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All revision notes Revision notes · Vibrations & WavesVibrations & Waves revision notes
Transverse and longitudinal waves, the wave equation, reflection, refraction and diffraction, sound and ultrasound, the electromagnetic spectrum, oscillations and signals. Each section follows one lesson: what you need to know, key terms, the equations with units, a worked example, common mistakes and an exam tip.
1 Waves
What you need to know
Transverse Waves
- Waves transfer energy from place to place without transferring matter. A ribbon on a rope moves up and down as a pulse passes, then ends where it started.
- In a transverse wave the material vibrates at right angles to the direction the wave travels. Waves on ropes, water ripples and all electromagnetic waves are transverse.
- The amplitude is the greatest distance from the rest position, measured from rest, not from crest to trough. A bigger amplitude carries more energy.
Longitudinal Waves
- In a longitudinal wave the material vibrates along the direction the wave travels. Sound is longitudinal.
- Where particles are squeezed together is a compression (higher pressure); where they are spread apart is a rarefaction (lower pressure).
- The wavelength is the distance from one compression to the next (or from one crest to the next on a transverse wave). Five compressions in a row span four wavelengths.
Wave Speed
- The frequency is the number of waves passing a point each second, in hertz (Hz). The period is the time for one wave: T = 1 ÷ f.
- In one period a crest moves one wavelength, so wave speed = frequency × wavelength, v = fλ.
- The amplitude does not change the speed: a taller wave travels no faster.
Round the Corner
- Waves spread out as they pass through a gap or round an edge: this is diffraction.
- Through the same gap, longer wavelengths diffract more. You hear a bass drum round a corner before a piccolo, because its waves are metres long; light, with a wavelength of about 0.0000005 m, hardly spreads round a door.
Key terms
- Transverse wave
- a wave whose vibrations are at right angles to its direction of travel
- Longitudinal wave
- a wave whose vibrations are along its direction of travel
- Amplitude
- the greatest displacement from the rest position, in m
- Wavelength
- the distance from one point on a wave to the same point on the next wave, in m
- Frequency
- the number of waves passing a point each second, in Hz
Equations
| Equation | What it says, symbols and units |
|---|---|
v = fλ | Wave speed is frequency times wavelength, for every kind of wave.
|
T = 1f | The period is the time for one complete wave; it is one over the frequency.
|
Diagram to know
A transverse wave drawn as a displacement–distance graph: mark the rest line, a crest, a trough, the amplitude (rest to crest) and one wavelength (crest to crest). Beside it, a longitudinal wave on a slinky with compressions (C) and rarefactions (R) labelled and one wavelength from C to C.
Worked example
A buoy at sea rises and falls once every 0.50 s. Crests are 4.0 m apart. Find the frequency and the speed of the waves, and how long a crest takes to travel 120 m.
- f = 1 ÷ T = 1 ÷ 0.50 = 2.0 Hz.
- v = fλ = 2.0 × 4.0 = 8.0 m/s.
- Time = distance ÷ speed = 120 ÷ 8.0 = 15 s.
Answer: 2.0 Hz; 8.0 m/s; 15 s
Common mistakes
- Measuring the amplitude from crest to trough. It is from the rest position to a crest.
- Saying the water or air travels with the wave. Only the energy moves on.
- Counting compressions instead of gaps: seven compressions span six wavelengths.
Exam tip
When you describe a transverse or longitudinal wave, compare the direction of the vibrations with the direction of energy transfer. "Up and down" alone is not enough for the mark.
AP Physics and NGSS: AP Physics 2 (Unit 14) and NGSS HS-PS4-1 use the same v = fλ; NGSS asks you to use it to reason about waves in different media.
2 When Waves Meet
What you need to know
Reflection
- All waves reflect. At a flat barrier the angle of incidence equals the angle of reflection, both measured from the normal (the line at 90° to the surface).
- Reflection changes only the direction: the speed, frequency and wavelength stay the same.
Refraction
- Refraction is a change of direction caused by a change of speed at a boundary. Water waves slow down in shallow water.
