Describing waves: transverse, longitudinal and polarisation

Describing a wave

• Amplitude: maximum displacement from the equilibrium position
• Wavelength λ: distance between two adjacent points in phase (crest to crest)
• Frequency f: number of complete oscillations per second (Hz)
• Period T: time for one complete oscillation; T = 1/f
• Speed v: distance travelled by the wave per second; v = fλ

Transverse and longitudinal

• Transverse: oscillations are perpendicular to the direction of energy transfer (waves on strings, all electromagnetic waves).
• Longitudinal: oscillations are parallel to the direction of energy transfer (sound). Sound consists of compressions (higher pressure, particles closer) and rarefactions (lower pressure, particles further apart), so it can be described by pressure variations or by molecular displacement.

Wave graphs

• Displacement against distance (a snapshot): gives wavelength and amplitude.
• Displacement against time (one point): gives period and amplitude.

For a longitudinal wave, a displacement-distance graph plots each particle's displacement along the direction of travel. Standing waves are drawn as an envelope showing nodes and antinodes.

Polarisation

A wave is plane polarised when its oscillations are in one plane only, the plane containing the direction of travel. Only transverse waves can be polarised, so polarisation of light is evidence that light is transverse. Two Polaroid filters at 90° (crossed) block the light completely.

Worked example

A displacement-time graph for a point on a wave shows 4 complete cycles in 0.020 s. Find the period and frequency.

1. T = 0.020 / 4 = 0.0050 s
2. f = 1 / T = 1 / 0.0050

Answer: T = 5.0 ms; f = 200 Hz

Check yourself

1. Which of these is a longitudinal wave?
   • Light
   • A wave on a guitar string
   • Sound in air
   • Microwaves
   Show answer

   Sound in air. Sound is a series of compressions and rarefactions, with oscillations parallel to its direction.

2. What does the polarisation of light show?
   • Light is a transverse wave
   • Light is a longitudinal wave
   • Light travels at constant speed
   • Light consists of photons
   Show answer

   Light is a transverse wave. Only transverse waves can be polarised.

3. A displacement-time graph shows 3 complete cycles in 0.012 s. Find the frequency in Hz.
   Show answer

   250 Hz. T = 0.012 / 3 = 0.0040 s; f = 1 / 0.0040 = 250 Hz.

4. A snapshot of a wave shows 5 complete wavelengths over a distance of 2.0 m. Find the wavelength in m.
   Show answer

   0.4 m. λ = 2.0 / 5 = 0.40 m.

5. What is the amplitude of a wave?
   • The distance from crest to trough
   • The distance between two crests
   • The number of waves per second
   • The maximum displacement from the equilibrium position
   Show answer

   The maximum displacement from the equilibrium position. Amplitude is measured from the middle (equilibrium) to a crest.

6. Unpolarised light passes through two Polaroid filters whose transmission axes are at 90°. What comes out?
   • The full intensity
   • No light
   • Half of the light
   • Light polarised at 45°
   Show answer

   No light. The first filter polarises the light; the second, at 90°, blocks that plane completely.

7. In a sound wave, what is a compression?
   • A region of lower pressure where molecules are further apart
   • The point of maximum displacement
   • A point where the air does not move
   • A region of higher pressure where molecules are closer together
   Show answer

   A region of higher pressure where molecules are closer together. Compressions are high-pressure regions; rarefactions are low-pressure regions.

8. Which graph lets you read off the wavelength of a wave?
   • Displacement against time
   • Frequency against time
   • Displacement against distance
   • Speed against distance
   Show answer

   Displacement against distance. Wavelength is a distance, so you need distance on the x-axis.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.