General wave properties

What Is Wave Motion?

Wave motion is a process in which energy is transferred from one place to another by means of oscillations or vibrations, without any net movement of the medium itself.

Key idea:

• Energy moves,

• Particles do not travel with the wave.

Fundamental Characteristics of Wave Motion

In wave motion:

• Particles of the medium vibrate about fixed positions.

• Each particle passes the vibration to the next.

• The disturbance travels through the medium as a wave.

This means:

• the medium transmits energy,

• the medium itself remains in roughly the same place.

Example 1: Wave Motion on a Rope

If one end of a rope is shaken:

• a wave travels along the rope,

• each part of the rope moves up and down,

• the rope itself does not move forward with the wave.

[Insert diagram of a transverse wave on a rope showing fixed particle positions and direction of energy transfer]

Example 2: Water Waves

When a stone is dropped into water:

• ripples spread outward,

• water particles move up and down in small circles,

• water does not flow outward with the wave.

This demonstrates that:

• wave motion transfers energy, not matter.

[Insert diagram of circular water waves showing particle motion]

Energy Transfer Without Matter Transfer (Exam-Critical)

A crucial feature of wave motion is:

There is no net transfer of matter.

• Particles oscillate about equilibrium positions.

• After the wave passes, particles return to their original positions.

• Only energy is transported.

This distinguishes wave motion from:

• flow of water,

• movement of objects.

Medium and Wave Motion

• Some waves require a medium (e.g. sound waves).

• Some waves do not require a medium (e.g. light waves).

However, the definition of wave motion remains the same:

• transfer of energy through oscillations.

Key Features of Wave Motion (Summary)

• Involves vibrations or oscillations.

• Transfers energy, not matter.

• Particles move about fixed positions.

• Can occur in solids, liquids, gases, or empty space (depending on wave type).

Key Exam-Ready Statements

• Wave motion is the transfer of energy without transfer of matter.

• Particles vibrate about fixed positions.

• The disturbance travels, not the medium.

• After the wave passes, particles return to equilibrium.

Questions

Question 1

What is meant by wave motion?

Question 2

Explain why wave motion does not involve the transfer of matter.

Question 3

Describe wave motion using an example of a wave on a rope or water.

Solutions

Solution 1

Wave motion is the transfer of energy from one place to another by vibrations without any net movement of the medium.

Solution 2

In wave motion, particles vibrate about fixed positions.

They pass energy to neighboring particles but do not move along with the wave.

After the wave passes, the particles return to their original positions.

Solution 3

When a rope is shaken, a wave travels along it.

Each part of the rope moves up and down while the wave moves horizontally.

The rope itself does not move forward, showing that energy is transferred without matter transfer.

Examiner-Level Guidance

• Always include “energy transfer without matter transfer”.

• Avoid saying particles “move with the wave”.

• Use examples to strengthen explanations.

• Distinguish clearly between wave motion and flow of matter.

Wave Front

A wave front is:

a line or surface joining all points on a wave that are in the same phase of vibration.

Key meaning:

• All points on a wave front are at the same stage of motion.

• Wave fronts show the direction in which a wave is travelling (perpendicular to the wave front).

[Insert diagram showing straight and circular wave fronts with direction of travel indicated]

Wavelength (λ)

The wavelength of a wave is:

the distance between two successive points on a wave that are in the same phase.

Examples of same-phase points:

• crest to crest,

• trough to trough,

• compression to compression.

Key idea:

• Wavelength measures the spatial length of one complete wave.

• Unit: metre (m).

[Insert diagram of a transverse wave with wavelength labelled]

3. Amplitude (A)

The amplitude of a wave is:

the maximum displacement of a vibrating particle from its equilibrium (rest) position.

Key idea:

• Amplitude indicates the energy carried by the wave.

• Larger amplitude → more energy.

• Unit: metre (m).

[Insert diagram showing amplitude measured from equilibrium to crest]

4. Frequency$(f)$

The frequency of a wave is:

the number of complete oscillations or waves produced or passing a point per second.

Key idea:

• Frequency tells how fast the source is vibrating.

• Unit: hertz (Hz).

5. Wave Speed (v)

The wave speed is:

the distance travelled by a wave per unit time.

It is related to wavelength and frequency by:

Key idea:

• Wave speed depends on the medium and wave type.

• Unit: metres per second (m s).

Visual Summary (For Conceptual Clarity)

Summary Table (Exam-Ready)

Key Exam-Ready Statements

• Wavelength and amplitude are measured distances.

• Frequency depends on the source, not the medium.

• Wave speed depends on the medium.

• Wave fronts are perpendicular to the direction of wave travel.

Questions

Question 1

Define wavelength.

