General Properties OF Waves — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

Section 1 of 30Waves and energy

Energy transfer

• Energy transfer waves transfer energy without transferring matter

Oscillation

• Oscillation the medium vibrates about a fixed point, for example water ripples move particles up and down and sound moves air back and forth

Evidence

• Evidence a floating object bobs up and down but does not travel with the wave

Section 2 of 30Features of a wave

Features of a wave

Amplitude

• Amplitude the maximum displacement of a wave from its undisturbed position, symbol A, unit m

Wavelength

• Wavelength the distance from one point on a wave to the same point on the next wave, symbol λ, unit m

Frequency

• Frequency the number of waves passing a point per second, symbol f, unit hertz (Hz)

Period

• Period the time for one complete wave to pass a point, T = 1 ÷ f
  What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)

Wavefront

• Wavefront a line joining points on a wave that are in step, usually the crests

Crest and trough

• Crest and trough the highest and lowest points of a wave relative to the undisturbed position

Wave speed

• Wave speed the distance travelled by a wave each second

Section 3 of 30The wave equation

The wave equation

Equation

• Equation v = fλ, with v in m/s, f in Hz and λ in m
  What the symbols mean: v = wave speed (m s⁻¹) · f = frequency (Hz) · λ = wavelength (m)

Both wave types

• Both wave types transverse and longitudinal waves obey the equation

Unit conversions

• Unit conversions convert cm to m by dividing by 100, kHz to Hz by multiplying by 1000 and MHz to Hz by multiplying by 1 000 000

Section 4 of 30Transverse and longitudinal waves

Property	Transverse	Longitudinal
Vibration	At right angles to the direction of travel	Parallel to the direction of travel
Pattern	Crests and troughs	Compressions and rarefactions
Vacuum	Only electromagnetic waves travel through it	Cannot travel through it
Examples	Light, water ripples, S-waves	Sound, P-waves

Section 5 of 30Reflection, refraction and diffraction

Reflection

• Reflection a wave bounces back at a boundary and stays in the original medium
• Angle of incidence equals angle of reflection
• Speed, wavelength and frequency are unchanged

Refraction

• Refraction a wave changes speed at a boundary between media
• Speed and wavelength change, frequency stays the same
• Slowing waves bunch together and turn towards the normal

Diffraction

• Diffraction waves spread out when they pass through a narrow gap or past an edge
• Wavelength and speed are unchanged
• Greatest when the gap width is about equal to the wavelength

Section 6 of 30Ripple tank

Purpose

• Purpose shows reflection, refraction and diffraction of water waves

Set-up

• Set-up a lamp above the tank projects the wavefronts onto a screen below

Measuring speed

• Measure the length across several wavefronts and divide by the number of waves to find λ
• Count the waves passing a point in a set time to find f
• Calculate v = fλ and repeat to average

Section 7 of 30More from the specification

1Wave

• Wave a disturbance that transfers energy from place to place without transferring matter

2Wavelength, frequency and amplitude

• Wavelength, frequency and amplitude wavelength is the distance between successive crests, frequency is waves per second in hertz, amplitude is the maximum displacement

3Wave speed equation

• Wave speed equation v = f x wavelength, with speed in metres per second

4Transverse and longitudinal waves

• Transverse and longitudinal waves particles vibrate at right angles to the direction of travel in transverse waves and parallel to it in longitudinal waves

5Refraction at a glass block

• Refraction at a glass block light bends towards the normal on entering glass because it slows down,
  • and the emergent ray is parallel to the incident ray

6Wave

• Wave a disturbance that transfers energy from place to place without transferring matter

7Wavelength, frequency and amplitude

• Wavelength, frequency and amplitude wavelength is the distance between successive crests, frequency is waves per second in hertz, amplitude is the maximum displacement

8Wave speed equation

• Wave speed equation v = f x wavelength, with speed in metres per second

9Transverse and longitudinal waves

• Transverse and longitudinal waves particles vibrate at right angles to the direction of travel in transverse waves and parallel to it in longitudinal waves

10Refraction at a glass block

• Refraction at a glass block light bends towards the normal on entering glass because it slows down,
  • and the emergent ray is parallel to the incident ray

Section 8 of 30Waves transfer energy, not matter

Key idea

• Key idea a wave carries energy from place to place without carrying the material of the medium.
• In a sound wave the air molecules do not travel with the wave; the wave travels.

Evidence

• Evidence a floating duck or leaf bobs up and down as ripples pass but does not move along with the wave.

