Waves
3. Waves — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions
15 min read 23 parts Lesson 1 of 35 1 quiz
Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
Lesson summary
Waves — notes: Describe wave properties and behaviour, use the wave equation, explain reflection, refraction and total internal reflection of light, and recall the electromagnetic spectrum and sound.Waves transfer energy without transferring matter — the wave travels but the par…
- Oscillation
- Exam wording
- Demonstrations
- Wavelength
- Crest and trough
- Wave speed
Part 1 of 21Waves and energy transfer
Waves and energy transfer
Waves transfer energy without transferring matter
- Waves transfer energy without transferring matter the wave travels but the particles only oscillate about fixed positions.
Evidence
- Evidence a toy duck on water bobs up and down but does not travel along with the wave.
Oscillation
- Oscillation ripples make water particles move up and down; sound makes air particles vibrate back and forth.
Exam wording
- Exam wording the particles are not the wave; the wave motion causes the particles to move.
Demonstrations
- Demonstrations ropes, springs and water waves in a ripple tank show frequency, wavelength, amplitude and wave speed.
Part 2 of 21Features of a wave
Features of a wave
Wavefront
- Wavefront a line joining points in step, usually crests, seen from above.
- Close wavefronts mean a short wavelength and far apart wavefronts mean a long wavelength;
- the ray shows the direction of travel.
Amplitude
- A is the maximum displacement from the undisturbed position (m), measured to a peak or trough, not crest to trough.
Wavelength
- λ is the distance from a point on the wave to the same point on the next wave (m).
- Transverse
- peak to peak;
- longitudinal: centre of one compression to the next.
- peak to peak;
Frequency
- Frequency f is the number of waves passing a point per second (Hz).
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, i.e. the speed at which energy is transferred.
Part 3 of 21The wave equation and period
Wave equation
- Wave equation v = f λ (m/s, Hz, m) for transverse and longitudinal waves.What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
Example
- λ = 5 cm = 0.05 m and f = 6.6 kHz = 6600 Hz give v = 6600 x 0.05 = 330 m/s.
- Convert cm to m and kHz to Hz (1 MHz = 1 000 000 Hz) before substituting.
Period
- T is the time for one complete wave to pass a point; f = 1 / T and T = 1 / f (s).
Example
- Example v = 0.27 m/s and crest to nearest trough = 0.75 cm, so λ = 2 x 0.75 = 1.5 cm = 0.015 m.
- f = v / λ = 0.27 / 0.015 = 18 Hz and T = 1 / 18 = 0.056 s.
Exam tip
- Exam tip use v, f and λ as the symbols; a word equation still earns the first mark.
Part 4 of 21Transverse and longitudinal waves
| Property | Transverse | Longitudinal |
|---|---|---|
| Structure | Crests and troughs | Compressions and rarefactions |
| Vibration | At right angles to the direction of propagation | Parallel to the direction of propagation |
| Vacuum | Electromagnetic waves can travel in a vacuum | Cannot travel in a vacuum |
| Medium | Solids and the surface of liquids (mechanical) | Solids, liquids and gases |
| Density and pressure | Constant | Vary along the wave |
Examples of transverse
- Examples of transverse electromagnetic waves, water ripples and seismic S-waves.
- (radio, visible light, X-rays)
Examples of longitudinal
- Examples of longitudinal sound and seismic P-waves; a slinky pushed back and forth shows them.
Definitions
- Definitions always state the direction of vibration relative to the direction of wave travel.
Part 5 of 21Reflection, refraction and diffraction
Reflection
- Reflection the wave bounces off a boundary and stays in the original medium;
- the angle of incidence equals the angle of reflection and the wavelength is unchanged.
Refraction
- Refraction a wave crossing a boundary changes speed, wavelength and direction, but not frequency.
- Slowing waves bunch together and turn towards the normal; speeding waves spread out and turn away.