Question 2

What is meant by the amplitude of a wave?

Question 3

State the meaning of frequency and give its SI unit.

Question 4

Explain what a wave front represents.

Solutions

Solution 1

Wavelength is the distance between two successive points on a wave that are in the same phase.

Solution 2

Amplitude is the maximum displacement of a vibrating particle from its equilibrium position.

Solution 3

Frequency is the number of complete oscillations per second, measured in hertz (Hz).

Solution 4

A wave front is a line or surface joining points that are vibrating in the same phase.

Examiner-Level Guidance

• Definitions must be precise and concise.

• Do not mix frequency with wave speed.

• Always link wavelength to same phase.

• Diagrams should show labels clearly and correctly.

Experiment (i): Demonstrating Wave Motion and Wave Fronts

Aim

To show that waves transfer energy without transferring matter and to identify wave fronts.

Apparatus

• Ripple tank (or shallow transparent tray)

• Water

• Wave generator / vibrating dipper (or tapping rod)

• Lamp and screen (for ripple tank)

[Insert diagram of a ripple tank showing circular and straight wave fronts]

Method (Procedure)

1. Fill the ripple tank with a shallow layer of water.

2. Switch on the lamp to project the water surface onto the screen.

3. Touch the water surface at a single point repeatedly using a vibrating dipper.

4. Observe the pattern formed on the screen.

5. Replace the point source with a straight vibrating bar and repeat the observation.

Observations

• Circular ripples spread out from a point source.

• Straight ripples move away from the vibrating bar.

• The water itself does not move across the tank.

• Lines joining crests form wave fronts.

Conclusion

• Energy travels outward through the water as a wave.

• The water particles vibrate about fixed positions.

• Wave fronts represent points vibrating in the same phase.

Explanation (Exam-Critical)

• Each ripple crest is a wave front.

• The direction of wave travel is perpendicular to the wave front.

• This confirms wave motion without matter transfer.

Experiment (ii): Relationship Between Speed, Frequency and Wavelength

Aim

To show experimentally that wave speed depends on frequency and wavelength according to:

Apparatus

• Ripple tank or stretched rope/slinky

• Wave generator (with adjustable frequency)

• Stopwatch

• Ruler or measuring scale

[Insert diagram showing measurement of wavelength and timing wave motion]

Method (Procedure – Ripple Tank)

1. Set the wave generator to a fixed frequency.

2. Measure the wavelength by measuring the distance across several crests and dividing by the number of waves.

3. Measure the time taken for a wave front to travel a known distance.

4. Calculate the wave speed using:

1. Change the frequency and repeat the measurements.

Observations

• Increasing frequency causes the wavelength to decrease.

• Wave speed remains approximately constant for the same depth of water.

Results and Relationship

From measurements:

This shows that:

• If frequency increases, wavelength decreases (for constant speed).

• Wave speed depends on the medium, not the frequency alone.

Alternative Method (Rope or Slinky)

• Vibrate one end of a rope at different frequencies.

• Measure wavelength using a ruler.

• Time the motion of wave pulses to find speed.

• Verify the wave equation experimentally.

Key Exam-Ready Statements

• Wave motion transfers energy, not matter.

• Wave fronts are lines of equal phase.

• Wave speed is given by:

• For a given medium, wave speed is constant.

Questions

Question 1

Describe an experiment to show wave motion and wave fronts.

Question 2

Explain how a ripple tank can be used to demonstrate wave fronts.

Question 3

Describe how you would verify the relationship between wave speed, frequency and wavelength.

Solutions

Solution 1

Water is placed in a ripple tank and disturbed using a vibrating source.

Ripples spread across the surface while the water itself remains in place.

The crests form wave fronts, showing wave motion without matter transfer.

Solution 2

A ripple tank projects ripples onto a screen.

The crests appear as lines or circles which represent wave fronts.

These lines show points vibrating in the same phase.

Solution 3

The wavelength is measured from crest to crest and frequency is set using a generator.

The time taken for waves to travel a known distance is measured.

Wave speed is calculated and shown to satisfy $v = f\lambda$.

Examiner-Level Guidance

• Practical answers must include apparatus, method, observation, and conclusion.

• Always state how wavelength and speed are measured.

• Mention that speed stays constant in the same medium.

• Clearly link observations to the wave equation.

B. The Wave Equation (Core Principle)

The fundamental relationship between wave speed, frequency, and wavelength is:

where:

• $v$ = wave speed (m/s)

• $f$ = frequency (Hz)

• $\lambda$ = wavelength (m)

This equation applies to all types of waves, including:

• water waves,

• sound waves,

• light waves.

