a wave belongs to, we describe it using the same set of measurements. They are easiest to picture on a transverse wave, but they describe longitudinal waves too.
Amplitude (A) is the maximum displacement of a point on the wave from its rest (undisturbed) position. On a transverse wave it is the height of a crest (or the depth of a trough) measured from the centre line — not the full distance from a crest down to a trough. The amplitude tells you how much energy the wave carries: a bigger amplitude means more energy. It is measured in metres (m).
Wavelength (λ) is the distance of one complete wave cycle — for example, from one crest to the next crest, or from one compression to the next compression. The symbol is the Greek letter lambda, λ, and it is measured in metres (m).
Frequency (f) is the number of complete waves (cycles) passing a point each second. It is measured in hertz (Hz): a frequency of 1 Hz means one wave passes each second, and 50 Hz means fifty waves pass each second.
Period (T) is the time taken for one complete wave to pass a point, measured in seconds (s). It is simply the time for a single cycle.
Wavefront — a wavefront is a line (or surface) joining all the points on a wave that are in step with one another, such as a line running along the top of a crest. The ripples spreading from a stone are circular wavefronts; far from the source, wavefronts look like straight parallel lines. Wavefronts are always drawn at right angles to the direction the wave is travelling, and neighbouring wavefronts are one wavelength apart.
The diagram below labels the amplitude and wavelength on a transverse wave.
Exam Tip: Amplitude is measured from the rest position to a crest — half the total crest-to-trough height. A very common misconception is to read the full peak-to-trough distance and call it the amplitude; that is twice the amplitude.
The most familiar longitudinal wave is sound. When an object vibrates — a loudspeaker cone, a guitar string, your vocal cords — it pushes and pulls on the air next to it. Pushing forward squashes the air particles into a compression (high pressure); pulling back leaves them spread apart in a rarefaction (low pressure). These compressions and rarefactions travel outward through the air as a sound wave, with the air particles oscillating back and forth along the same direction the wave travels.
As with every wave, the air particles themselves do not travel from the source to your ear; they merely oscillate about their fixed positions, passing the energy along from one particle to the next. A voice reaches you across a room as energy carried by the air, not as air blown from the speaker's mouth into your ear.
Because sound is carried by vibrating particles, it must travel through a medium — a solid, liquid or gas — and it cannot travel through a vacuum, because there are no particles to compress and rarefy. This is the classic bell-in-a-jar demonstration: as the air is pumped out of a sealed jar containing a ringing electric bell, the sound fades to nothing even though you can still see the hammer striking, because there is less and less air to carry the sound.
Two properties of a sound wave decide how we perceive it. The frequency controls the pitch — how high or low the note sounds. A high frequency gives a high-pitched note (a whistle); a low frequency gives a low-pitched note (a bass drum). The amplitude controls the loudness — a large amplitude gives a loud sound (it carries more energy), while a small amplitude gives a quiet one.
Exam Tip: Keep the two sound links separate. Frequency controls pitch; amplitude controls loudness. A frequent slip is to claim a louder sound has a higher frequency — it does not; a louder sound simply has a bigger amplitude.
Frequency and period describe the same behaviour from two angles. Frequency counts how many waves pass each second; period measures how long a single wave takes. They are reciprocals of each other:
T=f1andf=T1
where T is the period in seconds and f is the frequency in hertz. If many waves pass each second (high frequency), each one takes only a short time (small period); if few pass each second (low frequency), each takes longer.
A wave has a frequency of 50 Hz. Calculate its period.
Step 1 — write the equation: T=f1.
Step 2 — substitute: T=501.
Step 3 — calculate: T=0.02 s.
Answer: the period is 0.02 s — each wave takes one-fiftieth of a second to pass.
A wave source produces one complete wave every 0.25 s. Calculate the frequency.
Step 1 — write the equation: f=T1.
Step 2 — substitute: f=0.251.
Step 3 — calculate: f=4 Hz.
Answer: the frequency is 4 Hz — four complete waves pass each second.
Exam Tip: A quick check on any T=f1 calculation: frequency in Hz and period in s should multiply to give 1 (f×T=1). If they do not, you have slipped somewhere.
It is worth returning to the central idea one more time, because it underlies the whole topic. When a wave travels:
The evidence is all around. A cork bobs but stays put as ripples pass; sound carries a voice across a room without any air being blown from speaker to listener; sunlight delivers energy across 150 million kilometres of empty space, yet no matter crosses that gap. In every case, energy is transferred while the matter stays (on average) in place. This is exactly what separates a wave from, say, a thrown ball or a flowing river, in which matter itself moves from one place to another.
Question (6 marks): A student says "all waves are the same — they just move stuff from one place to another." Using transverse and longitudinal waves as examples, explain what is wrong with this statement and how the two types of wave differ.
Mid-band response: "The student is wrong because waves carry energy, not stuff. A transverse wave moves up and down, like water. A longitudinal wave is like sound, with squashed bits."
Examiner-style commentary: The key idea (energy, not matter) is present, and the two examples are correct, but the descriptions are vague. To climb a band, define each wave type by the direction of oscillation relative to energy transfer, and name crests/troughs and compressions/rarefactions.
Stronger response: "The student is wrong: a wave transfers energy from place to place, but the particles of the material just oscillate about a fixed point and do not travel with the wave. In a transverse wave, like water or light, the oscillations are perpendicular to the direction the wave travels, giving crests and troughs. In a longitudinal wave, like sound, the oscillations are parallel to the direction of travel, giving compressions and rarefactions."
Examiner-style commentary: A clear, correct answer with the right definitions and examples. To reach the top band, state explicitly that the particles return to their starting positions, and add that longitudinal waves need a medium whereas electromagnetic transverse waves can cross a vacuum.
Top-band response: "The statement is wrong because a wave does not move matter from place to place — it transfers energy. As a wave passes, the particles of the material oscillate about a fixed position and return to where they started; only the energy (and the wave pattern) travels onward. The two families differ in the direction of oscillation relative to the direction of energy transfer. In a transverse wave — such as a water wave or any electromagnetic wave — the oscillations are perpendicular to the direction of energy transfer, producing crests and troughs. In a longitudinal wave — such as a sound wave — the oscillations are parallel to the direction of energy transfer, producing compressions (particles squashed together) and rarefactions (particles spread apart). A further difference is that a longitudinal wave always needs a medium of particles, whereas electromagnetic transverse waves can travel through a vacuum."
Examiner-style commentary: Full marks. It corrects the misconception with the energy-not-matter principle, gives the precise definition of each wave type relative to the energy-transfer direction, names the correct features and examples, and adds the vacuum distinction — a complete comparison.
This content is aligned with OCR Gateway Combined Science A (J250), Topic P4 Waves and radioactivity. Refer to the official OCR specification for exact wording.