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Physics · Waves

Properties of waves

Describe waves using amplitude, wavelength, frequency and period, apply \(v = f\lambda\) and \(T = 1 \div f\), and investigate waves in a ripple tank and in a solid (Required Practical 8).

  • 6 key terms
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Warm-up

Answer each one, then check.

  1. 1

    What is the unit of frequency?

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    Hertz (Hz)

  2. 2

    What is the unit of wavelength?

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    Metres (m)

  3. 3

    What is the speed of sound in air?

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    About 330 m/s

  4. 4

    What is a crest?

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    The highest point of a transverse wave

  5. 5

    What is period?

    Show answerHide answer

    The time for one wave to pass

Learning Objectives

  1. 1Define amplitude, wavelength, frequency and period.
  2. 2Recall and apply \(T = 1 \div f\) and \(v = f\lambda\).
  3. 3Identify amplitude and wavelength from diagrams.
  4. 4Describe methods to measure the speed of sound and of ripples, and Required Practical 8.
  5. 5Explain how v, f and λ change when sound passes from one medium to another (Physics only).

THE WAVE EQUATION

wave speed \(=\) frequency \(\times\) wavelength \(v = f\lambda\)

Period \(T = \dfrac{1}{f}\). \(v = f\lambda\) is given on the equation sheet. Wave speed is in m/s, frequency in Hz, wavelength in m and period in s.

Wave Quantities

Learn the definitions and units.

  • Amplitude

    Symbol: A. Unit: m. Meaning: Maximum displacement from the undisturbed position

  • Wavelength

    Symbol: \(\lambda\). Unit: m. Meaning: Distance between equivalent points on adjacent waves

  • Frequency

    Symbol: f. Unit: Hz. Meaning: Number of waves passing a point each second

  • Period

    Symbol: T. Unit: s. Meaning: Time for one complete wave

  • Wave speed

    Symbol: v. Unit: m/s. Meaning: Speed at which the wave moves or transfers energy

Using the Wave Equation

Sound waves of frequency 50 Hz travel at 330 m/s. Calculate the wavelength.

Show the solutionHide the solution
  1. 1 Rearrange \(\lambda = v \div f\)
  2. 2 Substitute \(\lambda = 330 \div 50\)
  3. 3 Answer \(\lambda = 6.6\) m

Answer6.6 m

Finding Speed

Water waves have a frequency of 2.0 Hz and a wavelength of 0.50 m. Calculate the wave speed.

Show the solutionHide the solution
  1. 1 Write the equation \(v = f\lambda\)
  2. 2 Substitute \(v = 2.0 \times 0.50\)
  3. 3 Answer \(v = 1.0\) m/s

Answer1.0 m/s

Period

A wave has a frequency of 250 Hz. Calculate the period.

Show the solutionHide the solution
  1. 1 Write the equation \(T = 1 \div f\)
  2. 2 Substitute \(T = 1 \div 250\)
  3. 3 Answer \(T = 0.0040\) s

Answer0.0040 s

Speed of Sound by Echo

Describe a method to measure the speed of sound in air.

Show the solutionHide the solution
  1. 1 Set up Stand a measured distance (for example 100 m) from a large wall and clap
  2. 2 Time Start a stopwatch at the clap and stop at the echo
  3. 3 Calculate \(v = \text{distance there and back} \div \text{time}\)
  4. 4 Repeat Take several readings and find a mean

AnswerSpeed = 2d ÷ t, with repeats to reduce error.

Changing Medium (Physics only)

A sound wave of frequency 500 Hz travels from air (330 m/s) into water (1500 m/s). What happens to f, v and λ?

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  1. 1 Frequency Unchanged: it is set by the source
  2. 2 Speed Increases to 1500 m/s
  3. 3 Wavelength \(\lambda = v \div f\) increases: from 0.66 m to 3.0 m

Answerf stays the same; v and λ both increase.

Wave Sums

Ripples have a wavelength of 4.0 cm and a frequency of 5.0 Hz. Calculate the speed in m/s. What is the period?

1. Convert cm to m.

2. Use v = fλ and T = 1/f.

A good answer shows: λ = 0.040 m; v = 5.0 × 0.040 = 0.20 m/s. T = 1 ÷ 5.0 = 0.20 s.

Can I...?

  1. 1Define amplitude.
  2. 2Define wavelength.
  3. 3Define frequency and period.
  4. 4Use \(v = f\lambda\).
  5. 5Use \(T = 1 \div f\).
  6. 6Read a wave diagram.
  7. 7Describe measuring wave speed.
  8. 8Explain changes at a boundary.