- The frequency is set by the source and does not change; so when the wave slows, its wavelength gets shorter (v = fλ).
- A wave arriving at an angle bends towards the normal when it slows down. Arriving along the normal, it slows but does not bend.
Diffraction
- Diffraction is greatest when the gap is about the same size as the wavelength. Through a gap much wider than the wavelength, waves go through mostly straight, spreading only at the edges.
- Diffraction does not change the wavelength, frequency or speed. Long-wave radio diffracts round hills; short-wavelength FM waves hardly bend.
Superposition
- Where two waves overlap, the total displacement is the sum of the two displacements (superposition).
- Crest on crest gives a bigger crest (constructive interference); crest on trough cancels (destructive interference). Noise-cancelling headphones use this.
- Two sounds of slightly different frequency drift in and out of step, giving beats: the number of beats each second is the difference of the two frequencies.
Key terms
- Normal
- a line drawn at 90° to a surface, from which angles are measured
- Refraction
- the change in direction of a wave when its speed changes at a boundary
- Diffraction
- the spreading of a wave through a gap or round an edge
- Superposition
- adding the displacements of two waves where they overlap
Equations
| Equation | What it says, symbols and units |
|---|---|
angle of incidence = angle of reflection | Both angles are measured from the normal. |
v = fλ | Wave speed is frequency times wavelength, for every kind of wave.
At a boundary f stays the same, so v and λ change in proportion. |
fbeat = f1 − f2 | Two close frequencies give this many beats each second (larger minus smaller).
Not on IGCSE 0625 or GCSE; superposition is AP Physics 2 and NGSS content. |
Diagram to know
Wavefronts crossing from deep to shallow water at an angle: equally spaced straight lines that get closer together over the shallow region and turn towards the normal. Draw a ray at right angles to the fronts on each side.
Worked example
In a ripple tank, 10 waves span 25 cm and the dipper vibrates at 6.0 Hz. Find the wave speed. Over a glass plate the waves slow to 9.0 cm/s: find their new frequency and wavelength.
- Wavelength = 25 ÷ 10 = 2.5 cm.
- v = fλ = 6.0 × 2.5 = 15 cm/s.
- The frequency is set by the dipper, so it stays 6.0 Hz. New wavelength = v ÷ f = 9.0 ÷ 6.0 = 1.5 cm.
Answer: 15 cm/s; then 6.0 Hz and 1.5 cm
Common mistakes
- Measuring angles from the surface instead of from the normal.
- Saying the frequency changes when a wave refracts. Only the speed and wavelength change.
- Saying a wide gap gives the most diffraction. The most spreading is when the gap is about one wavelength.
Exam tip
When you draw waves after a gap, keep the wavelength (the spacing of the fronts) the same as before the gap. Examiners check the spacing with a ruler.
AP Physics and NGSS: AP Physics 2 adds interference patterns with path difference and the edge of a diffracted beam, sin θ = λ ÷ a. NGSS HS-PS4-1 uses superposition qualitatively.
3 Wave Speed & The Medium
What you need to know
Speed of Sound
- Sound travels through air at about 340 m/s (330 to 350 m/s, depending on the temperature).
- To measure it, time a sound over a measured distance and use v = d ÷ t. Over a few metres the time is milliseconds, far shorter than a reaction time of about 0.2 s, so use electronic timing; with a stopwatch, use a distance of hundreds of metres.
Sound Needs a Medium
- Sound is a mechanical wave: particles pass the vibration on, so it needs a medium (a solid, liquid or gas).
- Sound cannot travel through a vacuum. In the bell-jar experiment the ring fades as the air is pumped out, while the bell can still be seen: light needs no medium.
Speed in Each Medium
- Sound is fastest in solids, slower in liquids and slowest in gases: about 5000 m/s in steel, 1500 m/s in water and 340 m/s in air.
- The source sets the frequency, which does not change from one medium to the next; so the wavelength changes in proportion to the speed.
Echo Sounding
- An echo is reflected sound. A pulse sent to a reflector and back travels the distance twice, so distance = speed × time ÷ 2.
- Echo sounding (sonar) uses this to measure the depth of the sea, find wrecks and shoals of fish.
