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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).

  • 9 key terms
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Teacher resources

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Student handouts

The same files the students see, to print or hand out.

Warm-up

Answer each one, then check.

  1. 1

    What is the unit of frequency?

    Show answerHide answer

    Hertz (Hz)

  2. 2

    What is the unit of wavelength?

    Show answerHide answer

    Metres (m)

  3. 3

    What is the speed of sound in air?

    Show answerHide answer

    About 330 m/s

  4. 4

    What is a crest?

    Show answerHide answer

    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?

Show the solutionHide the solution
  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.

Required Practical 8: Ripple Tank Method

Measuring frequency, wavelength and speed of water waves.

  1. 1 Set up

    Fill a ripple tank and set the signal generator so the dipper makes steady waves; a lamp above casts shadows on paper below.
  2. 2 Wavelength

    Measure across 10 wavelengths with a ruler on the shadow pattern and divide by 10.
  3. 3 Frequency

    Count the waves passing a point in 10 seconds and divide by 10, or read the generator.
  4. 4 Speed

    Calculate v = fλ.
  5. 5 Improve

    A strobe or a photo with a ruler in shot freezes the pattern for easier measuring.

Measuring Waves on a String

The second part of Required Practical 8.

  • Set up

    A string runs over a pulley with masses hung on the end, and a vibration generator near the other end.

  • Standing wave

    Adjust the frequency until a clear, stationary pattern of loops appears. Measure across several half-wavelengths with a metre ruler.

  • Calculate

    Read the frequency from the signal generator and use v = fλ. Changing the frequency changes the wavelength, but the speed stays the same for the same string and tension.

Reading a Wave Diagram

Where marks are lost on labelled diagrams.

  • Amplitude

    Measure from the middle line (undisturbed position) to a crest, not from trough to crest.

  • Wavelength

    Measure from one crest to the next crest, or between any two matching points.

  • Time axis

    If the x-axis is time instead of distance, the gap between crests is the period, not the wavelength.

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.
  • Measure amplitude from the middle line, not trough to crest.
  • Measure across several waves and divide for accuracy.

Exam focus

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

Rearrange v = fλ to λ = v ÷ f, substitute 330 ÷ 50 and give 6.6 m. If the frequency is given in kHz, multiply by 1000 first.

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.
Hertz
The unit of frequency: one wave per second.
Undisturbed position
The position of the medium when no wave is passing.
Signal generator
A device that produces a vibration at a set frequency.

Questions and answers

13 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

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

Mark scheme — 2 marks available

  • Rearranges to λ = v ÷ f — 1 mark
  • 6.6 m — 1 mark

Model answer

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

2. Exam question Use the diagram 4 marks Easier

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.

Mark scheme — 4 marks available

  • Amplitude 0.30 m — 1 mark
  • Wavelength 4.0 m — 1 mark
  • Correct substitution — 1 mark
  • 20 m/s — 1 mark

Model answer

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

3. Exam question Calculate 2 marks Easier

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

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 0.0040 s — 1 mark

Model answer

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

4. Exam question Describe 4 marks Easier

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

Mark scheme — 4 marks available

  • 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

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.

5. Exam question Explain 4 marks Easier

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.

Mark scheme — 4 marks available

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

Model answer

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

6. Multiple choice 1 mark Core

A diagram shows a wave 8 cm from trough to crest. What is the amplitude?

  1. A 8 cm
  2. B 4 cm Correct
  3. C 16 cm
  4. D 2 cm

Why: Amplitude is from the middle to a crest, so half of 8 cm.

7. Multiple choice 1 mark Core

In a ripple tank, 10 waves span 15 cm. What is the wavelength?

  1. A 1.5 cm Correct
  2. B 150 cm
  3. C 15 cm
  4. D 0.15 cm

Why: 15 ÷ 10 = 1.5 cm.

8. Multiple choice 1 mark Stretch

A wave has a period of 0.02 s and a wavelength of 4 m. What is its speed?

  1. A 0.08 m/s
  2. B 50 m/s
  3. C 200 m/s Correct
  4. D 4.02 m/s

Why: f = 1 ÷ 0.02 = 50 Hz; v = 50 × 4 = 200 m/s.

9. Multiple choice 1 mark Easier

The unit of frequency is...

  1. A metre
  2. B second
  3. C hertz Correct
  4. D newton

Why: Waves per second.

10. Multiple choice 1 mark Core

Wave speed is...

  1. A frequency ÷ wavelength
  2. B frequency + wavelength
  3. C wavelength ÷ period × 2
  4. D frequency × wavelength Correct

Why: v = fλ.

11. Multiple choice 1 mark Core

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

  1. A 30 m/s Correct
  2. B 13 m/s
  3. C 0.3 m/s
  4. D 3.3 m/s

Why: 10 × 3.

12. Multiple choice 1 mark Core

The period of a 5 Hz wave is...

  1. A 5 s
  2. B 0.2 s Correct
  3. C 0.5 s
  4. D 25 s

Why: 1 ÷ 5.

13. Multiple choice 1 mark Stretch

When a wave enters a new medium its...

  1. A frequency doubles
  2. B amplitude doubles
  3. C frequency stays the same Correct
  4. D period changes

Why: It is set by the source.