Summary & Exam Focus

  • \(v = f\lambda\) and \(T = 1 \div f\).
  • Amplitude from the undisturbed position to a crest.
  • Wavelength between equivalent points.
  • Frequency stays constant when a wave changes medium.

Exam focus

Sound of frequency 50 Hz travels at 330 m/s. Calculate the wavelength. (2 marks) (2 marks)

Rearrange v = fλ.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Amplitude
The maximum displacement of a point on a wave from its undisturbed position.
Wavelength
The distance from a point on one wave to the same point on the next wave.
Frequency
The number of waves passing a point each second.
Period
The time for one complete wave.
Wave speed
The speed at which energy is transferred through a medium.
Ripple tank
A shallow tray of water used to show wave behaviour.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    Sound waves travel through air at 330 m/s. A sound has a frequency of 50 Hz. Calculate the wavelength of the sound waves. Use the equation: wave speed = frequency × wavelength

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    Model answer

    \(\lambda = 330 \div 50 = 6.6\) m

    Mark scheme

    • Rearranges to λ = v ÷ f — 1 mark
    • 6.6 m — 1 mark
  2. Question 2 Use the diagram 4 marks

    The diagram shows a water wave. (a) State the amplitude of the wave. (b) State the wavelength. (c) The wave passes a point 5 times each second. Calculate the wave speed.

    A sine wave graph with amplitude 0.30 m and wavelength 4.0 m.
    Show answerHide answer

    Model answer

    (a) 0.30 m. (b) 4.0 m. (c) \(v = f\lambda = 5 \times 4.0 = 20\) m/s.

    Mark scheme

    • Amplitude 0.30 m — 1 mark
    • Wavelength 4.0 m — 1 mark
    • Correct substitution — 1 mark
    • 20 m/s — 1 mark
  3. Question 3 Calculate 2 marks

    A wave has a frequency of 250 Hz. Calculate its period.

    Show answerHide answer

    Model answer

    \(T = 1 \div f = 1 \div 250 = 0.0040\) s

    Mark scheme

    • Correct substitution — 1 mark
    • 0.0040 s — 1 mark
  4. Question 4 Describe 4 marks

    Describe how you would measure the speed of sound in air using a wall and a stopwatch.

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    Model answer

    Stand a measured distance from a large wall. Clap and start the stopwatch; stop it when you hear the echo. The sound has travelled to the wall and back, so speed = 2 × distance ÷ time. Repeat and calculate a mean.

    Mark scheme

    • Measured distance to a wall — 1 mark
    • Timing clap to echo — 1 mark
    • Distance travelled is there and back — 1 mark
    • Repeat and mean — 1 mark
  5. Question 5 Explain 4 marks

    A sound wave travels from air into water. Its frequency is 500 Hz. The speed of sound is 330 m/s in air and 1500 m/s in water. Explain what happens to the frequency, speed and wavelength, and calculate the wavelength in water.

    Show answerHide answer

    Model answer

    The frequency stays the same (500 Hz). The speed increases. The wavelength increases: \(\lambda = 1500 \div 500 = 3.0\) m.

    Mark scheme

    • Frequency unchanged — 1 mark
    • Speed increases — 1 mark
    • Wavelength increases — 1 mark
    • 3.0 m — 1 mark

Quick check

  1. The unit of frequency is...

    1. Ametre
    2. Bsecond
    3. Chertz
    4. Dnewton
    Show answerHide answer

    C: hertz

    Waves per second.

  2. Wave speed is...

    1. Afrequency ÷ wavelength
    2. Bfrequency + wavelength
    3. Cwavelength ÷ period × 2
    4. Dfrequency × wavelength
    Show answerHide answer

    D: frequency × wavelength

    v = fλ.

  3. A wave of frequency 10 Hz and wavelength 3 m has a speed of...

    1. A30 m/s
    2. B13 m/s
    3. C0.3 m/s
    4. D3.3 m/s
    Show answerHide answer

    A: 30 m/s

    10 × 3.

  4. The period of a 5 Hz wave is...

    1. A5 s
    2. B0.2 s
    3. C0.5 s
    4. D25 s
    Show answerHide answer

    B: 0.2 s

    1 ÷ 5.

  5. When a wave enters a new medium its...

    1. Afrequency doubles
    2. Bamplitude doubles
    3. Cfrequency stays the same
    4. Dperiod changes
    Show answerHide answer

    C: frequency stays the same

    It is set by the source.

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