Cambridge IGCSE0972

General properties of waves

Physics 0972 Chapter Notes

What this chapter covers

General properties of waves
ShareWhatsAppPost
General properties of waves notes

Unable to load PDF

The notes viewer could not load. Please refresh the page.

Read online free. Download a watermarked copy with a free account.

Read the notes

The full General properties of waves notes as text: skim, search, and jump between subtopics.

~13 min read

In this chapter

  1. 1Waves and Energy Transfer
  2. 2Transverse and Longitudinal Waves
  3. 3Key Wave Properties
  4. 4The Wave Equation
  5. 5Wave Behaviour and Ripple Tanks

1. Waves and Energy Transfer

A wave is a disturbance that transfers energy from one place to another. Crucially, waves transfer energy without transferring matter. Imagine a cork floating on a pond. If you create ripples, the waves will move across the pond and make the cork bob up and down. The cork itself doesn't travel across the pond with the wave; it only oscillates around its fixed position. The energy you provided by making the ripple has been transferred to the cork. This is the fundamental principle of all waves: they are carriers of energy through a medium (like water or air) or through a vacuum (like space).

Key term

Wave: A disturbance that transfers energy through a medium or space, with no net movement of matter.

Worked example 13 marks

A Mexican wave travels around a football stadium. Explain how this is an example of a wave transferring energy without transferring matter.

  1. 1

    Step 1: Identify the components. The 'medium' is the crowd of people. The 'wave' is the pattern of people standing up and sitting down.

  2. 2

    Step 2: Describe the motion of matter. Each person (the matter) simply stands up and then sits back down in their original position. They do not run around the stadium.

  3. 3

    Step 3: Describe the transfer of energy. The 'wave' of movement and the associated energy travels all the way around the stadium. A person is prompted to stand by seeing their neighbour do it, passing the signal along.

  4. 4

    Conclusion: Therefore, energy is transferred around the stadium, but the people (matter) stay in their fixed positions, demonstrating the principle of wave motion.

Recap

  • Waves transfer energy from a source to an absorber.
  • Waves do not cause a net transfer of matter.
  • Particles in the medium oscillate (vibrate) about fixed positions.
  • Examples of waves include light, sound, and water waves.

Quick check

  1. What is the primary quantity transferred by a wave?1 mark

2. Transverse and Longitudinal Waves

Waves are classified into two main types based on the direction of their oscillation relative to the direction of energy transfer.

  1. Transverse Waves: In a transverse wave, the oscillations are perpendicular (at 90°) to the direction of energy transfer. Think of shaking a rope up and down; the wave travels horizontally along the rope, but the rope itself moves vertically. All electromagnetic waves (like light, radio waves, and X-rays) and ripples on water are examples of transverse waves. They have characteristic 'peaks' (the highest points) and 'troughs' (the lowest points).
  2. Longitudinal Waves: In a longitudinal wave, the oscillations are parallel to the direction of energy transfer. Imagine pushing and pulling the end of a slinky spring. The wave is a series of squashed-up sections and stretched-out sections that travel along the spring. The coils of the spring move back and forth, in the same direction the wave is travelling. Sound waves and some seismic waves (P-waves) are longitudinal. The squashed-up parts are called 'compressions' and the stretched-out parts are called 'rarefactions'.

Key term

Transverse Wave: A wave in which the oscillations are perpendicular to the direction of energy transfer.

Examiner insight

Examiners look for clear descriptions that link the direction of oscillation to the direction of energy transfer. Using the words 'perpendicular' for transverse and 'parallel' for longitudinal is essential for full marks.

Common pitfall

A common mistake is to say that sound is a transverse wave. Remember: Sound is longitudinal; Light is transverse.

Worked example 13 marks

A sound wave travels through air.(a) Is the sound wave transverse or longitudinal?(b) Describe the motion of the air particles as the sound wave passes.

  1. 1

    Part (a): Sound waves are longitudinal waves.

  2. 2

    Part (b): The air particles oscillate backwards and forwards.

  3. 3

    Part(b) continued: Their oscillation is parallel to the direction in which the sound energy is travelling. This creates areas of higher pressure (compressions) and lower pressure (rarefactions).