Diffraction
- Diffraction waves spread out when passing through a gap or around an edge; wavelength stays constant.
Note
- Note refraction is the only effect that changes wavelength;
- direction change is a consequence of the speed change.
Part 6 of 21Factors affecting diffraction (Extended)
Gap size
- Gap size diffraction is greatest when the gap is about the same as the wavelength;
- wider gaps give less spreading and a very large gap gives none.
Wavelength
- Wavelength longer wavelengths diffract more around edges than shorter ones.
Drawing
- Drawing show semicircular wavefronts centred on the gap when the gap is similar to the wavelength, with unchanged spacing.
Part 7 of 21Ripple tank investigations
Set-up
- Set-up a motor-driven paddle makes waves, a lamp above projects wavefronts onto a screen below.
Reflection
- Reflection wavefronts reflect off a metal bar with i = r;
- at 45 degrees the incident and reflected wavefronts meet at right angles.
Refraction
- Refraction a glass block under the water makes the water shallower, so waves slow down and the wavelength shortens while the frequency is unchanged.
Diffraction
- Diffraction barriers with a gap or an edge show spreading;
- changing the gap size or motor frequency changes the effect.
Frequency and wavelength
- Frequency and wavelength a higher motor frequency gives a shorter wavelength.
Exam tip
- Exam tip a change of direction at a depth change is refraction; diffraction happens at a gap or edge.
Part 8 of 21Reflection of light and the plane mirror
Normal and angles
- Normal and angles the normal is drawn at 90 degrees to the boundary; i and r are measured from the normal.
- Arrows show the directionincident toward the boundary, reflected away from it.
Law of reflection
- Law of reflection i = r; it is used in mirrors, cameras, optical fibres and periscopes.
Plane mirror image
- Plane mirror image is the same size as the object, the same distance behind the mirror as the object is in front, and virtual.
Virtual image
- Virtual image formed where traced-back rays appear to cross; it cannot be projected onto a screen.
Part 9 of 21Practical: investigating reflection by a plane mirror
- Independent variable is the angle of incidence; dependent is the angle of reflection.
1
Draw a line about 10 cm long on paper and a 90 degree normal through its middle.
2
Place the mirror on the first line.
3
Aim a ray-box beam at the point where the lines cross.
4
Mark a point on the incident beam and a point about 10 cm along the reflected beam.
5
Remove the ray box and mirror, join the marks to the crossing point.
6
Measure i and r from the normal with a protractor.
7
Repeat for at least three more angles (for example 10, 30, 45, 80 degrees); i should equal r.
Part 10 of 21Reflection practical: errors and safety
Reflection practical: errors and safety
Systematic errors
- Systematic errors incorrect 90 degree lines or a distorted mirror.
- (use a set square)
Random errors
- Random errors marking beam positions inaccurately and protractor resolution.
- (sharp pencil, centre of beam)
Controlled variables
- Controlled variables distance of the ray box, beam width and wavelength of light.
Safety
- Safety a hot ray box can burn, do not look into the beam, keep liquids away from electrics and handle the mirror carefully.
- (cool under running water for 5 minutes)
Part 11 of 21Refraction of light
Direction change
- Direction change from less to more optically dense (air to glass) light bends towards the normal;
- from more to less dense it bends away; along the normal it does not bend.
Memory aid
- Enters Towards, Leaves Away.
Glass block
- Glass block the refracted ray at the first boundary is the incident ray at the second.
Cause
- Cause light slows in a denser medium and speeds up in a less dense one;
- frequency, and therefore colour, does not change.
Properties that change
- Properties that change speed and wavelength only.
- (red light has low frequency, blue high frequency)
Part 12 of 21Practical: refraction using rectangular, semicircular and prism blocks
- Independent variable is the shape of the block; dependent is the angle of refraction.
1
Place the block on paper and draw round it.
2
Direct a ray-box beam at a side face.