Key terms
- Medium
- the material a wave travels through
- Mechanical wave
- a wave passed on by the vibration of particles, such as sound
- Echo
- a sound wave reflected from a surface
- Vacuum
- a space with no particles in it
Equations
| Equation | What it says, symbols and units |
|---|---|
v = xt | Wave speed from how far a wave travels in a measured time, as with an echo.
|
d = v × t2 | Distance to a reflector from an echo: the pulse goes there and back.
|
Worked example
A ship's echo sounder sends a pulse straight down. The echo returns after 0.80 s. Sound travels at 1500 m/s in sea water. How deep is the sea?
- Distance travelled by the pulse = v × t = 1500 × 0.80 = 1200 m.
- That is down and back up, so the depth = 1200 ÷ 2 = 600 m.
Answer: 600 m
Common mistakes
- Forgetting to halve the distance in an echo question.
- Using the speed of sound in air for a sound in water or steel.
- Leaving a time in milliseconds when the speed is in m/s: 14.7 ms is 0.0147 s.
Exam tip
In a "describe how to measure the speed of sound" question, name the equipment, the distance you measure and how, the time you measure and how, then v = d ÷ t, and say you repeat and average.
AP Physics and NGSS: NGSS HS-PS4-5 asks how wave technologies such as sonar capture and transmit information. AP Physics 2 treats sound in Unit 14 with the same equations.
4 Frequency, Wavelength & Human Hearing
What you need to know
Oscilloscope
- On an oscilloscope time runs across the screen. Period = number of divisions for one cycle × time base; then f = 1 ÷ T.
- A higher frequency sounds higher in pitch: its peaks are closer together on the screen. The height of the trace shows the amplitude.
Hearing Range
- Humans hear from about 20 Hz to 20 000 Hz. The upper limit falls with age.
- Sound above 20 000 Hz is ultrasound; sound below 20 Hz is infrasound. Both are real sound that people cannot hear; a dog hears up to about 45 000 Hz.
Frequency & Wavelength
- In one medium the wave speed is fixed, so a higher frequency means a shorter wavelength: λ = v ÷ f.
- In air, an elephant's 14 Hz rumble has a wavelength of about 24 m; a bat's 50 kHz squeak about 7 mm.
Ultrasound
- Ultrasound partly reflects at every boundary between two materials. The time of each echo gives the depth of the boundary, d = vt ÷ 2.
- Uses: finding cracks in metal (an early echo shows a flaw), prenatal scans and sonar. Ultrasound is not ionising, so it is safer than X-rays for scanning a baby.
Key terms
- Pitch
- how high or low a note sounds; set by the frequency
- Period
- the time for one complete vibration, in s
- Ultrasound
- sound with a frequency above 20 000 Hz
- Time base
- the time each horizontal division of an oscilloscope screen represents
Equations
| Equation | What it says, symbols and units |
|---|---|
T = 1f | The period is the time for one complete wave; it is one over the frequency.
|
v = fλ | Wave speed is frequency times wavelength, for every kind of wave.
|
T = divisions for one cycle × time base | Reading a period off an oscilloscope screen.
|
Worked example
A singer's note is shown on an oscilloscope. One cycle spans 2.5 divisions and the time base is 2 ms/div. Find the frequency, and the wavelength of the note in air (speed 340 m/s).
- T = 2.5 × 2 ms = 5.0 ms = 0.0050 s.
- f = 1 ÷ T = 1 ÷ 0.0050 = 200 Hz.
- λ = v ÷ f = 340 ÷ 200 = 1.7 m.
Answer: 200 Hz; 1.7 m
Common mistakes
- Forgetting to change ms or μs into seconds before f = 1 ÷ T.
- Saying a bigger amplitude gives a higher pitch. Amplitude sets loudness; frequency sets pitch.
- Calling ultrasound a different kind of wave. It is ordinary sound, too high for us to hear.
Exam tip
Count divisions across several whole cycles, then divide by the number of cycles. It is more precise than reading one short cycle, and examiners often give a trace with 4 or 5 cycles for exactly that reason.