Recap

  • In transverse waves, oscillations are perpendicular to the direction of energy transfer.
  • Light and all other electromagnetic waves are transverse.
  • In longitudinal waves, oscillations are parallel to the direction of energy transfer.
  • Sound waves are longitudinal.
  • Longitudinal waves consist of compressions and rarefactions.

Quick check

  1. Give two examples of transverse waves.2 marks
  2. What is the name for the stretched-out parts of a longitudinal wave?1 mark

3. Key Wave Properties

To describe waves mathematically, we use several key properties. These can be visualised on a graph of displacement against distance for a transverse wave:

  • Amplitude (A): This is the maximum displacement or distance moved by a point on the wave from its equilibrium (rest) position. On a diagram, it's the height from the centre line to a peak or a trough. A larger amplitude means the wave is carrying more energy. For sound, this corresponds to loudness; for light, it corresponds to brightness.
  • Wavelength (λ): This is the distance between two consecutive identical points on a wave. The easiest way to measure it is from one peak to the next peak, or one trough to the next trough. It is measured in metres (m).
  • Frequency (f): This is the number of complete waves that pass a fixed point per second. It is measured in Hertz (Hz). 1 Hz means one wave per second.
  • Period (T): This is the time it takes for one complete wave to pass a point (or for one full oscillation to occur). It is measured in seconds (s). The period is the inverse of the frequency: T = 1/f.

T = 1 / f

Key term

Wavelength (λ): The distance between two consecutive corresponding points on a wave, such as from one peak to the next.

Common pitfall

Confusing wavelength and amplitude on a diagram. Wavelength is the horizontal distance for one cycle, while amplitude is the vertical distance from the centre line to a peak.

Worked example 12 marks

The diagram shows a wave on a string. The wave is moving to the right. From the diagram, determine(a) the amplitude and(b) the wavelength of the wave.

  1. 1

    Assume the diagram shows a wave with peaks at +2 cm and troughs at -2 cm, and one full wave cycle spans 4 cm on the horizontal axis.

  2. 2

    Part(a) Amplitude: The amplitude is the maximum displacement from the equilibrium position (the x-axis). The peak is at +2 cm. So, the amplitude is 2 cm.

  3. 3

    Part(b) Wavelength: The wavelength is the length of one complete wave. The diagram shows one full cycle from x=0 to x=4 cm. So, the wavelength is 4 cm.

Worked example 23 marks

A radio wave has a frequency of 102 MHz. Calculate its period.

  1. 1

    Step 1: Write down the formula relating period and frequency. T = 1 / f.

  2. 2

    Step 2: Convert the frequency into standard units (Hz). 1 MHz = 1,000,000 Hz. So, f = 102 x 1,000,000 Hz = 1.02 x 10⁸ Hz.

  3. 3

    Step 3: Substitute the value into the formula. T = 1 / (1.02 x 10⁸ Hz).

  4. 4

    Step 4: Calculate the result. T ≈ 9.8 x 10⁻⁹ s (or 9.8 nanoseconds).

Recap

  • Amplitude is the maximum displacement from the rest position.
  • Wavelength (λ) is the length of one complete wave.
  • Frequency (f) is the number of waves passing a point per second.
  • Period (T) is the time for one complete wave to pass.
  • Period and frequency are related by T = 1/f.

Quick check

  1. A wave has a frequency of 200 Hz. What is its period?2 marks

4. The Wave Equation

The speed, frequency, and wavelength of a wave are all related by a single, fundamental equation known as the wave equation. The speed of a wave is how fast the energy is transferred. It is determined by the properties of the medium the wave is travelling through. The equation is:

Wave Speed = Frequency × Wavelength

In symbols, this is written as: v = fλ

Where:

  • v is the wave speed, measured in metres per second (m/s).
  • f is the frequency, measured in Hertz (Hz).
  • λ (the Greek letter 'lambda') is the wavelength, measured in metres (m).

This equation tells us that for a wave travelling at a constant speed, its frequency and wavelength are inversely proportional. This means if the frequency increases, the wavelength must decrease, and vice versa.

v = fλ

Key term

Frequency (f): The number of complete waves passing a point per second, measured in Hertz (Hz).

Examiner insight

Marks are consistently awarded for showing the correct formula, the substitution of values, and the final answer with units. A mark can be lost for missing units or incorrect unit conversion.

