Wave speed, frequency and wavelength

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Notes de leçon

Big idea: wave speed, frequency and wavelength

  • Key concept: Relationships. Wave speed equals frequency times wavelength. Waves transfer energy without a net transfer of the medium through the whole wave journey.
  • Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
  • Global context: Scientific and technical innovation. Wave relationships help explain sound, light and communications.

Wave Basics & Energy Transfer

  • Waves transfer energy without transferring matter.
  • Objects floating on water bob up and down but do not move with the wave – evidence that matter is not transferred.
  • Waves are described as oscillations or vibrations about a fixed point.
  • Ripples cause water particles to oscillate up and down; sound waves cause air particles to vibrate back and forth.

A toy duck bobbing up and down on water waves, illustrating that waves transfer energy but not matter.

A toy duck bobbing up and down on water waves, illustrating that waves transfer energy but not matter.

Features of a Wave

  • Amplitude – maximum displacement from undisturbed position; measured in metres (m).
  • Wavelength (λ) – distance from one point on the wave to the same point on the next wave; measured in metres (m).
  • Frequency (f) – number of waves passing a point per second; measured in hertz (Hz).
  • Crest (peak) – highest point above undisturbed position; trough – lowest point below.
  • Wavefront – a line representing a single wave; arrow (ray) shows direction of travel.
  • Wave speed – distance travelled by a wave each second.

Amplitude and wavelength

Amplitude and wavelength

The Wave Equation

  • Wave speed equation: v = f × λ (v = wave speed in m/s, f = frequency in Hz, λ = wavelength in m).
  • Period (T) – time for one complete oscillation; T = 1/f (seconds).
  • Frequency and period are related: f = 1/T and T = 1/f.
  • Both transverse and longitudinal waves obey the wave equation.

Ripple tank patterns for low- and high-frequency vibration: higher frequency gives a shorter wavelength.

Ripple tank patterns for low- and high-frequency vibration: higher frequency gives a shorter wavelength.

Transverse Waves

  • Transverse waves: vibration is perpendicular to direction of energy transfer.
  • Have peaks and troughs.
  • Examples: electromagnetic waves (light, radio, X-rays), ripples on water, seismic S-waves.
  • Mechanical transverse waves can travel in solids and on liquid surfaces, but not in liquids or gases.
  • Non-mechanical transverse waves (e.g., light) can travel in a vacuum.

Longitudinal Waves

  • Longitudinal waves: vibration is parallel to direction of energy transfer.
  • Have compressions (particles close together) and rarefactions (particles spaced apart).
  • Examples: sound waves, seismic P-waves.
  • Can travel in solids, liquids, and gases; cannot travel in a vacuum.
  • Density and pressure change along the wave.

Wave Behaviour: Reflection, Refraction, Diffraction

  • All waves can undergo reflection, refraction, and diffraction.
  • Reflection – wave hits a boundary and stays in the original medium; angle of incidence = angle of reflection.
  • Refraction – wave changes speed when entering a different medium; wavelength changes but frequency stays the same; direction may change (towards normal if slowing down, away if speeding up).
  • Diffraction – waves spread out when passing through a narrow gap or around an edge.
  • Diffraction is most prominent when gap width ≈ wavelength; larger gap → less diffraction.
  • Longer wavelengths diffract more than shorter wavelengths.

Ripple Tank Experiments

  • A ripple tank demonstrates wave properties using water waves.
  • Reflection: wavefronts reflect off a metal bar placed in the water.
  • Refraction: a glass block creates shallow water; waves slow down and wavelength decreases.
  • Diffraction: barriers with gaps or edges show spreading of waves.
  • Changing motor frequency changes wavelength: higher frequency → shorter wavelength.

Think like a scientist

  • Use a wave simulation to vary frequency while holding wave speed constant.
  • Comparison: the wave frequency in hertz. Outcome: wavelength in metres.
  • Control: keep the wave speed constant. Explain why this makes the comparison fairer.
  • Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
  • Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
  • Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

  • Wave relationships help explain sound, light and communications.
  • Changing frequency does not always leave speed unchanged; the constant-speed model needs a specified medium and conditions.
  • Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Diapos

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  1. 1.Which of the following is the correct definition of a wave?

    Easy
    • AA transfer of energy without transfer of matter
    • BA transfer of matter without transfer of energy
    • CA transfer of both energy and matter
    • DA transfer of neither energy nor matter

  2. 2.The source vibrates with twice the amplitude while its frequency and wave speed stay constant. What happens to the wavelength?

    Easy
    • AIt stays the same
    • BIt doubles
    • CIt halves
    • DIt becomes zero

  3. 3.Which of the following is a transverse wave?

    Easy
    • ASound wave
    • BSeismic P-wave
    • CLight wave
    • DLongitudinal wave in a slinky

  4. 4.A wave has a speed of 3.0 m/s and a wavelength of 0.5 m. What is its frequency?

    Medium
    • A1.5 Hz
    • B6.0 Hz
    • C0.17 Hz
    • D3.5 Hz

  5. 5.The source frequency doubles while the wave speed stays constant. What happens to the distance between neighbouring compressions?

    Easy
    • AIt halves
    • BIt doubles
    • CIt remains unchanged
    • DIt becomes four times larger

  6. 6.Which of the following changes occurs when a water wave passes from deep water into shallow water?

    Medium
    • AIts frequency increases
    • BIts wavelength decreases
    • CIts speed increases
    • DIts amplitude remains constant

  7. 7.A wave has a time period of 0.25 s. What is its frequency?

    Easy
    • A0.25 Hz
    • B4.0 Hz
    • C2.5 Hz
    • D0.4 Hz

  8. 8.Diffraction of waves is most pronounced when:

    Easy
    • AThe gap is much larger than the wavelength
    • BThe gap is approximately equal to the wavelength
    • CThe gap is much smaller than the wavelength
    • DThe wavelength is zero

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