AP Physics and NGSS: NGSS HS-PS4-5 covers ultrasound imaging as a technology that uses waves. AP Physics 2 meets the same f = 1 ÷ T and v = fλ in its waves unit.
5 Waves Meet Matter
What you need to know
Ripple Tank Lab
- In a ripple tank, a straight barrier reflects waves with the angle of incidence equal to the angle of reflection.
- Through a gap about one wavelength wide the ripples spread out as near semicircles; through a wide gap they go almost straight on with curved ends. At a single edge, longer waves bend further into the shadow.
- Beyond any gap the wavefronts keep the same spacing: diffraction changes direction, not wavelength.
Reflect, Transmit, Absorb
- When a wave meets a boundary its energy is shared three ways: reflected, absorbed and transmitted. The three always add up to the energy that arrived.
- How it splits depends on the material and the wavelength. A heavy brick wall reflects most sound; low notes get through walls better than high notes; soft foam absorbs high notes well.
- Absorbed energy is not lost: it warms the material slightly.
How You Hear
- The ear turns sound in air into vibrations of the eardrum and three small bones (a solid), then into the fluid of the cochlea.
- These parts have mass and stiffness, so they respond only to a limited range of frequencies: about 20 Hz to 20 kHz in a young person.
Key terms
- Transmitted
- passed on through a material
- Absorbed
- taken in by a material, raising its internal energy
- Wavefront
- a line joining points on a wave that are in step, such as a line along a crest
- Cochlea
- the fluid-filled part of the inner ear that turns vibrations into nerve signals
Equations
| Equation | What it says, symbols and units |
|---|---|
angle of incidence = angle of reflection | Both angles are measured from the normal. |
energy arriving = energy reflected + energy absorbed + energy transmitted | At any boundary, conservation of energy shares the wave's energy three ways. |
Diagram to know
Ripples meeting a gap: straight, evenly spaced fronts before the gap. For a narrow gap (about one wavelength) draw semicircular fronts after it; for a wide gap draw straight fronts with only the ends curving. Keep the spacing the same everywhere.
Worked example
A sound wave carrying 0.60 J of energy reaches a wall. 0.51 J is reflected and 0.06 J is absorbed. How much energy is transmitted, and what percentage of the energy that arrived is that?
- Transmitted = 0.60 − 0.51 − 0.06 = 0.03 J.
- Percentage = 0.03 ÷ 0.60 × 100 = 5%.
Answer: 0.03 J, which is 5%
Common mistakes
- Drawing the wavelength shorter or longer after a gap.
- Saying absorbed energy disappears. It is transferred to the thermal store of the material.
- Mixing up reflection and diffraction in the ripple tank: reflection is at a barrier, diffraction at a gap or edge.
Exam tip
In a diffraction drawing, show at least three wavefronts after the gap, all with the same spacing as before it, and make the spreading clearly bigger for the narrower gap.
AP Physics and NGSS: NGSS MS-PS4-2 covers waves being reflected, absorbed or transmitted by different materials. AP Physics does not examine the ear.
6 Standing Waves & Resonance
What you need to know
A String's Note
- A vibration's frequency sets its pitch and its amplitude sets its loudness. Plucking a string harder makes it louder, not higher.
- A tighter, shorter or lighter string vibrates at a higher frequency. Half the length gives twice the frequency: an octave up.
- The string shakes the air beside it, and the sound reaches you as a longitudinal wave.
Standing Waves
- Waves on a string fixed at both ends reflect and overlap, making a standing wave. Only certain frequencies give a still pattern: whole-number multiples of the lowest one, the fundamental.
- Nodes never move; antinodes between them vibrate most. Each loop is half a wavelength, so λ = 2L ÷ n.
- A standing wave stores energy; the pattern does not travel along the string.
Pipes
- Air in a pipe forms a longitudinal standing wave. An open end is an antinode and a closed end is a node.
- An open pipe holds half a wavelength at its fundamental (f₁ = v ÷ 2L); a pipe closed at one end holds a quarter (f₁ = v ÷ 4L), so it plays an octave lower.
