Answer key · Unit 20

The dynamic Earth.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Misconception catalogue

Answer key 4

Lesson 1 of 4 · About 25 minutes

Seismic waves

An earthquake sends out two kinds of wave, P and S, at different speeds. The gap between their arrivals gives the distance to the source, and three stations locate it on the map.

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The 6 steps and their answers

Step 1 of 6
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Two kinds of wave
Practice · Choose
Question
An earthquake sends out P waves and S waves in every direction. Which wave will reach a distant seismograph first?

Correct answer
- Correct The P wave, because compression waves travel faster in rock than shear waves
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
60 °
Time since the quake
0.4 (Quake strikes → Waves cross the Earth)
Choices
Shown in a random order.
- Correct The P wave, because compression waves travel faster in rock than shear waves
- Wrong The S wave, because it is stronger and does most of the damage
  Misconception: Thinks the strongest shaking, the S waves or the surface waves, arrives first.
  Feedback from the catalogue
  The order of arrival is set by speed, not strength. P waves are compression waves, like sound, and rock resists being squeezed more than being sheared, so they are the fastest: about 6–13 km/s. S waves, shear waves, are about $1.7$ ⁠ times slower. So P waves arrive first, which is why they are called “primary”.
- Wrong Both together, because they left the source at the same moment
  Misconception: Thinks the gap between the P and S arrivals is the same at every station, since both waves leave the quake together.
  Feedback from the catalogue
  Both waves set off together, but they travel at different speeds, so the gap between them grows along the way, like a fast runner and a slow one starting together. At a distance $d$ ⁠, $\Delta t = \dfrac{d}{v_S} - \dfrac{d}{v_P}$ ⁠: in proportion to the distance. That is exactly why a distance can be measured from it.
Feedback for a right answer
The P wave, the “primary”. The S wave, the “secondary”, arrives after it, and the gap between them will soon give the distance.

Worked solution
1. A P wave is a longitudinal wave: the rock is squeezed and stretched along the direction of travel, like sound.
2. An S wave is a transverse wave: the rock moves sideways, at right angles to the direction of travel, which is possible only in a material that resists shearing.
3. Rock resists squeezing more than shearing, so P waves are about $1.7$ ⁠ times faster: about 6 km/s in the crust, against about 3.5 km/s.
Strength does not set the speed. The S waves and the surface waves after them move the ground harder, but arrive later.
Step 2 of 6
Open this step
Arrival times
Practice · Calculate
Question
The Seismometer is locked $30^\circ$ ⁠ from the quake, about 3300 km along the surface. The seismogram beside the Scene shows when each wave arrived. How long passed between the arrival of the P wave and the arrival of the S wave?

Correct answer
5.013 min ± 3%
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
30 °fixed
Time since the quake
Waves cross the Earth
Accepted within
± 3%
Computed from the Scene at this step’s setting
S arrival minus P arrival at the picked seismometer, NaN where either is missing/nodes/earth/outputs/spGap
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 6.137 min ± 2%
  Misconception: Gives one wave's arrival time instead of the gap between the S and P arrivals.
  Feedback from the catalogue
  The time a wave arrives also depends on the moment the quake began, and a station does not know when that was. What a seismogram measures without needing the clock at the source is the gap between the S arrival and the P arrival: $\Delta t = t_S - t_P$ ⁠. The distance is worked out from that.
- 11.15 min ± 2%
  Misconception: Gives one wave's arrival time instead of the gap between the S and P arrivals.
  Feedback from the catalogue
  The time a wave arrives also depends on the moment the quake began, and a station does not know when that was. What a seismogram measures without needing the clock at the source is the gap between the S arrival and the P arrival: $\Delta t = t_S - t_P$ ⁠. The distance is worked out from that.
Feedback for a right answer
About five minutes. The gap grows with distance, so it measures the distance to the quake.

Hint
Read both arrival times, and subtract.

Worked solution
1. The P wave arrives about $6.1$ ⁠ minutes after the quake.
2. The S wave arrives about $11.2$ ⁠ minutes after it.
3. The gap: $11.2 - 6.1 \approx 5.0$ ⁠ minutes.
At a real station nobody knows when the quake began, so the arrival times on their own are not enough. The gap, on the other hand, is measured on the seismogram directly.
Step 3 of 6
Open this step
The gap grows
Practice · Predict, then look
Question
At $30^\circ$ ⁠ from the quake the gap between the P and S waves is about five minutes. The Seismometer is moved to $60^\circ$ ⁠, twice as far. What will happen to the gap?