Physical Meaning of the Equation (Conceptual Depth)

1. Wave Speed (v)

• The speed at which energy or disturbance travels through a medium.

• Determined mainly by the medium, not the source.

2. Frequency $(f)$

• How many complete waves pass a point each second.

• Controlled by the source of the wave.

3. Wavelength (λ)

• The distance between successive points in the same phase.

• Depends on both frequency and wave speed.

Key Relationship Insight (Exam-Critical)

For a given medium:

• Wave speed is constant.

• Increasing frequency causes wavelength to decrease.

• Decreasing frequency causes wavelength to increase.

This inverse relationship is central to wave physics.

[Insert diagram showing two waves with same speed but different frequencies and wavelengths]

Rearranging the Wave Equation

The wave equation can be rearranged depending on what is required:

Students must be able to:

• choose the correct form,

• substitute values correctly,

• include correct units.

Worked Examples

Example 1: Calculating Wave Speed

A wave has a frequency of 5 Hz and a wavelength of 2 m.

Calculate the wave speed.

Answer: The wave speed is 10 m/s.

Example 2: Calculating Frequency

A sound wave travels at 340 m/s and has a wavelength of 0.85 m.

Find its frequency.

Answer: The frequency is 400 Hz.

Example 3: Calculating Wavelength

A radio wave travels at 3.0 × 10⁸ m/s with a frequency of 6.0 × 10⁷ Hz.

Find its wavelength.

Answer: The wavelength is 5 m.

Common Exam Mistakes (Avoid These)

• Mixing up frequency and wave speed.

• Forgetting to convert units (e.g. cm to m).

• Writing the equation incorrectly.

• Not stating final units.

Key Exam-Ready Statements

• The wave equation is v=fλ.

• Wave speed depends on the medium.

• Frequency depends on the source.

• Wavelength adjusts to maintain constant speed in a medium.

Questions

Question 1

State the wave equation and define each symbol.

Question 2

A wave has a frequency of 20 Hz and a wavelength of 0.5 m.

Calculate its speed.

Question 3

The speed of sound in air is 340 m/s.

Calculate the wavelength of a sound wave with frequency 170 Hz.

Solutions

Solution 1

Wave equation:

where:

• $v$ = wave speed (m/s)

• $f$ = frequency (Hz)

• $\lambda$ = wavelength (m)

Solution 2

Solution 3

Examiner-Level Guidance

• Always start with the correct equation.

• Show clear substitution.

• Include units in the final answer.

• Use standard form when necessary.

What Is a Displacement–Time Graph?

A displacement–time graph shows:

• displacement of a particle from its equilibrium position (vertical axis),

• against time (horizontal axis).

It describes the motion of a single particle in a wave, not the shape of the whole wave in space.

Axes and Key Features (Exam-Critical)

Axes

• Vertical axis: Displacement (m)

• Horizontal axis: Time (s)

Key Features Shown on the Graph

• Amplitude

• Period

• Frequency

• Direction of particle motion

[Insert labelled displacement–time graph showing amplitude and period]

Sketching a Displacement–Time Graph

Step-by-Step Guide

1. Draw perpendicular axes and label them correctly.

2. Draw a smooth, repeating curve (usually sinusoidal).

3. Mark:
   • maximum positive displacement,
   • maximum negative displacement,
   • equilibrium position (zero displacement).

Important:

• The curve shows oscillation of one particle.

• The graph does not show wave speed or wavelength directly.

Interpreting a Displacement–Time Graph

1. Amplitude

Amplitude is:

• the maximum displacement from the equilibrium position.

On the graph:

• it is the vertical distance from the centre line to a crest or trough.

Larger amplitude → more energy.

2. Period (T)

The period is:

• the time taken for one complete oscillation.

On the graph:

• it is the horizontal distance between two successive crests,

• or two successive troughs,

• or any two identical points in the motion.

Unit: seconds (s).

3. Frequency (f)

Frequency is:

• the number of oscillations per second.

It is related to the period by:

Unit: hertz (Hz).

4. Direction of Motion of the Particle

From a displacement–time graph:

• a positive slope means the particle is moving upward,

• a negative slope means the particle is moving downward,

• a zero slope (flat) means the particle is momentarily at rest.

What a Displacement–Time Graph Does NOT Show

Very important for exams:

• It does not show wavelength.

• It does not show wave speed directly.

• It describes motion at one point, not the whole wave.

Comparison: Displacement–Time vs Displacement–Distance

Key Exam-Ready Statements

• A displacement–time graph shows oscillation of a single particle.

• Amplitude is the maximum displacement.

• Period is the time for one complete oscillation.

• Frequency is the reciprocal of period.

• The slope shows direction of motion.