Resonance
- Everything that can vibrate has a natural frequency. Pushed at that frequency, its amplitude builds up: resonance.
- Examples: a swing pushed in time, the Millennium Bridge swaying under walkers in step, a glass shattered by a note. Dampers stop resonance building up.
- A pendulum's natural frequency depends on its length, not its mass: T = 2π√(L ÷ g) for small swings.
Key terms
- Standing wave
- a wave pattern that stays in place, made by two waves travelling in opposite directions
- Node
- a point on a standing wave that does not move
- Antinode
- a point on a standing wave with the largest vibration
- Fundamental
- the lowest frequency at which an object forms a standing wave
- Resonance
- the large build-up of amplitude when an object is driven at its natural frequency
Equations
| Equation | What it says, symbols and units |
|---|---|
λ = 2Ln, f1 = v2L | A string fixed at both ends (or an open pipe) holds n half-wavelengths; the fundamental has one.
Beyond IGCSE 0625; AP Physics 2 and NGSS. |
f1 = v4L | Fundamental of a pipe closed at one end: a quarter of a wavelength fits.
AP Physics 2; the small end correction is ignored. |
T = 2π√(L ÷ g) | Period of a simple pendulum for small swings (under about 15°).
AP Physics 1 (Unit 7). |
Diagram to know
A string fixed at both ends vibrating in three loops: nodes (N) at both ends and at one-third and two-thirds of the length, antinodes (A) in the middle of each loop. Mark one wavelength as two loops.
Worked example
A string 0.90 m long, fixed at both ends, vibrates in 3 loops. Waves travel along it at 120 m/s. Find the wavelength, the frequency of this pattern and the fundamental frequency.
- Each loop is half a wavelength: λ = 2L ÷ n = 2 × 0.90 ÷ 3 = 0.60 m.
- f = v ÷ λ = 120 ÷ 0.60 = 200 Hz.
- Fundamental f₁ = v ÷ 2L = 120 ÷ 1.80 = 67 Hz (to 2 s.f.). Check: three loops is three times the fundamental, 3 × 66.7 = 200 Hz.
Answer: 0.60 m; 200 Hz; 67 Hz
Common mistakes
- Taking a whole loop as a whole wavelength. One loop is half a wavelength.
- Saying a harder pluck raises the pitch. It raises the amplitude, so the loudness.
- Saying a heavier pendulum bob swings more slowly. The period does not depend on the mass.
Exam tip
Resonance answers need three ideas: the object has a natural frequency, it is driven at that same frequency, and the amplitude builds up. Write all three.
AP Physics and NGSS: Standing waves on strings and in pipes are AP Physics 2 (Unit 14) and NGSS HS-PS4-1; AP 2 adds the odd-only harmonics of a closed pipe (f₁, 3f₁, 5f₁). The pendulum and resonance are AP Physics 1 Unit 7.
7 Simple Harmonic Motion
What you need to know
The Restoring Force
- An oscillator has an equilibrium position. Displaced from it, a restoring force pulls it back. It is fastest at equilibrium, so it overshoots.
- In simple harmonic motion (SHM) the restoring force is proportional to the displacement and points back towards equilibrium: F = −kx.
- The amplitude is the greatest displacement from equilibrium.
Period of a Spring
- For a mass on a spring, T = 2π√(m ÷ k). Four times the mass gives twice the period; a stiffer spring gives a shorter period.
- The period does not depend on the amplitude. Time 10 oscillations and divide by 10 for a more precise value.
The Pendulum
- For small swings (under about 15°) a pendulum moves in SHM with T = 2π√(L ÷ g). Four times the length gives twice the period.
- The period does not depend on the mass of the bob; weaker gravity gives a slower swing.
Graphs of SHM
- Displacement against time is a cosine curve when timed from release at x = A. Its height is the amplitude and one wave along the time axis is one period.
- Velocity is a quarter of a cycle out of step: greatest as x passes zero, zero at the ends. Acceleration is always opposite to the displacement.
Energy in SHM
- With no friction the total energy stays the same: all elastic potential at the ends, all kinetic in the middle. E = ½kA².