Common pitfall

Forgetting to convert units before using the equation is the most common source of error. For example, using wavelengths in cm or frequencies in kHz will give the wrong answer.

Fun fact

The wave equation applies to all waves. For electromagnetic waves in a vacuum, 'v' is always the speed of light (c), about 300,000,000 m/s. This is why high-frequency gamma rays have tiny wavelengths and low-frequency radio waves have wavelengths that can be kilometres long.

Worked example 13 marks

Sound waves travel through air at 340 m/s. Calculate the wavelength of a sound wave with a frequency of 250 Hz.

  1. 1

    Step 1: Write down the wave equation: v = fλ.

  2. 2

    Step 2: Rearrange the equation to solve for wavelength (λ). λ = v / f.

  3. 3

    Step 3: Substitute the known values into the equation. v = 340 m/s and f = 250 Hz.

  4. 4

    Step 4: Calculate the result. λ = 340 / 250 = 1.36 m.

Worked example 23 marks

A water wave has a wavelength of 2.0 m. 5 waves pass a fixed point in 10 seconds. Calculate the speed of the water wave.

  1. 1

    Step 1: First, calculate the frequency (f). Frequency is the number of waves per second. f = 5 waves / 10 s = 0.5 Hz.

  2. 2

    Step 2: Write down the wave equation: v = fλ.

  3. 3

    Step 3: Substitute the known values. f = 0.5 Hz and λ = 2.0 m.

  4. 4

    Step 4: Calculate the speed. v = 0.5 Hz × 2.0 m = 1.0 m/s.

Worked example 33 marks

Light from a laser has a wavelength of 630 nm and travels at a speed of 3.0 x 10⁸ m/s. Calculate its frequency.

  1. 1

    Step 1: Convert the wavelength to standard units (metres). 1 nm = 1 x 10⁻⁹ m. So, λ = 630 x 10⁻⁹ m.

  2. 2

    Step 2: Write down the wave equation: v = fλ.

  3. 3

    Step 3: Rearrange the equation to solve for frequency (f). f = v / λ.

  4. 4

    Step 4: Substitute the values. f = (3.0 x 10⁸ m/s) / (630 x 10⁻⁹ m).

  5. 5

    Step 5: Calculate the result. f = 4.76 x 10¹⁴ Hz.

Recap

  • The wave equation is v = fλ.
  • Wave speed (v) is in m/s, frequency (f) is in Hz, and wavelength (λ) is in m.
  • Always convert quantities to their standard SI units before calculating.
  • If wave speed is constant, frequency and wavelength are inversely proportional.
  • You must be able to rearrange the equation to find any of the three variables.

Quick check

  1. A wave has a speed of 20 m/s and a frequency of 4 Hz. What is its wavelength?2 marks

5. Wave Behaviour and Ripple Tanks

A ripple tank (a shallow tray of water with a light source) is used to demonstrate three key wave behaviours:

  1. Reflection: This is when a wave hits a barrier and bounces off. The law of reflection states that the angle of incidence (the angle the incoming wave makes with the normal) is equal to the angle of reflection (the angle the reflected wave makes with the normal). A 'normal' is a line drawn at 90° to the barrier. If plane waves hit a straight barrier head-on, they reflect straight back.
  2. Refraction: This is the change in direction of a wave as it passes from one medium to another, which causes a change in speed. In a ripple tank, this is shown by making the water depth different in two regions. When waves move from deep water (faster speed) to shallow water (slower speed), they slow down and their wavelength decreases. If they enter at an angle, they also bend towards the normal. The frequency of the wave does not change during refraction.
  3. Diffraction: This is the spreading out of waves as they pass through a gap or move past an edge. The amount of diffraction is most significant when the size of the gap is similar to the wavelength of the waves. If the gap is much larger than the wavelength, the waves pass through with very little spreading. If the wavelength is much larger than the gap, most of the wave is blocked.

Key term

Diffraction: The spreading out of waves as they pass through an aperture or around an obstacle.

Examiner insight

When describing refraction, a high-level answer will always state that frequency remains constant. This is a key piece of knowledge that examiners look for.

Common pitfall

Confusing refraction and diffraction. Refraction is about changing medium and speed. Diffraction is about spreading around obstacles or through gaps.