Questions

Question 1

What information is shown on a displacement–time graph?

Question 2

State how the period of a wave can be obtained from a displacement–time graph.

Question 3

A displacement–time graph has a period of 0.20 s.

Calculate the frequency of the wave.

Question 4

Explain how amplitude is identified on a displacement–time graph.

J. Worked Solutions (Grade A/A*)

Solution 1

A displacement–time graph shows how the displacement of a vibrating particle changes with time.

Solution 2

The period is the time between two successive identical points on the graph, such as two crests.

Solution 3

Solution 4

Amplitude is the maximum vertical distance from the equilibrium position to a crest or trough on the graph.

Examiner-Level Guidance

• Always label axes correctly.

• Do not confuse period with wavelength.

• State that the graph is for one particle only.

• Use clear terminology: displacement, equilibrium, oscillation.

What Is a Displacement–Distance Graph?

A displacement–distance graph shows:

• displacement of particles from the equilibrium position (vertical axis),

• against distance along the medium (horizontal axis),

• at a particular instant in time.

It represents a snapshot of the wave shape.

Axes and Meaning (Exam-Critical)

Axes

• Vertical axis: Displacement (m)

• Horizontal axis: Distance (m)

Key interpretation:

• Each point on the graph represents the displacement of a different particle along the wave at the same time.

[Insert labelled displacement–distance graph showing amplitude and wavelength]

Sketching a Displacement–Distance Graph

Step-by-Step Guide

1. Draw perpendicular axes and label them correctly.

2. Draw a smooth repeating curve (for a transverse wave).

3. Indicate:
   • crests (maximum positive displacement),
   • troughs (maximum negative displacement),
   • equilibrium (zero displacement).

Important:

• The graph shows the shape of the wave, not how it changes with time.

• The wave may be moving, but the graph is taken at one instant only.

Interpreting a Displacement–Distance Graph

1. Amplitude

Amplitude is:

• the maximum displacement of the wave from the equilibrium position.

On the graph:

• measured vertically from the centre line to a crest or trough.

Larger amplitude → greater wave energy.

2. Wavelength (λ)

Wavelength is:

• the distance between two successive points that are in the same phase.

Examples:

• crest to crest,

• trough to trough,

• compression to compression (for longitudinal waves).

On the graph:

• measured horizontally.

Unit: metre (m).

3. Phase Relationship

• Points one wavelength apart are in phase.

• Points half a wavelength apart are out of phase.

This helps explain interference and superposition later.

What a Displacement–Distance Graph Does NOT Show

Very important for exams:

• It does not show time.

• It does not show frequency or period directly.

• It does not show wave speed unless combined with time information.

Comparison with Displacement–Time Graph

Key Exam-Ready Statements

• A displacement–distance graph shows the shape of a wave.

• It represents the wave at a fixed instant in time.

• Wavelength is measured along the distance axis.

• Amplitude is measured from equilibrium to crest/trough.

Questions

Question 1

What information is shown by a displacement–distance graph?

Question 2

State how the wavelength of a wave is obtained from a displacement–distance graph.

Question 3

Explain how amplitude is identified on a displacement–distance graph.

Question 4

A displacement–distance graph shows a wavelength of 0.80 m.

State what this means physically.

Solutions

Solution 1

A displacement–distance graph shows how the displacement of particles varies with distance along the wave at a particular instant in time.

Solution 2

The wavelength is the horizontal distance between two successive points that are in the same phase, such as two crests.

Solution 3

Amplitude is the maximum vertical distance from the equilibrium position to a crest or trough on the graph.

Solution 4

A wavelength of 0.80 m means the distance between two successive points in the same phase of the wave is 0.80 m.

Examiner-Level Guidance

• Always state that the graph is taken at a fixed time.

• Do not confuse wavelength with period.

• Label axes and key features clearly in sketches.

• Use correct terminology: displacement, equilibrium, phase.

Overview: Two Fundamental Types of Waves

Waves are classified based on the direction of particle vibration compared with the direction of wave travel (energy transfer).

There are two main types:

• Transverse waves

• Longitudinal waves

Transverse Waves

Definition (Exam-Exact)

A transverse wave is a wave in which:

particles of the medium vibrate perpendicular (at right angles) to the direction of wave travel.

Nature of Transverse Waves

In transverse waves:

• energy travels in one direction,

• particles vibrate up and down or sideways,

• particle motion is across the direction of wave motion.

Key features:

• Crests (points of maximum upward displacement),

• Troughs (points of maximum downward displacement).