- Twice the amplitude gives four times the energy and twice the top speed. With friction the motion is damped: each swing is smaller than the last.
Key terms
- Equilibrium position
- where the resultant force on the oscillator is zero
- Restoring force
- a force that always points back towards equilibrium
- Simple harmonic motion
- oscillation in which the restoring force is proportional to the displacement
- Damping
- the loss of energy from an oscillator, so its amplitude falls
Equations
| Equation | What it says, symbols and units |
|---|---|
F = −kx | The restoring force in SHM: proportional to the displacement, in the opposite direction.
|
T = 2π√(m ÷ k) | Period of a mass on a spring; independent of the amplitude.
|
T = 2π√(L ÷ g) | Period of a simple pendulum for small swings; independent of the mass.
|
E = ½kA2, vmax = A√(k ÷ m) | Total energy of a spring oscillator, and its top speed at equilibrium.
|
Diagram to know
Three graphs against time, one above the other with the same time axis: displacement (a cosine), velocity (a negative sine, zero where displacement is greatest) and acceleration (the displacement curve upside down).
Worked example
A 0.50 kg mass oscillates on a spring with k = 20 N/m and an amplitude of 0.10 m. Find the period, the frequency, the total energy and the greatest speed.
- m ÷ k = 0.50 ÷ 20 = 0.025, and √0.025 = 0.158.
- T = 2π × 0.158 = 0.99 s, so f = 1 ÷ T = 1.0 Hz.
- E = ½kA² = ½ × 20 × 0.10² = 0.10 J.
- vmax = A√(k ÷ m) = 0.10 × √40 = 0.63 m/s.
Answer: 0.99 s; 1.0 Hz; 0.10 J; 0.63 m/s
Common mistakes
- Thinking a bigger amplitude gives a longer period. In SHM it does not.
- Using the weight instead of the mass in T = 2π√(m ÷ k).
- Saying the acceleration is zero at the ends. That is where the velocity is zero and the acceleration is greatest.
Exam tip
To find k from experiment, plot T² against m: it is a straight line through the origin with gradient 4π² ÷ k. A straight-line graph is easier to check than a curve.
AP Physics and NGSS: This lesson is AP Physics 1 Unit 7 (and NGSS HS-PS2-1 and HS-PS3-2 for the force and energy ideas). IGCSE and GCSE do not include SHM.
8 Wave Phenomena Sandbox
What you need to know
Earthquake Waves
- Earthquakes send out seismic waves. P waves are longitudinal, faster, and cross solids and liquids. S waves are transverse, slower, and cross solids only.
- S waves do not arrive on the far side of the Earth (the S-wave shadow), which shows the outer core is liquid.
- The gap between the P and S arrivals grows with distance, so it gives the distance to the earthquake.
The EM Spectrum
- The electromagnetic spectrum in order of increasing frequency (decreasing wavelength): radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
- All electromagnetic waves are transverse, cross a vacuum and travel at the same speed in a vacuum, c = 3.0 × 108 m/s, so c = fλ.
- Ultraviolet, X-rays and gamma rays are ionising: they can knock electrons off atoms and damage cells.
Tsunami Warning
- Seismic waves through rock travel far faster than a tsunami across the ocean, so a seismometer can give a warning before the tsunami arrives.
- A tsunami slows as it reaches shallow water near the coast: its wavelength shortens and its height grows. Its very long waves diffract round islands.
Key terms
- P wave
- a longitudinal seismic wave that travels through solids and liquids
- S wave
- a transverse seismic wave that travels through solids only
- Electromagnetic spectrum
- the family of transverse waves from radio to gamma rays, all with speed c in a vacuum
- Ionising
- able to remove electrons from atoms
Equations
| Equation | What it says, symbols and units |
|---|---|
v = xt | Wave speed from how far a wave travels in a measured time, as with an echo.