3
Mark a point on the incoming ray, where it enters, where it exits, and a point about 5 cm along the emergent ray.
4
Draw normals, remove the block and join the points with straight lines.
5
Repeat with different angles of incidence and label each path (1, 2, 3 or A, B, C).
6
Repeat for the other block shapes; protractor resolution is 1 degree and ruler 1 mm.
Part 13 of 21Refractive index
Properties
- Properties n is always greater than 1, has no units and is larger for more optically dense materials.
- (glass about 1.5, diamond about 2.4)
Ratio of speeds
- Ratio of speeds n = speed of light in a vacuum / speed of light in the material.
Ratio of angles
- Ratio of angles n = sin i / sin r (i before r in the alphabet,
- so i is on top).What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction
- (both measured from the normal)
Example
- Example n = 1.53 and i = 15 degrees: sin r = sin 15 / 1.53 = 0.1692, so r = 9.7 degrees.
Common mistake
- Common mistake sin i / sin r is not i / r; find sin r first and then use the inverse sine.
Part 14 of 21Total internal reflection and the critical angle
Total internal reflection and the critical angle
Internal reflection
- Internal reflection at small angles inside a dense medium most light is refracted out and a weak ray is reflected back.
Total internal reflection (TIR)
- Total internal reflection (TIR) all the light is reflected back into the denser medium when light goes from a denser to a less dense material and the angle of incidence is greater than the critical angle.
Critical angle c
- Critical angle c the angle of incidence at which the angle of refraction is 90 degrees.
- (light runs along the boundary)
Equation
- Equation sin c = 1 / n,
- so n = 1 / sin c; a larger refractive index gives a smaller critical angle.What the symbols mean: c = critical angle · n = refractive index of the denser material (no unit)
Condition
- TIR needs the incident material to be denser than the second material and i greater than c.
Part 15 of 21Critical angle examples
Glass cube
- TIR first occurs at X when the angle of incidence is 90 - 25 = 65 degrees, so the critical angle is 65 degrees.
Opal and diamond
- Opal and diamond opal n = 1.5 gives sin c = 0.6667 and c = 42 degrees;
- diamond n = 2.4 gives sin c = 0.4167 and c = 25 degrees.
- Diamond has the smaller critical angle, so more light is totally internally reflected and it sparkles more.
Part 16 of 21Uses of total internal reflection
Optical fibres
- Optical fibres light is totally internally reflected each time it hits the edge, so signals travel along the fibre.
- Used in communications (landline phones, internet, cable TV), endoscopes and decorative lamps.
Endoscope
- Endoscope a camera on a fibre goes down the throat;
- light is reflected along the fibre to an eyepiece so doctors can see inside the body.
Right-angled prisms
- Right-angled prisms used in binoculars, telescopes, cameras and safety reflectors.
Periscope
- Periscope two right-angled prisms totally internally reflect light so you can see over tall objects.
Thin-film colours
- Thin-film colours partial internal reflection at boundaries produces a spectrum of colours.
- (CD surface, soap bubbles, oil on water)
Answering
- Answering give the whole name total internal reflection, name the object then the device (periscope).
- (right-angled prism)
Part 17 of 21Images, lenses and sight correction
Real image
- Real image formed where rays actually cross; it can be projected on a screen.
Virtual image
- Virtual image formed where rays only appear to cross when traced back; it cannot be projected.
Converging lens
- Converging lens brings parallel rays to the principal focus;
- the focal length is the distance from the lens centre to the focus.
- With the object beyond 2F the image is real, inverted and diminished;
- between F and the lens it acts as a magnifying glass giving an upright, virtual, enlarged image.
Correcting sight
- Correcting sight a converging lens corrects long sight and a diverging lens corrects short sight.
Part 18 of 21Dispersion of light
Dispersion
- Dispersion white light split into a spectrum when refracted through a prism because different colours (frequencies) travel at different speeds in glass.