Examples of Transverse Waves

• Waves on a stretched rope or string

• Water surface waves

• Light (electromagnetic) waves

• Other electromagnetic waves (radio, infrared, X-rays)

[Insert diagram showing a transverse wave with crests, troughs, particle vibration direction, and wave direction labelled]

Particle Motion (Key Interpretation)

• Particles oscillate about fixed positions.

• There is no net movement of particles along the wave.

• Only energy is transferred.

Longitudinal Waves

Definition (Exam-Exact)

A longitudinal wave is a wave in which:

particles of the medium vibrate parallel (in the same direction) to the direction of wave travel.

Nature of Longitudinal Waves

In longitudinal waves:

• particles move back and forth,

• vibration is along the direction of wave motion,

• wave consists of alternating regions of:
  • compressions (high pressure / high density),
  • rarefactions (low pressure / low density).

Examples of Longitudinal Waves

• Sound waves in air

• Compression waves in a slinky spring

• Seismic P-waves (primary waves)

[Insert diagram showing a longitudinal wave with compressions, rarefactions, particle vibration direction, and wave direction labelled]

Particle Motion (Key Interpretation)

• Particles vibrate back and forth about equilibrium positions.

• Energy moves forward through successive compressions and rarefactions.

• Matter itself does not travel with the wave.

Direct Comparison (Exam-Critical)

Key Exam-Ready Statements

• Transverse waves vibrate perpendicular to wave travel.

• Longitudinal waves vibrate parallel to wave travel.

• Crests and troughs occur in transverse waves.

• Compressions and rarefactions occur in longitudinal waves.

• Both transfer energy without transferring matter.

Questions

Question 1

Define a transverse wave.

Question 2

Define a longitudinal wave.

Question 3

State two differences between transverse and longitudinal waves.

Question 4

Sound waves are longitudinal.

Explain what this means in terms of particle motion.

Solutions

Solution 1

A transverse wave is one in which particles vibrate perpendicular to the direction of wave travel.

Solution 2

A longitudinal wave is one in which particles vibrate parallel to the direction of wave travel.

Solution 3

In transverse waves, particles vibrate perpendicular to wave direction and crests and troughs are formed.

In longitudinal waves, particles vibrate parallel to wave direction and compressions and rarefactions are formed.

Solution 4

In sound waves, air particles vibrate back and forth in the same direction as the wave travels.

This produces compressions and rarefactions that carry energy through the air.

Examiner-Level Guidance

• Always use perpendicular and parallel correctly.

• Mention particle vibration, not particle travel.

• Do not confuse wave direction with particle motion.

• Diagrams significantly improve explanation marks.

Transverse Waves — Examples and Explanation

Definition Reminder (Context)

In a transverse wave, particles vibrate perpendicular to the direction of wave travel.

Common Examples of Transverse Waves

1. Waves on a stretched rope or string
   • Rope moves up and down.
   • Wave travels along the rope.

2. Water surface waves
   • Water particles move up and down.
   • Wave spreads horizontally across the surface.

3. Light waves (electromagnetic waves)
   • Do not require a medium.
   • Vibrations are perpendicular to direction of travel.

4. Other electromagnetic waves
   • Radio waves
   • Infrared radiation
   • X-rays

[Insert diagram showing a transverse wave with crests, troughs, particle motion, and wave direction]

Key Identification Clue (Exam Tip)

If the wave has crests and troughs, it is transverse.

Longitudinal Waves — Examples and Explanation

Definition Reminder (Context)

In a longitudinal wave, particles vibrate parallel to the direction of wave travel.

Common Examples of Longitudinal Waves

1. Sound waves in air
   • Air particles vibrate back and forth.
   • Wave moves through compressions and rarefactions.

2. Compression waves in a slinky spring
   • Coils move forward and backward.
   • Regions of compression and rarefaction are visible.

3. Seismic P-waves (primary waves)
   • Travel through solids, liquids, and gases.
   • Cause particles to vibrate parallel to wave motion.

[Insert diagram showing a longitudinal wave with compressions, rarefactions, particle motion, and wave direction]

Key Identification Clue (Exam Tip)

If the wave shows compressions and rarefactions, it is longitudinal.

Summary Table (Exam-Ready)

Key Exam-Ready Statements

• Water surface waves are transverse.

• Light waves are transverse and do not need a medium.

• Sound waves are longitudinal.

• Longitudinal waves consist of compressions and rarefactions.

• In both types, energy is transferred without matter transfer.

Questions

Question 1

Give two examples of transverse waves.

Question 2

Give two examples of longitudinal waves.

Question 3

State one example of a wave that does not require a medium and identify its type.

Solutions

Solution 1

Examples of transverse waves include waves on a rope and water surface waves.

Solution 2

Examples of longitudinal waves include sound waves in air and compression waves in a slinky spring.