Correct answer
- Correct It will grow
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
30 °
Time since the quake
Waves cross the Earth
Choices
- Correct It will grow
- Wrong It will stay about five minutes, because both waves set off together
  Misconception: Thinks the gap between the P and S arrivals is the same at every station, since both waves leave the quake together.
  Feedback from the catalogue
  Both waves set off together, but they travel at different speeds, so the gap between them grows along the way, like a fast runner and a slow one starting together. At a distance $d$ ⁠, $\Delta t = \dfrac{d}{v_S} - \dfrac{d}{v_P}$ ⁠: in proportion to the distance. That is exactly why a distance can be measured from it.
- Wrong It will shrink, because the S wave will catch up
  Feedback
  The S wave is slower the whole way, so it only falls further and further behind.
Once the prediction is locked in, the Scene changes
Seismometer
60 °
The Scene then shows: 8.245 min · S arrival minus P arrival at the picked seismometer, NaN where either is missing/nodes/earth/outputs/spGap
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
About $8.3$ ⁠ minutes: the path is longer, and the S wave falls further behind.

Worked solution
1. At a distance $d$ ⁠, the P wave arrives after $\dfrac{d}{v_P}$ ⁠ and the S wave after $\dfrac{d}{v_S}$ ⁠.
2. The gap: $\Delta t = d\left(\dfrac{1}{v_S} - \dfrac{1}{v_P}\right)$ ⁠, in proportion to the path.
3. At $60^\circ$ ⁠: about $8.3$ ⁠ minutes. Not exactly twice, because the deeper waves travel through faster rock.
Like two runners starting together: the longer the course, the further the slow one falls behind.
Step 4 of 6
Open this step
How far
Practice · Calculate
Question
A seismograph in Eilat records a small quake: the S wave arrives 10 s after the P wave. In the crust, P waves travel at 6.0 km/s and S waves at 3.5 km/s. How far away is the source?

Correct answer
84 km ± 3%
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
30 °
Time since the quake
Waves cross the Earth
Accepted within
± 3%
A fixed value in the question
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 60 km ± 3%
  Misconception: Works out the distance to a quake as one wave's speed times the S−P gap.
  Feedback from the catalogue
  The gap $\Delta t$ ⁠ is not the time one wave travelled, but the difference between two travel times: $\Delta t = \dfrac{d}{v_S} - \dfrac{d}{v_P}$ ⁠. So $d = \dfrac{\Delta t}{\dfrac{1}{v_S} - \dfrac{1}{v_P}}$ ⁠. Multiplying $\Delta t$ ⁠ by one speed gives too short a distance.
- 35 km ± 3%
  Misconception: Works out the distance to a quake as one wave's speed times the S−P gap.
  Feedback from the catalogue
  The gap $\Delta t$ ⁠ is not the time one wave travelled, but the difference between two travel times: $\Delta t = \dfrac{d}{v_S} - \dfrac{d}{v_P}$ ⁠. So $d = \dfrac{\Delta t}{\dfrac{1}{v_S} - \dfrac{1}{v_P}}$ ⁠. Multiplying $\Delta t$ ⁠ by one speed gives too short a distance.
Feedback for a right answer
About 84 km: about 8 km for every second of gap.

Hint
$\Delta t = \dfrac{d}{v_S} - \dfrac{d}{v_P}$ ⁠. Take out $d$ ⁠.

Worked solution
1. The travel times: $t_P = \dfrac{d}{v_P}$ ⁠ and $t_S = \dfrac{d}{v_S}$ ⁠.
2. The gap: $\Delta t = d\left(\dfrac{1}{v_S} - \dfrac{1}{v_P}\right) = d\left(\dfrac{1}{3.5} - \dfrac{1}{6.0}\right) = d \cdot 0.119\ \mathrm{s/km}$ ⁠.
3. $d = \dfrac{10}{0.119} \approx 84\ \mathrm{km}$ ⁠.
A seismologist’s rule of thumb: every second of gap is about 8 km. Answering $60$ ⁠ means multiplying the gap by the P wave’s speed, as if it were that wave’s travel time.
Step 5 of 6
Open this step
Reading distance from the gap
Practice · Reach the target
Question
A distant station recorded a gap of $8$ ⁠ minutes between the P wave and the S wave. Move the Seismometer until the gap there is $8$ ⁠ minutes, and press Check. That will tell you how many degrees the station is from the quake.

