Waves: revision notes and practice

What you will learn

• Describe transverse and longitudinal waves and distinguish their measurable features.
• Use wave speed, wavelength, frequency and period equations correctly.
• Explain wave measurement, reflection and changes at boundaries.

Key rules

Wave speed

v = fλ. Use frequency f in hertz (Hz), wavelength λ in metres (m), and speed v in m/s.

Rearrange the wave equation

Wavelength λ = v/f and frequency f = v/λ. Convert centimetres to metres by dividing by 100.

Period

Period T = 1/f. Period is the time for one complete cycle, in seconds. Larger frequency means shorter period.

Worked examples

Example 1: A wave has frequency 5 Hz and wavelength 0.8 m. Find its speed.

1. Use v = fλ.
2. v = 5 × 0.8 = 4 m/s.

4 m/s

Example 2: Find the period of a wave with frequency 250 Hz.

1. Use T = 1/f.
2. T = 1 ÷ 250 = 0.004 s.
3. This is exactly 4 ms.

0.004 s

A practice question

A wave has frequency 16 Hz and wavelength 3.5 m. Calculate its wave speed in m/s.

1. A wave transfers energy through a disturbance

A wave is a travelling disturbance that transfers energy without a net transfer of the medium's material with the wave. On a vibrating rope, each small part moves around its rest position while the disturbance travels along the rope. A floating marker can help show the difference between local motion and the travelling pattern.

Mechanical waves need a medium. Sound cannot travel through a vacuum because there are no particles to pass on the disturbance. Electromagnetic waves, including visible light, can travel through a vacuum. Do not assume every wave must involve particles moving from source to receiver.

2. Compare transverse and longitudinal motion

For a transverse wave, oscillations are perpendicular to the direction of energy transfer. A wave on a rope is a clear model. For a longitudinal wave, oscillations are parallel to energy transfer. Sound in air produces alternating compressions, where particles are closer together, and rarefactions, where they are farther apart.

In a spring model, mark one coil and watch it move back and forth while compressions travel along. This avoids confusing particle motion with wave travel. Water-surface ripples are treated as transverse at GCSE, although real surface-particle motion is more complicated than an ideal up-and-down model.

3. Measure wavelength and amplitude separately

Wavelength, λ, is the distance between matching points in adjacent cycles, such as crest to crest or compression to compression. It is measured along the direction of travel. Amplitude is the greatest displacement from the rest position, measured in the direction of the oscillation. Crest-to-trough height is twice the amplitude for a symmetrical wave.

A larger amplitude does not automatically mean a larger wavelength or faster wave. For sound, greater amplitude generally means louder sound; frequency determines pitch. On diagrams, check whether the horizontal axis is position or time before calling a horizontal separation a wavelength.

4. Frequency and period describe the same repetition

Frequency f is the number of complete cycles per second, measured in hertz, Hz. Period T is the time for one complete cycle, measured in seconds. At 20 Hz, 20 cycles happen each second, so one cycle lasts 1/20 = 0.05 s. Higher frequency means shorter period.

Time several cycles to reduce the percentage effect of timing uncertainty: if 10 cycles take 4 s, T = 4/10 = 0.4 s and f = 2.5 Hz. Count complete cycles carefully; five crests seen in one spatial row span four crest-to-crest gaps, not five wavelengths.

T = 1/f; f = 1/T

5. Link speed to frequency and wavelength

In one period the wave pattern travels one wavelength, which leads to v = fλ. A wave with frequency 8 Hz and wavelength 0.25 m travels at 2 m/s. Rearrange to λ = v/f or f = v/λ. Use metres, not centimetres, if speed must be in m/s.

At a fixed speed, doubling frequency halves wavelength. Convert 40 cm to 0.40 m before calculating: at 12 m/s, that wavelength corresponds to 30 Hz. Amplitude is not part of this equation. A large wave drawn on the page need not travel faster than a small one.

v = fλ; v in m/s, f in Hz, λ in m

6. Follow waves at a boundary

At a boundary, some wave energy can be reflected, transmitted or absorbed. For reflection from a flat surface, measure angles from the normal, a line perpendicular to the surface: incidence angle equals reflection angle. A ray diagram represents the travel direction, not the shape of a whole wave.

When a wave enters a medium where its speed differs, its wavelength changes while its frequency stays set by the source. Refraction can change direction if the wave enters at an angle to the normal. Entering along the normal can change speed and wavelength without changing direction. Detailed refraction explanations have Higher requirements in AQA.

7. Put sound and light into context

Sound in air is longitudinal; a vibrating source produces pressure variations. An echo is reflected sound. If using an echo time to estimate distance, divide the sound's total travel distance by two because it travels to the reflecting surface and back. Use the sound speed supplied, since it depends on conditions.

Electromagnetic waves are transverse. All travel at the same speed in a vacuum, approximately 3.0 × 10⁸ m/s, but have different frequencies and wavelengths. Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma describe regions of the spectrum. Detailed uses, hazards, lenses and Higher-only detection examples need further revision beyond this guide.

8. Measure a wave reliably in a practical

In a teacher-supervised ripple-tank investigation, measure the distance across several adjacent crest gaps and divide by the number of gaps. This is more reliable than measuring one small wavelength. Determine frequency from repeated cycles or the vibrator setting, then calculate speed using v = fλ. Keep water depth constant when comparing trials at one speed.

For a vibrating string, note the tension and use the apparatus your teacher specifies. Avoid confusing a stationary pattern with a single travelling wave. Use repeats, a ruler beside the pattern and suitable lighting; describe uncertainty from blurred crests or changing water depth rather than writing only 'the equipment was inaccurate'.

Check your understanding

How to earn the marks

• Name the direction of oscillation relative to travel when comparing wave types.
• Check the diagram's axis: a time axis gives period, a position axis gives wavelength.
• Count wavelength gaps and convert cm or mm before substituting.
• For an echo, remember the outward and return journey; use the given wave speed.

A common mistake

Amplitude is maximum displacement from the rest position; it is different from wavelength and does not appear in v = fλ.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.6.1.1–4.6.1.2; 4.6.2.2

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• Edexcel GCSE Physics — 4.3–4.10; 4.16P–4.17

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Gateway GCSE Physics A — P5.1; PM5.1

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Twenty First Century GCSE Physics B — P1.3–P1.4

  Foundation covers basic wave properties and measurements. Explaining refraction through changing wave speed (P1.3.9–P1.3.10) is Higher content, so Foundation practice uses further calculations and a practical instead.

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