Worked example 13 marks

Plane waves in a ripple tank approach a gap that is slightly wider than the wavelength of the waves. Draw a diagram to show the waves before and after passing through the gap.

  1. 1

    Step 1: Draw a barrier with a gap in the middle.

  2. 2

    Step 2: To the left of the barrier, draw at least three parallel, equally spaced straight lines. These represent the incoming plane waves (wavefronts). Add an arrow to show the direction of travel.

  3. 3

    Step 3: To the right of the barrier, show the waves passing through the gap. The central part of the waves should continue as straight lines.

  4. 4

    Step 4: The edges of the waves should curve outwards, showing that the wave has spread out. The wavelength (spacing between the curved lines) should remain the same as the incoming waves.

Worked example 22 marks

Explain why a wave's frequency does not change when it is refracted.

  1. 1

    Step 1: State the source of frequency. The frequency of a wave is determined by its source. For example, how many times per second the wave generator in the ripple tank oscillates.

  2. 2

    Step 2: Explain the process at the boundary. As the wave crosses the boundary from one medium to another, the rate at which wavefronts arrive at the boundary must equal the rate at which they leave it.

  3. 3

    Step 3: Conclude. If the number of waves arriving per second was different from the number leaving per second, waves would either be created or destroyed at the boundary, which is impossible. Therefore, the frequency must remain constant.

Recap

  • Reflection is the bouncing of waves off a barrier (angle of incidence = angle of reflection).
  • Refraction is the change in speed and direction of a wave when it enters a new medium.
  • During refraction, frequency stays constant while speed and wavelength change.
  • Diffraction is the spreading of waves as they pass through a gap or around an edge.
  • Maximum diffraction occurs when the gap size is approximately equal to the wavelength.

Quick check

  1. Which wave phenomenon causes echoes?1 mark
  2. For diffraction to be most noticeable, how should the size of the gap compare to the wavelength?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define a longitudinal wave and give one example of such a wave.2 marks
  2. A wave is shown on a displacement-distance graph. Its amplitude is 0.5 m and its wavelength is 4 m. An observer notes that 5 complete waves pass a fixed point in 10 seconds. Calculate (i) the frequency and (ii) the period of the wave.3 marks
  3. A radio station broadcasts at a frequency of 98.5 MHz. Radio waves are electromagnetic waves that travel at a speed of 3.0 x 10⁸ m/s. Calculate the wavelength of these radio waves.3 marks
  4. Describe the difference in the motion of particles in a medium for a transverse wave compared to a longitudinal wave. You may use labelled diagrams to support your answer.4 marks
  5. A student uses a ripple tank to investigate wave properties. Plane waves are directed at an angle from a deep region into a shallow region of water. Describe and explain what happens to the speed, wavelength, and frequency of the waves as they enter the shallow region.4 marks
  6. Sound travels as a wave through the air. Explain how the properties of a sound wave relate to the perceived characteristics of a loud, low-pitched sound.3 marks
  7. An earthquake produces both longitudinal P-waves and transverse S-waves. P-waves travel at 8.0 km/s and S-waves travel at 5.0 km/s. A seismic station detects the P-waves from an earthquake, and then detects the S-waves 60 seconds later. Calculate the distance to the earthquake's epicentre.5 marks
  8. Draw a diagram to show plane waves with a wavelength of 2 cm approaching a gap that is also 2 cm wide. Sketch the pattern of the wavefronts after they have passed through the gap. Name the wave effect shown.3 marks
  9. An oscilloscope is connected to a microphone to display a sound wave. The screen shows 2.0 complete waves in a horizontal distance of 8.0 cm. The time-base setting is 2 ms/cm. Calculate (i) the period and (ii) the frequency of the sound wave.4 marks
  10. State the wave equation, defining all the terms and giving their standard SI units.3 marks

Go deeper

Practise and revise with member-only material for this chapter.

Workbook

Exam-style practice questions with full worked solutions.

Unlock with a plan

Chapter at a Glance

A single-page summary of every key idea for fast revision.

Unlock with a plan

Free notes are just the start.

Unlock every Workbook and Chapter at a Glance, and generate your own worksheets and predicted papers.

Explore plans

Related chapters

Physical quantities and measurement techniquesMotionMass and weightDensityForcesMomentum