Goal
- 8 min ± 3%
  At the start of the step: 5.013 min
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
30 °
Time since the quake
Waves cross the Earth
Read from the Scene at
S arrival minus P arrival at the picked seismometer, NaN where either is missing/nodes/earth/outputs/spGap
One setting that reaches it
Wave type
P waves
Seismometer
56 °
Feedback for a right answer
About $57^\circ$ ⁠, more than a sixth of the way round the Earth.

Feedback for a wrong answer
Not yet. If the gap is too short, move the seismometer farther away; if too long, bring it closer.

Hint
At $30^\circ$ ⁠ the gap is about five minutes, and at $60^\circ$ ⁠ about eight and a half.

Worked solution
1. The gap grows with distance, so there is one distance at which it is $8$ ⁠ minutes.
2. At $50^\circ$ ⁠ it is about $7.2$ ⁠ minutes, and at $60^\circ$ ⁠ about $8.3$ ⁠.
3. Exactly eight minutes comes at about $57^\circ$ ⁠, about 6300 km along the surface.
This is how seismologists read a distance from a table, or from a graph of arrival times built from thousands of quakes.
Step 6 of 6
Open this step
Three stations
Practice · Choose
Question
From the gap between the P and S waves, each station knows how far away the source is. How many stations does it take, at least, to find where it is on the map?

Correct answer
- Correct Three: each station gives a circle, and three circles cross at one point
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
60 °
Time since the quake
Waves cross the Earth
Choices
Shown in a random order.
- Correct Three: each station gives a circle, and three circles cross at one point
- Wrong One: the wave arrives from the direction of the source
  Misconception: Thinks one seismometer can locate an earthquake's epicentre.
  Feedback from the catalogue
  One seismograph gives only a distance: the epicentre lies somewhere on a circle round the station. A second station gives a second circle, and two circles cross at two points. Only a third station decides between them. So an epicentre is located from at least three stations, and in practice from hundreds.
- Wrong Two: the source is halfway between them
  Feedback
  Two circles cross at two points, and either could be the source. A third circle is needed to choose.
Feedback for a right answer
Three. One gives a circle, two give two points, and three decide.

Worked solution
1. One station knows only a distance $d_1$ ⁠: the source lies on a circle of radius $d_1$ ⁠ round it.
2. A second station adds a circle, and two circles cross at two points.
3. A third station’s circle passes through only one of them: that is the source.
This is triangulation, and GPS uses the same idea. In practice hundreds of stations are used, and they find the depth and the time of the quake too.

Lesson 2 of 4 · About 25 minutes

What is inside the Earth

Nobody has drilled deeper than twelve kilometres, but seismic waves cross the whole Earth. The S-wave shadow reveals a liquid outer core, the P-wave shadow the refraction in it, and faint waves in the shadow a solid inner core.

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The 5 steps and their answers

Step 1 of 5
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The S-wave shadow
Practice · Predict, then look
Question
The Seismometer is $120^\circ$ ⁠ from the quake, and Wave type is S waves. Will S waves reach it?

Correct answer
- Correct No, never
Setup, choices and feedback
The Scene at this step
Wave type
S wavesfixed
Seismometer
120 °fixed
Time since the quake
0.3 (Quake strikes → Waves cross the Earth)
Choices
- Correct No, never
- Wrong Yes, late, after passing through the core
  Misconception: Thinks the whole of the Earth's core is solid.
  Feedback from the catalogue
  If the whole core were solid, S waves would pass through it and reach the far side of the Earth too. They do not: beyond about $104^\circ$ ⁠ from the quake there are no direct S waves at all. A liquid cannot hold a shearing force, so a shear wave cannot travel through it. So the outer core is liquid, molten iron and nickel. Only the inner core is solid, because of the enormous pressure.
- Wrong Yes, but weak, because the path is long
  Feedback
  A long path weakens a wave, but does not make it vanish. Here no direct S wave arrives at all.
Once the prediction is locked in, the Scene changes
Time since the quake
Waves cross the Earth
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Never: $120^\circ$ ⁠ is inside the S-wave shadow. Something inside the Earth stops them.