Oscillations

• Oscillations particles of the medium vibrate about fixed positions.
• Water particles move up and down in ripples and air particles move back and forth in sound.

Section 9 of 30Ways to show wave motion

Ropes and springs

• Ropes and springs vibrations sent along a rope or a slinky show wave motion.

Ripple tank

• Ripple tank water waves in a ripple tank show wavelength, frequency, amplitude and speed.

Section 10 of 30Wavefronts

Definition

• Definition a wavefront is a line joining points that are in step, usually the crests, seen from above.

Ray

• Ray an arrow showing the direction in which the wave moves.

Spacing

• Spacing the distance between wavefronts is the wavelength.
• Close wavefronts mean a short wavelength and widely spaced wavefronts mean a long wavelength.

Section 11 of 30Wave terms and symbols

Term	Definition	Symbol and unit
Amplitude	Maximum displacement from the undisturbed position	A, metres
Wavelength	Distance from a point on one wave to the same point on the next	λ, metres
Frequency	Number of waves passing a point per second	f, hertz (Hz)
Crest (peak)	Highest point above the undisturbed position	—
Trough	Lowest point below the undisturbed position	—
Wave speed	Distance travelled by the wave each second	v, m/s

Section 12 of 30Reading a wave graph

Amplitude

• Amplitude measure from the undisturbed (centre) line to a peak or trough, not from crest to trough.

Wavelength

• Wavelength measure from a point to the same point on the next wave, such as crest to crest.

Longitudinal waves

• Longitudinal waves measure wavelength from the centre of one compression to the centre of the next.

Wave speed

• Wave speed it is the speed at which energy is transferred through the medium.

Section 13 of 30More key facts: Features of Waves

More key facts: Features of Waves

Drawing waves

• Drawing waves draw the undisturbed line, then crests and troughs of equal height for constant amplitude.

Amplitude and energy

• Amplitude and energy a larger amplitude means the wave carries more energy.

Light and sound

• Light and sound both are waves but sound needs a medium while light does not.

Frequency counting

• Frequency counting the number of complete waves passing a point in one second.

Ripple tank

• Ripple tank a lamp above projects the wavefronts onto a screen below the tank.

Section 14 of 30More from the specification

1Transverse and Longitudinal Wave Motion

• Transverse waves have particle oscillations perpendicular to energy transfer,
  • (e.g. water ripples, light)
• whereas longitudinal waves oscillate parallel to energy transfer (e.g. sound).

2The Wave Equation

• All progressive waves obey the wave equation v = fλ, linking wave speed v (m s⁻¹), frequency f (Hz), and wavelength λ (m).

3Wave Reflection and Refraction

• Reflection occurs when wave crests bounce off a planar surface;
  • refraction occurs when waves change speed and wavelength as they cross into a medium of different optical or physical depth.

4Diffraction and Wave Spreading

• Diffraction is the spreading of waves as they pass through a gap or around an obstacle;
  • diffraction is most pronounced when the gap width is roughly equal to the wavelength.

5Diffraction

• Spreading of waves through a gap or around an edge

6Reflection

• Light bouncing off a surface.

7Refraction

• Change in direction of light when it changes speed between media.

8Spread

• The extent to which repeated readings differ.

9Period

• Time for one revolution.

10Transverse wave

• Wave whose vibration is at right angles to the direction of propagation

Section 15 of 30The wave equation

Equation

• Equation v = fλ.
  What the symbols mean: v = wave speed (m s⁻¹) · f = frequency (Hz) · λ = wavelength (m)
• v is wave speed in m/s, f is frequency in Hz and λ is wavelength in m.

Applies to all waves

• Applies to all waves transverse and longitudinal waves both obey it.

Unit conversions

• Unit conversions convert before substituting.
• 1 kHz = 1000 Hz and 1 MHz = 1 000 000 Hz.
• Centimetres must be changed to metres.

Section 16 of 30Frequency and period

Period

• Period the time for one complete wave to pass a fixed point, T in seconds.

Relationship

• Relationship f = 1 ÷ T and T = 1 ÷ f.

Crest to trough

• Crest to trough this is half a wavelength, so double it to find λ.

Section 17 of 30Transverse waves

Transverse waves

Definition

• Definition the vibrations are at right angles to the direction the wave travels.

Features

• Features they have crests and troughs.