For seismic waves: arrival time = distance ÷ speed, for P and S separately. |
c = 3.0 × 108 m/s | All electromagnetic waves travel at this speed in a vacuum, and at about the same speed in air.
|
c = fλ | Light and all electromagnetic waves: c = 3.00 × 10⁸ m/s in a vacuum.
|
Diagram to know
A cross-section of the Earth with the focus of a quake at the top: P-wave paths reaching all round but bent at the core, S-wave paths stopping at the outer core, and the S-wave shadow zone on the far side labelled.
Worked example
P waves travel at 8.0 km/s and S waves at 4.0 km/s. A station is 600 km from an earthquake. When does each wave arrive, and what is the gap between them?
- P wave: t = d ÷ v = 600 ÷ 8.0 = 75 s.
- S wave: t = 600 ÷ 4.0 = 150 s.
- Gap = 150 − 75 = 75 s.
Answer: P after 75 s, S after 150 s; the gap is 75 s
Common mistakes
- Swapping P and S: P waves are the primary (first, faster) waves and they are longitudinal.
- Listing the EM spectrum in the wrong order. Learn it by frequency from radio up to gamma.
- Saying different EM waves travel at different speeds in a vacuum. They all travel at c.
Exam tip
For "what does the S-wave shadow tell us", write the chain in full: S waves are transverse, transverse waves cannot travel through liquids, S waves do not reach the far side, so part of the core (the outer core) is liquid.
AP Physics and NGSS: NGSS HS-ESS2-3 uses seismic data as evidence for the Earth's layers; AP Physics does not examine seismic waves.
9 Using the EM Spectrum
What you need to know
A Job for Every Band
- Each band is used for what it passes through and what absorbs it.
- Radio: radio and television broadcasts, contactless cards and tags, astronomy. Microwaves: satellite links, mobile phones, Wi-Fi and microwave ovens (water absorbs them, heating food from the inside).
- Infrared: remote controls, thermal imaging cameras, electric heaters and grills, optical fibres. Visible light: seeing, photography, lighting.
- Ultraviolet: security marking (special inks glow under UV), sterilising water. X-rays: medical scans and airport security. Gamma rays: sterilising food and medical equipment, detecting and treating cancer.
How Much Is Too Much
- The harm a wave can do rises with frequency. Microwaves heat cells inside the body; infrared burns the skin; ultraviolet damages surface cells and eyes and can cause skin cancer.
- X-rays and gamma rays are ionising and penetrate deep, so they can mutate or kill cells and cause cancer.
- A more powerful beam, or a longer exposure, puts more energy into the body: E = Pt.
Aerials and Atoms
- Radio waves are made by charges oscillating in a transmitting aerial. When they are absorbed by a receiving aerial they make the charges oscillate: an alternating current at the same frequency as the wave.
- Infrared, light, ultraviolet and X-rays come from changes in atoms, as electrons move between energy levels; gamma rays come from changes in the nucleus.
Wave or Particle?
- Light makes interference fringes, so it travels as a wave. In the photoelectric effect it is absorbed in packets of energy called photons, E = hf.
- Brighter light means more photons each second, not bigger ones; only a high enough frequency frees electrons from a metal.
Key terms
- Microwaves
- EM waves between radio and infrared, used for satellite links, mobile phones and cooking
- Ultraviolet
- EM waves just beyond violet light; ionising, causes sunburn and skin cancer
- Aerial
- a conductor that sends or receives radio waves through oscillating charges
- Photon
- a packet of electromagnetic energy, E = hf
Equations
| Equation | What it says, symbols and units |
|---|---|
c = fλ | Light and all electromagnetic waves: c = 3.00 × 10⁸ m/s in a vacuum.
|
E = Pt | Energy absorbed from a beam: its power times the exposure time.
|
E = hf | Light comes in photons; higher frequency means more energy per photon. h = 6.63 × 10⁻³⁴ J s.
Not on IGCSE 0625 or GCSE; NGSS HS-PS4-3 (wave and particle models of light). |
Worked example
A microwave oven uses waves of frequency 2.45 × 109 Hz. Find their wavelength. The food absorbs 800 W for 90 s: how much energy does it absorb?
- λ = c ÷ f = 3.0 × 108 ÷ 2.45 × 109 = 0.12 m (about 12 cm).