Solution 3

Light is a wave that does not require a medium and it is a transverse wave.

Examiner-Level Guidance

• Always name the wave type with the example.

• Do not classify water waves as longitudinal.

• Mention particle motion direction if explanation is required.

• Avoid vague answers like “sea waves” without clarification.

Core Principle (Unifying Idea)

The type of wave formed depends on the direction in which the source vibrates relative to the direction in which the wave travels.

• Source vibrates perpendicular → Transverse wave

• Source vibrates parallel → Longitudinal wave

Formation of Transverse Waves

1. Demonstration Using a Rope or String

Apparatus

• Long rope or string

• Fixed support (wall hook or clamp)

• Hand of the experimenter

[Insert labelled diagram showing transverse wave formation on a rope]

Method (Procedure)

1. Tie one end of the rope to a fixed support.

2. Hold the free end firmly.

3. Move the free end up and down repeatedly.

4. Observe the motion of the rope as the disturbance travels along it.

Observations

• The wave travels horizontally along the rope.

• Each part of the rope moves up and down.

• Crests and troughs are clearly visible.

Explanation (Formation Mechanism)

• The hand vibrates perpendicular to the direction of wave travel.

• This causes particles of the rope to vibrate at right angles to the wave direction.

• A transverse wave is formed.

Conclusion

A transverse wave is formed when the source vibrates perpendicular to the direction of energy transfer.

Formation of Longitudinal Waves

2. Demonstration Using a Slinky Spring

Apparatus

• Long slinky spring

• Smooth surface or floor

[Insert labelled diagram showing longitudinal wave formation in a slinky]

Method (Procedure)

1. Stretch the slinky out on a smooth surface.

2. Hold one end firmly.

3. Push and pull the free end back and forth along the length of the slinky.

4. Observe the motion of the coils.

Observations

• Regions where coils are close together (compressions) move along the slinky.

• Regions where coils are spread apart (rarefactions) follow.

• The coils vibrate back and forth in the same direction as the wave travels.

Explanation (Formation Mechanism)

• The hand vibrates parallel to the direction of wave travel.

• This produces alternating compressions and rarefactions.

• A longitudinal wave is formed.

Conclusion

A longitudinal wave is formed when the source vibrates parallel to the direction of energy transfer.

Formation of Sound Waves (Everyday Context)

Sound waves are longitudinal waves formed when:

• a source (e.g. loudspeaker, tuning fork, vocal cords) vibrates,

• surrounding air particles are pushed back and forth,

• compressions and rarefactions travel through the air.

[Insert diagram showing sound wave formation with compressions and rarefactions]

Direct Comparison: How the Two Wave Types Are Formed

Key Exam-Ready Statements

• Transverse waves are formed by perpendicular vibrations.

• Longitudinal waves are formed by parallel vibrations.

• The motion of the source determines the wave type.

• Both wave types transfer energy without transferring matter.

Questions

Question 1

Describe how a transverse wave can be formed using a rope.

Question 2

Explain how a longitudinal wave is formed in a slinky spring.

Question 3

State one key difference in how transverse and longitudinal waves are formed.

Solutions

Solution 1

One end of the rope is fixed and the other end is moved up and down.

The disturbance travels along the rope while the rope particles vibrate perpendicular to the direction of wave travel.

This forms a transverse wave.

Solution 2

The slinky is pushed and pulled back and forth along its length.

This creates compressions and rarefactions that move along the slinky.

The particles vibrate parallel to the direction of wave travel, forming a longitudinal wave.

Solution 3

In transverse waves the source vibrates perpendicular to wave travel, while in longitudinal waves the source vibrates parallel to wave travel.

Examiner-Level Guidance

• Always describe source motion first, then wave motion.

• Use the words perpendicular and parallel precisely.

• Mention compressions and rarefactions for longitudinal waves.

• Diagrams significantly strengthen practical explanations.

Core Concept: Formation of Water Waves

Water waves are formed when a disturbance is created on the surface of water.

Key ideas:

• The disturbance causes water particles to oscillate about fixed positions.

• Energy spreads across the surface as a wave.

• Water itself does not move with the wave.

Water waves are mainly transverse waves at the surface.

Experiment: Formation of Water Waves Using a Ripple Tank

Aim

To demonstrate how water waves are formed and how wave fronts appear.

Apparatus

• Ripple tank (or shallow transparent tray)

• Water

• Vibrating dipper / wave generator (or tapping rod)

• Lamp and screen (for ripple tank observation)

[Insert labelled diagram of a ripple tank showing wave formation from a point source]

Method (Procedure)

1. Pour a shallow, even layer of water into the ripple tank.

2. Switch on the lamp so the water surface is projected onto the screen.

3. Gently touch the water surface at one point using a vibrating dipper.

4. Allow the dipper to vibrate continuously.

5. Observe the pattern formed on the screen.

Observations

• Circular ripples spread outward from the point of disturbance.