Medium

• Medium mechanical transverse waves travel through solids and on liquid surfaces, but not through the body of a liquid or a gas.
• Electromagnetic transverse waves travel through a vacuum.

Section 18 of 30Longitudinal waves

Longitudinal waves

Definition

• Definition the vibrations are parallel to the direction the wave travels.

Features

• Features regions of compression alternate with regions of rarefaction (particles spread apart).
  • (particles close)

Medium

• Medium they travel through solids, liquids and gases but not a vacuum, since particles are needed.

Section 19 of 30Comparing the two types

Property	Transverse	Longitudinal
Structure	Crests and troughs	Compressions and rarefactions
Vibration	Perpendicular to travel	Parallel to travel
Vacuum	Only electromagnetic waves	No
Medium	Solids and liquid surfaces	Solids, liquids, gases
Density and pressure	Constant	Vary along the wave

Section 20 of 30More key facts: The Wave Equation and Types of Wave

More key facts: The Wave Equation and Types of Wave

Rearrangements

• Rearrangements f = v ÷ λ and λ = v ÷ f.

Large units

• Large units radio frequencies are in kHz and MHz, so multiply by 1000 or 1 000 000.

Light

• Light with v = 3.0 × 10⁸ m/s, a 100 MHz radio wave has wavelength 3.0 m.

Sound

• Sound a 340 Hz note in air has wavelength 1.0 m at 340 m/s.

Seismic waves

• P-waves are longitudinal and S-waves are transverse.

Slinky

• Slinky shake it side to side for transverse and push it forwards and backwards for longitudinal.

Section 21 of 30More from the specification

More from the specification

Wave Generation in a Ripple Tank

• In a laboratory ripple tank, an oscillating paddle generates continuous water waves whose moving wavefronts can be illuminated and projected onto a screen.

Reflection of Water Wavefronts

• When water wavefronts strike a solid reflecting barrier, they undergo reflection with the angle of incidence equal to the angle of reflection, preserving wave speed and wavelength.

Refraction Across Varying Depths

• When water waves enter a shallow region over a submerged plate, their speed and wavelength decrease,
• causing wavefronts entering at an angle to bend toward the normal.

Diffraction of Waves Through Gaps

• When water waves encounter an opening, diffraction causes the wavefronts to spread out;
  • maximum semicircular spreading occurs when the gap width approximates the wavelength distance.

Energy transfer

• Movement of energy from one store to another.

Diffraction

• Spreading of waves through a gap or around an edge

Ripple

• The small fluctuation left in the smoothed output

Wavefront

• Line joining points on a wave that are in step

Amplitude

• Maximum displacement from equilibrium.

Reflection

• Light bouncing off a surface.

Distance

• Total length of path travelled, a scalar.

Refraction

• Change in direction of light when it changes speed between media.

Position

• Location relative to a reference point.

Section 22 of 30Reflection, refraction and diffraction

All waves

• All waves both transverse and longitudinal waves can be reflected, refracted and diffracted.

Medium

• Medium the material a wave travels through; plural is media.

Section 23 of 30Reflection

Definition

• Definition the wave hits a boundary and bounces back into the original medium.

Law

• Law the angle of incidence equals the angle of reflection.

Drawing

• Drawing keep the wavelength unchanged and make the angles equal.

Section 24 of 30Refraction

Definition

• Definition a wave changes speed when it crosses a boundary between two media.

What changes

• What changes speed, wavelength and direction, but not frequency.
• Refraction is the only wave effect that changes the wavelength.

Slowing down

• Slowing down the waves bunch up so the wavelength decreases and the waves turn towards the normal.

Speeding up

• Speeding up the waves spread out so the wavelength increases and they turn away from the normal.

Section 25 of 30Diffraction

Definition

• Definition waves spread out when they pass through a gap or round an edge.

Wavelength

• Wavelength it stays the same during diffraction.

Gap size

• Gap size diffraction is greatest when the gap is about the same size as the wavelength.
• A gap much larger than the wavelength gives very little spreading.

Edges

• Edges waves curve round the edge of a barrier, and longer wavelengths bend more than shorter ones.

Drawing

• Drawing draw semicircular wavefronts centred on the gap when the gap is similar to the wavelength.

Section 26 of 30Ripple tank demonstrations

Viewing

• Viewing a lamp above the tank projects the wavefronts onto a screen below.

Changing wavelength

• Changing wavelength a higher motor frequency gives a shorter wavelength, and a lower frequency gives a longer wavelength.

