GCSE — physicsFoundational5 min read

Properties of Waves

Amplitude, wavelength, frequency, period; v = fλ; transverse vs longitudinal

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# Properties of Waves — GCSE Physics

Waves are everywhere — from the light that lets you see, to the sound that lets you hear, to the seismic waves that shake the ground during earthquakes. Understanding wave properties is essential for GCSE Physics.

1. What Is a Wave?

A wave is a disturbance that transfers energy from one place to another without transferring matter.

Key idea: the particles of the medium vibrate about their rest position but do not travel with the wave. Only the energy moves.

Example: A Mexican wave in a stadium — people stand up and sit down (vibrate), but nobody moves along the row. The wave pattern moves, not the people.

2. Types of Waves

2.1 Transverse Waves

In a transverse wave, the oscillations (vibrations) are perpendicular (at right angles) to the direction of energy transfer.

Examples:

  • Light and all electromagnetic waves
  • Water waves (on the surface)
  • Waves on a string or rope
  • S-waves (seismic)

Visualise: shake a rope side to side — the wave travels along the rope, but each point moves up and down.

2.2 Longitudinal Waves

In a longitudinal wave, the oscillations are parallel to the direction of energy transfer.

The wave consists of compressions (particles close together) and rarefactions (particles spread apart).

Examples:

  • Sound waves
  • Ultrasound
  • P-waves (seismic)
  • Waves in a slinky spring pushed and pulled

Visualise: push and pull a slinky — the coils bunch up (compressions) and spread out (rarefactions) along the direction of travel.

3. Wave Properties

Property Symbol Definition Unit
Amplitude AA Maximum displacement from the rest position metres (m)
Wavelength λ\lambda Distance between two consecutive identical points (e.g., crest to crest) metres (m)
Frequency ff Number of complete waves passing a point per second hertz (Hz)
Period TT Time for one complete wave to pass a point seconds (s)
Wave speed vv Speed at which the wave travels m/s

Amplitude

  • Measured from the rest position to the crest (or trough)
  • NOT from crest to trough (that's twice the amplitude)
  • Greater amplitude = more energy carried by the wave
  • For sound: greater amplitude = louder
  • For light: greater amplitude = brighter

Wavelength (λ\lambda)

  • Crest to crest, or trough to trough, or any point to the next identical point
  • For longitudinal waves: compression to compression, or rarefaction to rarefaction

Frequency (ff) and Period (TT)

f=1TT=1f\boxed{f = \frac{1}{T}} \qquad \boxed{T = \frac{1}{f}}

  • If f=5f = 5 Hz, then T=1/5=0.2T = 1/5 = 0.2 s
  • Higher frequency = shorter period
  • For sound: higher frequency = higher pitch

4. The Wave Equation

v=f×λ\boxed{v = f \times \lambda}

Where:

  • vv = wave speed (m/s)
  • ff = frequency (Hz)
  • λ\lambda = wavelength (m)

Rearranging

f=vλλ=vff = \frac{v}{\lambda} \qquad \lambda = \frac{v}{f}

5. Measuring Wave Speed

Method 1: Ripple Tank (Water Waves)

  1. Use a stroboscope to "freeze" the wave pattern
  2. Measure the wavelength using a ruler
  3. Measure the frequency using the stroboscope
  4. Calculate v=fλv = f\lambda

Method 2: Timing Waves

  1. Count the number of waves passing a point in a measured time
  2. f=number of waves/timef = \text{number of waves} / \text{time}
  3. Measure wavelength
  4. Calculate v=fλv = f\lambda

Method 3: Sound

  1. Measure the distance to a large wall
  2. Clap and time the echo
  3. v=2d/tv = 2d/t (sound travels there and back)

Worked Example: Example 1

Problem

Question: A wave has a frequency of 250 Hz and a wavelength of 1.36 m. Calculate the wave speed.

v=fλ=250×1.36=340 m/sv = f\lambda = 250 \times 1.36 = 340 \text{ m/s}

This is the speed of sound in air!

Solution

Worked Example: Example 2

Problem

Question: Radio waves travel at 3×1083 \times 10^8 m/s. A radio station broadcasts at a frequency of 100 MHz. Calculate the wavelength.

λ=vf=3×108100×106=3 m\lambda = \frac{v}{f} = \frac{3 \times 10^8}{100 \times 10^6} = 3 \text{ m}

Solution

Worked Example: Example 3

Problem

Question: A wave has a period of 0.02 s and a wavelength of 0.5 m. Calculate the wave speed.

f=1T=10.02=50 Hzf = \frac{1}{T} = \frac{1}{0.02} = 50 \text{ Hz} v=fλ=50×0.5=25 m/sv = f\lambda = 50 \times 0.5 = 25 \text{ m/s}

Solution

Worked Example: Example 4

Problem

Question: 20 waves pass a point in 4 seconds. The wavelength is 0.8 m. Calculate the wave speed.

f=204=5 Hzf = \frac{20}{4} = 5 \text{ Hz} v=fλ=5×0.8=4 m/sv = f\lambda = 5 \times 0.8 = 4 \text{ m/s}

Solution

7. Practice Questions

    1. State the difference between transverse and longitudinal waves. Give an example of each. (4 marks)
    1. A sound wave has a frequency of 440 Hz. The speed of sound is 340 m/s. Calculate the wavelength. (2 marks)
    1. A wave has an amplitude of 0.3 m and a wavelength of 2.4 m. (a) What is the distance from crest to trough? (1 mark) (b) What is the distance between two adjacent crests? (1 mark)
    1. A student observes 12 water waves passing a point in 6 seconds. The distance between 3 consecutive crests is 1.0 m. Calculate the wave speed. (3 marks)
    1. Electromagnetic waves travel at 3×1083 \times 10^8 m/s. Calculate the frequency of green light with a wavelength of 5.5×10−75.5 \times 10^{-7} m. (2 marks)

    Answers

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Frequently Asked Questions

Do waves transfer matter?

No — waves transfer energy, not matter. The particles vibrate but return to their original position.

Can sound travel through a vacuum?

No — sound needs a medium (particles to vibrate). Light and other electromagnetic waves CAN travel through a vacuum.

What determines the speed of a wave?

The medium it travels through. Sound is faster in solids than gases. Light is fastest in a vacuum and slows in denser media.

Summary

  • Waves transfer energy without transferring matter
  • Transverse: oscillations perpendicular to travel direction (light, water)
  • Longitudinal: oscillations parallel to travel direction (sound)
  • Key properties: amplitude, wavelength (λ\lambda), frequency (ff), period (TT)
  • f=1/Tf = 1/T and v=fλv = f\lambda
  • Greater amplitude = more energy; higher frequency = higher pitch (sound) or different colour (light)
Tags:
#gcse#physics#waves#wavelength#frequency#transverse#longitudinal

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