- E = Pt = 800 × 90 = 72 000 J.
Answer: 0.12 m; 72 000 J
Common mistakes
- Saying all EM radiation is dangerous because it is "radiation". Only ultraviolet, X-rays and gamma rays are ionising.
- Giving a use without the reason: microwaves heat food because water molecules absorb them.
- Saying a stronger radio beam can ionise. More power only heats more; ionising depends on frequency.
Exam tip
For "explain why this band is used", link a property to the job: "X-rays pass through soft tissue but are absorbed by bone, so bones show up as a shadow." A use with no property scores at most half the marks.
AP Physics and NGSS: AQA's aerials point is Higher tier. NGSS HS-PS4-3 compares the wave and particle models of light; HS-PS4-4 covers the effects of absorbed radiation on matter. AP Physics 1 does not cover the EM spectrum.
10 Signals
What you need to know
Talking to Satellites
- Communication with satellites is mainly by microwaves: they pass through the atmosphere, cloud and the ionosphere. Mobile phones and Wi-Fi also use microwaves.
- A geostationary satellite orbits 35 800 km above the equator once a day, so it stays over one spot (satellite TV, some phones); a signal up and down takes about a quarter of a second. Low-orbit satellites answer faster but cross the sky.
- Bluetooth uses radio waves, which pass through walls but are weakened. Optical fibres carry visible light or infrared at very high data rates.
Analogue or Digital
- An analogue signal varies continuously and can take any value. A digital signal takes only two values, 0 and 1.
- To make a digital signal, the analogue signal is sampled many times a second and each sample is sent as a binary number. More samples and more bits per sample make a closer copy. Sound can be sent either way.
Noise and Regeneration
- Every signal picks up noise. An analogue repeater amplifies the noise along with the signal, so it gets worse at each stage.
- A digital repeater decides 0 or 1 and sends a clean pulse: regeneration. So digital signals travel further without losing quality and carry data at a higher rate.
Key terms
- Geostationary satellite
- a satellite that orbits once a day above the equator, staying over one point
- Analogue signal
- a signal that can take any value in a range
- Digital signal
- a signal that takes only two values, 0 and 1
- Regeneration
- restoring a digital signal to clean pulses at a repeater
- Bit rate
- the number of bits sent each second
Equations
| Equation | What it says, symbols and units |
|---|---|
t = dc | Time for a signal to travel a distance at the speed of light.
|
R = f × n | Bit rate of a digitised signal: samples each second times bits in each sample.
|
Diagram to know
An analogue signal as a smooth wave, and below it the same signal as a digital pulse train of two levels. Then the two after travelling with noise: the analogue one noisy after amplification, the digital one restored to clean pulses after regeneration.
Worked example
A geostationary satellite is 35 800 km above the ground. How long does a signal take to go up to it and straight back down? A phone line samples a voice 8000 times a second at 8 bits per sample: what is its bit rate?
- Distance up and down = 2 × 35 800 = 71 600 km = 7.16 × 107 m.
- t = d ÷ c = 7.16 × 107 ÷ 3.0 × 108 = 0.24 s.
- Bit rate = 8000 × 8 = 64 000 bits per second.
Answer: 0.24 s; 64 000 bit/s
Common mistakes
- Saying digital signals have no noise. They pick up noise too; it is removed when they are regenerated.
- Using only the height of the satellite for the delay, not up and back down.
- Saying satellites use radio waves that reflect off the ionosphere. Satellite links use microwaves, which pass through it.
Exam tip
"Give two advantages of digital signals" has two standard answers: they can be regenerated so they travel long distances without losing quality, and they carry data at a higher rate. Use those words.
AP Physics and NGSS: These are IGCSE 0625 Supplement points (3.3.5 to 3.3.10); AQA covers the uses of microwaves in communication. NGSS HS-PS4-2 asks you to evaluate the advantages of digital transmission and storage.
Written in Physiworld's own words. The course tags come from the same mapping as the syllabus maps; equations are on the IGCSE, GCSE, AP Physics 1 and NGSS formula sheets. Values use g = 9.8 N/kg.
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