Order
- Order red is refracted least and violet most.
Monochromatic light
- Monochromatic light has a single frequency and does not split.
Part 19 of 21Electromagnetic spectrum
Electromagnetic spectrum
Order of increasing frequency
- Order of increasing frequency radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
Common features
- Common features all are transverse, travel at 3.0 x 108 m/s in a vacuum and transfer energy.
Uses
- Uses radio and TV (radio waves), mobile phones and cooking (microwaves), remote controls and heaters (infrared), vision (visible), sterilising and detecting forgeries (UV), medical imaging (X-rays), sterilisation and treating cancer (gamma).
Dangers
- Dangers microwaves heat cells, UV and X-rays and gamma rays are ionising and can damage cells and cause cancer.
Part 20 of 21Sound
Sound waves
- Sound waves are longitudinal, produced by vibrations, and need a medium; they cannot travel in a vacuum.
Speed
- Speed is slowest in gases, faster in liquids and fastest in solids; in air it is about 330 m/s.
Pitch and loudness
- Pitch and loudness pitch depends on frequency and loudness on amplitude.
Human hearing
- Human hearing range is about 20 Hz to 20 000 Hz; ultrasound is above 20 000 Hz.
Echoes
- Echoes sound reflects from surfaces; speed = 2 x distance / time for an echo.
Part 21 of 21Worked examples
A wave has wavelength 5 cm and frequency 6.6 kHz. Calculate its speed. [4]4 marks
Worked examplesConvert: λ = 0.05 m and f = 6600 Hz.v = f λ = 6600 x 0.05.v = 330 m/s.A wave of speed 0.27 m/s has 0.75 cm from crest to nearest trough. Find the frequency and period. [5]5 marks
Worked examplesλ = 2 x 0.75 = 1.5 cm = 0.015 m.f = v / λ = 0.27 / 0.015 = 18 Hz.T = 1 / 18 = 0.056 s.A ray enters glass of n = 1.53 at 15 degrees to the normal. Find the angle of refraction. [3]3 marks
Worked examplesn = sin i / sin r so sin r = sin 15 / 1.53 = 0.1692.r = sin-1(0.1692) = 9.7 degrees.Compare opal (n = 1.5) and diamond (n = 2.4) and explain which sparkles more. [5]5 marks
Worked examplessin c = 1 / n: opal 0.6667 so c = 42 degrees; diamond 0.4167 so c = 25 degrees.TIR occurs when i is greater than c.Diamond has the smaller c, so more rays are totally internally reflected and it sparkles more.Explain how a toy duck shows that waves do not transfer matter. [2]2 marks
Worked examplesThe duck moves up and down but not along the surface.The wave transfers energy while the water particles only oscillate about fixed positions.
Key terms
| Term | Meaning |
|---|---|
| Wavelength | Distance between a point on a wave and the same point on the next wave. |
| Frequency | Number of waves passing a point per second, in hertz. |
| Refraction | Change in speed (and direction) of a wave crossing a boundary. |
| Diffraction | Spreading of waves through a gap or around an edge. |
| Refractive index | n = sin i / sin r = speed in vacuum / speed in material. |
| Critical angle | Angle of incidence giving an angle of refraction of 90 degrees. |
| Total internal reflection | Complete reflection of light inside a denser medium above the critical angle. |
| Virtual image | An image formed where rays only appear to cross; it cannot be projected. |
Avoid these mistakes
1
Saying refraction changes frequency — frequency is unchanged; speed and wavelength change.
2
Measuring amplitude from crest to trough — it is measured from the undisturbed position to a peak or trough.
3
Cancelling sine termssin i / sin r is not i / r.
4
Describing TIR as occurring from less dense to more dense — it needs light to go from a denser to a less dense medium above the critical angle.
5
Forgetting unit conversions (cm to m, kHz to Hz) in v = f λ.
Marked practiceQuizzes for this lesson
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