• The ripples move across the surface while the water remains in place.

• The crests form circular wave fronts.

Explanation (Formation Mechanism)

• The vibrating dipper transfers energy to the water surface.

• Water particles vibrate up and down about their equilibrium positions.

• Each vibrating particle transfers energy to neighbouring particles.

• This produces outward-moving water waves.

Conclusion

Water waves are formed by a vibrating source that causes particles to oscillate, transferring energy across the surface without transferring water itself.

Formation of Straight (Plane) Water Waves

Modified Demonstration

Method

1. Replace the point dipper with a straight vibrating bar.

2. Allow the bar to touch the water surface repeatedly.

Observations

• Straight, parallel ripples move away from the bar.

• The wave fronts are straight lines.

[Insert diagram showing straight wave fronts produced by a vibrating bar]

Conclusion

• A point source produces circular wave fronts.

• A straight source produces plane (straight) wave fronts.

Key Learning Outcomes (Exam-Critical)

• Water waves are produced by disturbances on the surface.

• The source must vibrate.

• Energy travels outward as a wave.

• Water particles only oscillate, they do not travel with the wave.

• Wave fronts can be circular or straight depending on the source.

Key Exam-Ready Statements

• Water waves are mainly transverse waves.

• A vibrating source forms water waves.

• Circular wave fronts come from a point source.

• Straight wave fronts come from a straight source.

• Energy is transferred without matter transfer.

Questions

Question 1

Describe an experiment to demonstrate the formation of water waves.

Question 2

What type of wave is a water surface wave and why?

Question 3

State the difference between wave fronts formed by a point source and a straight source.

Solutions

Solution 1

Water is placed in a ripple tank and disturbed using a vibrating dipper.

Circular ripples spread across the surface while the water remains in place.

The ripples show wave fronts and demonstrate wave motion.

Solution 2

Water surface waves are transverse because the water particles vibrate up and down while the wave travels horizontally.

Solution 3

A point source produces circular wave fronts, while a straight source produces straight wave fronts.

Examiner-Level Guidance

• Always mention apparatus → method → observation → conclusion.

• Use the term wave fronts correctly.

• State clearly that water does not move with the wave.

• Diagrams are highly recommended in exam answers.

Core Principle (Conceptual Foundation)

For water waves:

• Deeper water → higher wave speed

• Shallower water → lower wave speed

When a wave moves from deep to shallow water at an angle, its speed changes, causing the wave to change direction (refraction).

Experiment: Effect of Depth on Wave Speed (Ripple Tank)

Aim

To show that water wave speed changes with depth.

Apparatus

• Ripple tank (or shallow transparent tray)

• Water

• Wave generator (vibrating dipper or bar)

• Glass plate or Perspex sheet (to create shallow region)

• Lamp and screen

• Ruler and stopwatch (or scale projected on screen)

[Insert labelled diagram of a ripple tank with deep and shallow regions created by a glass plate]

Method (Procedure)

1. Fill the ripple tank with water to a uniform depth.

2. Place a glass plate on the tank floor to create a shallow region, leaving the rest deeper.

3. Use a vibrating bar to generate straight (plane) waves.

4. Allow the waves to travel from deep water into shallow water.

5. Observe the spacing of the wave fronts in both regions.

6. Measure the wavelength in deep water and in shallow water (using the projected image).

Observations

• Wave fronts are further apart in deep water.

• Wave fronts are closer together in shallow water.

• When waves enter shallow water at an angle, their direction changes.

Results and Interpretation

• Larger wavelength in deep water → higher wave speed.

• Smaller wavelength in shallow water → lower wave speed.

Since frequency remains constant:

A decrease in wavelength means a decrease in wave speed.

Conclusion

The experiment shows that water waves travel faster in deeper water and slower in shallower water.

Explanation (Why Depth Affects Speed)

• In deep water, particles can move more freely.

• Energy is transferred more quickly, increasing wave speed.

• In shallow water, interaction with the bottom restricts motion.

• Energy transfer slows, reducing wave speed.

Link to Refraction (Exam-Critical Connection)

• When part of a wave enters shallow water first, that part slows down.

• The rest of the wave continues at a higher speed.

• This causes the wave to change direction.

[Insert diagram showing wave refraction at a boundary between deep and shallow water]

Key Exam-Ready Statements

• Water wave speed depends on depth.

• Waves move faster in deep water.

• Waves move slower in shallow water.

• Frequency remains constant when depth changes.