Property	Set-up	Observation
Reflection	Metal bar placed in the water, at 45° if wanted	Angle of incidence equals angle of reflection
Refraction	Glass block under water makes it shallower	Waves slow down, wavelength shortens, frequency unchanged
Diffraction at a gap	Two barriers with a gap	Waves spread more as gap gets nearer to the wavelength
Diffraction at an edge	One barrier	Waves curve round the edge

Section 27 of 30More key facts: Wave Behaviour and the Ripple Tank

Wave speed in water

• Wave speed in water it depends on depth, so waves slow down in shallow water.

Boundary behaviour

• Boundary behaviour a wave at a boundary can be reflected, refracted or both.

Normal line

• Normal line angles of incidence, reflection and refraction are measured from it.

Safety in ripple tanks

• Safety in ripple tanks keep water away from electrical connections.

Section 28 of 30More from the specification

More from the specification

Transverse vs longitudinal wave properties

• In transverse waves, oscillations are perpendicular to energy propagation;
  • in longitudinal waves (e.g. sound), oscillations are parallel to propagation.

Wave speed equation

• All waves obey the fundamental wave equation v = f * lambda, where v is wave speed (m/s), f is frequency (Hz), and lambda is wavelength (m).

Reflection, refraction, and diffraction

• Waves reflect at equal angles, refract when changing speed across media boundaries,
• and diffract when passing through apertures comparable to their wavelength.

Wave amplitude definition

• Wave amplitude definition maximum displacement of oscillating particles from their undisturbed equilibrium position to a crest or trough.

Wave speed equation

• Wave speed equation relates wave speed to frequency and wavelength through the universal relation v = f λ.

Water surface wave propagation

• Water surface wave propagation vibrating dippers generate circular or straight transverse wave crests propagating across the water surface in ripple tanks.

Period

• Time for one revolution.

Crest

• The highest point of a wave.

Energy transfer

• Movement of energy from one store to another.

Amplitude

• Maximum displacement from equilibrium.

Distance

• Total length of path travelled, a scalar.

Position

• Location relative to a reference point.

Trough

• The lowest point of a wave.

Section 29 of 30Key terms

Term	Meaning
Wavelength	Distance between a point on one wave and the same point on the next wave
Frequency	Number of waves passing a point per second
Amplitude	Maximum displacement from the undisturbed position
Wavefront	Line joining points on a wave that are in step
Diffraction	Spreading of waves through a gap or around an edge

Term	Meaning
Wavefront	A line joining points on a wave that are in step.
Amplitude	Maximum displacement from the undisturbed position.
Wavelength	Distance between the same points on successive waves.
Frequency	Number of waves passing a point each second, in hertz.
Crest	The highest point of a wave.
Trough	The lowest point of a wave.

Term	Meaning
Wave speed	Distance a wave travels each second, v = fλ.
Period	Time for one complete wave to pass a point.
Transverse wave	A wave whose vibrations are perpendicular to its direction of travel.
Longitudinal wave	A wave whose vibrations are parallel to its direction of travel.
Compression	A region where particles are close together.
Rarefaction	A region where particles are spread apart.

Term	Meaning
Reflection	A wave bouncing back at a boundary.
Refraction	A change in wave speed, and usually direction, at a boundary.
Diffraction	The spreading of a wave through a gap or round an edge.
Normal	A line at right angles to a boundary.
Medium	The material through which a wave travels.
Ripple tank	A shallow tank used to show properties of water waves.

Section 30 of 30Exam technique

1

Saying a wave carries matter — it carries energy while the medium only oscillates.

2

Measuring amplitude from crest to trough — it is measured from the undisturbed position to a crest or trough.

3

Saying the frequency changes in refraction — frequency stays the same while speed and wavelength change.

4

Forgetting unit conversions in v = fλ — convert to m and Hz first.

1

Measuring amplitude from crest to trough — it is from the centre line to a crest or trough.

2

Saying a wave carries the medium along with it.

3

Confusing the wave with the particles that vibrate.

4

Using L for wavelength — use λ.

1

Forgetting to convert kHz or cm before using v = fλ.

2

Using crest-to-trough as the whole wavelength.

3

Calling sound a transverse wave.

4

Saying P-waves are transverse — P-waves are longitudinal and S-waves are transverse.

1

Saying the frequency changes when a wave is refracted.

2

Drawing diffracted waves with a changed wavelength.

3

Calling a change of direction at a depth change diffraction.

4

Saying a longer wavelength diffracts less.