The wave model
🎯What you need to be able to do
- Distinguish transverse from longitudinal waves and give examples of each.
- Use wavelength, frequency, period, amplitude and wave speed, and apply \( c = f\lambda \).
- Read both displacement–distance and displacement–time graphs, and say which quantity each one gives.
- Use wavefronts and rays.
- Describe sound as a longitudinal wave and place the parts of the electromagnetic spectrum in order.
📚The physics
A wave transfers energy without transferring matter. That sentence is the whole model in one line, and it is worth taking seriously: the duck on a passing ripple bobs up and down and stays where it is. The water does not travel; the disturbance does.
Transverse waves oscillate perpendicular to the direction of energy transfer — waves on a string, water surface waves, and all electromagnetic waves. Longitudinal waves oscillate parallel to it, producing compressions and rarefactions — sound is the standard example. Only transverse waves can be polarised, which is a useful way to tell the two apart experimentally.
The quantities, and where each is measured. Amplitude is the maximum displacement from equilibrium. Wavelength \(\lambda\) is the distance between adjacent points in phase. Period \(T\) is the time for one complete oscillation, and \( f = 1/T \). They connect through
which is really just “distance over time” in disguise: one wavelength travels past in one period.
The most useful consequence of \( c = f\lambda \) is what happens when a wave crosses into a new medium. The frequency is set by the source and cannot change. The speed is set by the medium and does change. So the wavelength must change to compensate. Light entering glass slows down and its wavelength shortens; its colour, which is frequency, stays the same. Students who assume frequency changes get refraction questions wrong for the rest of the theme.
Two graphs that look identical and mean different things. A displacement–distance graph is a snapshot of the whole wave at one instant; the distance between repeats is the wavelength. A displacement–time graph follows a single point as time passes; the distance between repeats is the period. Always read the axis label before measuring anything — this is the single most common careless error in the wave topics.
Wavefronts and rays are two views of the same thing. A wavefront joins points in phase, such as the crest lines of a ripple; a ray is a line showing the direction of energy travel. Rays are always perpendicular to wavefronts. Wavefronts are more natural for interference and diffraction; rays are more natural for reflection and refraction.
Sound travels as a longitudinal pressure wave and needs a medium — a bell in a vacuum jar goes silent while remaining visible, which is a neat demonstration of the difference between sound and light. It travels faster in solids than in liquids, and faster in liquids than in gases, because the particles are more closely coupled.
The electromagnetic spectrum is one family of transverse waves, all travelling at \( 3.0 \times 10^{8} \) m s\(^{-1}\) in a vacuum, differing only in frequency. In order of increasing frequency and decreasing wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Within the visible band, red has the longest wavelength and violet the shortest.
✏️Worked example
(a) Amplitude and wavelength. Amplitude is 4.0 cm, read from the graph as displacement from equilibrium, not peak to trough. Wavelength is 0.80 m — and it is a wavelength rather than a period because the horizontal axis is distance.
(b) Frequency and period. \( f = 15/6.0 = 2.5 \) Hz, so \( T = 1/2.5 = 0.40 \) s.
(c) Wave speed. \( c = f\lambda = 2.5 \times 0.80 = 2.0 \) m s\(^{-1}\).
(d) The rope is replaced by a heavier one on which the wave travels at 1.2 m s\(^{-1}\), driven by the same oscillator. What is the new wavelength? The oscillator fixes the frequency at 2.5 Hz, so \( \lambda = c/f = 1.2/2.5 = 0.48 \) m. The wave is slower and shorter, but not lower in pitch.
🔭See it happen
PhET, Wave on a String. Set it to oscillate, then change the tension while leaving the frequency alone, and watch the wavelength stretch and shrink while the driver keeps its rhythm. That is part (d) happening in front of you.
📝Practise
Work through these, then reveal the answer. Each question targets a different objective from the list above.
1. A tuning fork of frequency 512 Hz sounds in air where the speed of sound is 340 m s\(^{-1}\). Find the wavelength.
2. Light of wavelength 600 nm in air enters glass of refractive index 1.5. Find its speed and wavelength in the glass, and state what happens to its frequency.
3. A wave has a frequency of 50 Hz. Find its period.
4. You are given a graph of displacement against distance and another of displacement against time for the same wave. State which quantity you can read from each.
5. List the electromagnetic spectrum in order of increasing frequency, and state which end has the longer wavelength.
6. An FM radio station broadcasts at 95.0 MHz. Find the wavelength of the waves.
🔗Go deeper — other people’s work
These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.
- The Physics Classroom — Waves, and Sound Waves and Music
- The Physics Hypertextbook — waves and the electromagnetic spectrum