• Refraction occurs due to a change in wave speed.

Questions

Question 1

Describe an experiment to show the effect of depth on the speed of water waves.

Question 2

What happens to the wavelength of water waves when they move into shallow water?

Question 3

Explain why water waves change direction when moving from deep to shallow water at an angle.

Solutions

Solution 1

Water is placed in a ripple tank and a glass plate is used to create a shallow region.

Plane waves are generated and allowed to pass from deep to shallow water.

The wavelength decreases in shallow water, showing a reduction in wave speed.

This demonstrates that wave speed depends on depth.

Solution 2

The wavelength decreases when water waves move into shallow water.

Solution 3

When waves enter shallow water, their speed decreases.

Part of the wave slows down before the rest, causing the wave to bend.

This change in direction is due to refraction.

Examiner-Level Guidance

• Always mention deep vs shallow regions explicitly.

• Link wavelength change to wave speed using:

• State clearly that frequency remains constant.

• Diagrams significantly improve marks in refraction questions.

Apparatus (Common to Both Demonstrations)

• Ripple tank

• Shallow, even layer of water

• Wave generator (vibrating bar preferred for plane waves)

• Lamp and screen

• Plane reflector (straight metal or plastic barrier)

• Glass/Perspex plate (to create shallow region)

[Insert labelled diagram of a ripple tank setup with wave generator, screen, and accessories]

PART (i): Reflection of Water Waves at a Plane Surface

Aim

To show that water waves are reflected at a plane surface and obey the law of reflection.

Method (Procedure)

1. Fill the ripple tank with a shallow, uniform depth of water.

2. Use a straight vibrating bar to generate plane waves.

3. Place a plane reflector in the path of the waves.

4. Switch on the lamp and observe the wave pattern on the screen.

Observations

• Incident wave fronts strike the plane surface.

• Reflected wave fronts move away from the surface.

• The reflected wave fronts are straight and parallel to the incident wave fronts.

[Insert diagram showing incident and reflected wave fronts at a plane reflector]

Description and Explanation

• Reflection occurs when waves bounce off a barrier.

• The angle of incidence equals the angle of reflection.

• The speed, frequency, and wavelength remain unchanged because the water depth is constant.

Conclusion (Exam-Ready)

Water waves are reflected at a plane surface, and the law of reflection applies:

angle of incidence=angle of reflection\text{angle of incidence} = \text{angle of reflection}

angle of incidence=angle of reflection

PART (ii): Refraction of Water Waves Due to a Change of Speed

Aim

To show that water waves change direction when their speed changes as they move between regions of different depth.

Method (Procedure)

1. Place a glass or Perspex plate on the bottom of the ripple tank to create a shallow region.

2. Generate plane waves using a vibrating bar.

3. Allow the waves to travel from deep water into shallow water at an angle.

4. Observe the wave fronts on the screen.

Observations

• Wave fronts change direction at the boundary.

• The spacing between wave fronts decreases in shallow water.

• The wave fronts bend towards the normal.

[Insert diagram showing refraction of water waves at a deep–shallow boundary]

Description and Explanation

• In deep water, waves travel faster.

• In shallow water, waves travel slower.

• When part of a wave slows down before the rest, the wave changes direction.

• Frequency remains constant, but wavelength and speed change.

Using the wave equation:

A decrease in wavelength means a decrease in wave speed.

Conclusion (Exam-Ready)

Refraction occurs because wave speed changes when water depth changes, causing the wave to bend at the boundary.

Direct Comparison (High-Yield Exam Table)

Key Exam-Ready Statements

• Reflection occurs at a plane surface.

• Refraction occurs due to a change in wave speed.

• Water waves slow down in shallow water.

• Frequency remains constant during refraction.

• Wave fronts bend towards the normal in shallow water.

Questions

Question 1

Describe how a ripple tank can be used to show reflection of water waves.

Question 2

Explain why water waves change direction when moving from deep to shallow water.

Question 3

State two differences between reflection and refraction of water waves.

Solutions

Solution 1

Plane waves are produced in a ripple tank using a vibrating bar.

A plane reflector is placed in the path of the waves.

The waves bounce off the surface, producing reflected wave fronts.

The angles of incidence and reflection are equal.

Solution 2

Water waves slow down in shallow water because their speed depends on depth.

Part of the wave slows before the rest, causing the wave to bend.

This change in direction is refraction.

Solution 3

Reflection involves bouncing off a surface without speed change, while refraction involves bending due to speed change.

Examiner-Level Guidance

• Always mention wave fronts, not just “waves”.

• State what changes and what remains constant.

• Link refraction explicitly to change in speed due to depth.

• Diagrams significantly improve clarity and marks.