Worked solution
1. S waves that leave the source steeply downward reach the core and stop there.
2. The waves that miss the core curve back to the surface, and the farthest of them reach about $103^\circ$ ⁠.
3. Beyond that, $120^\circ$ ⁠ included, there are no direct S waves: this is the S-wave shadow, and it covers more than a third of the Earth’s surface.
Time since the quake has reached the end, $28$ ⁠ minutes after the quake: the seismometers in the shadow stayed dark.
Step 2 of 5
Open this step
A liquid core
Practice · Choose
Question
S waves do not cross the core, and P waves do. What does that tell us about the outer core?

Correct answer
- Correct That it is liquid, because a liquid does not resist shearing and so carries no S waves
Setup, choices and feedback
The Scene at this step
Wave type
S waves
Seismometer
120 °
Time since the quake
Waves cross the Earth
Choices
Shown in a random order.
- Correct That it is liquid, because a liquid does not resist shearing and so carries no S waves
- Wrong That it is too dense, and S waves cannot get into it
  Misconception: Thinks S waves stop at the core because it is too dense or too deep for them.
  Feedback from the catalogue
  Density does not stop a wave: P waves pass through the same dense core. S waves stop because they are shear waves: the particles move at right angles to the direction of travel, and for that motion to be passed on, the material has to resist shearing. A liquid does not resist shearing, so it carries no S waves.
- Wrong That it is hard and solid, and the waves bounce off it
  Misconception: Thinks the whole of the Earth's core is solid.
  Feedback from the catalogue
  If the whole core were solid, S waves would pass through it and reach the far side of the Earth too. They do not: beyond about $104^\circ$ ⁠ from the quake there are no direct S waves at all. A liquid cannot hold a shearing force, so a shear wave cannot travel through it. So the outer core is liquid, molten iron and nickel. Only the inner core is solid, because of the enormous pressure.
- Wrong That it is too hot, and the heat absorbs the S waves
  Feedback
  Heat on its own does not absorb waves: P waves cross the same hot core. What matters is the state: solid or liquid.
Feedback for a right answer
Liquid. The S-wave shadow is the main evidence for a core of liquid metal.

Worked solution
1. In the Unit on waves we saw that a wave travels through a material when the material pulls each particle back to its place.
2. In a P wave the particles are squeezed and stretched, and every material, solid, liquid or gas, resists squeezing. In an S wave they move sideways, which needs a material that resists shearing: only a solid.
3. So S waves stop at the boundary of the core: it is liquid.
In 1914 Beno Gutenberg measured the depth of that boundary: about 2900 km. The outer core is molten iron and nickel.
Step 3 of 5
Open this step
The edge of the shadow
Practice · Calculate
Question
Wave type is locked on S waves. Move the Seismometer and find the distance from the quake beyond which S waves no longer arrive. At what angle does the shadow begin?

Correct answer
103.1 ° ± 2 °
Setup, choices and feedback
The Scene at this step
Wave type
S wavesfixed
Seismometer
90 °
Time since the quake
Waves cross the Earth
Accepted within
± 2 °
Computed from the Scene at this step’s setting
Where the chosen wave's shadow zone begins, degrees from the quake/nodes/earth/outputs/shadowFrom
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 113.8 ° ± 1.5 °
  Misconception: Pictures seismic waves crossing the Earth in straight lines, ignoring that they bend.
  Feedback from the catalogue
  The speed of seismic waves grows with depth, because the rock is more compressed and stiffer. So, like light passing between materials, they refract all the time, and their paths curve upward, back towards the surface. A straight line just grazing the core would reach about $114^\circ$ ⁠; the curved paths graze it already at about $103^\circ$ ⁠.
Feedback for a right answer
About $103^\circ$ ⁠. From the size of the shadow the radius of the core can be worked out: about 3500 km, more than half the radius of the Earth.

Hint
The seismometers in the shadow stay dark. Look for the last one that lights up.

Worked solution
1. In the Scene, the last seismometer an S wave reaches is about $103^\circ$ ⁠ from the quake.
2. Beyond it the shadow begins, and runs to the far side, $180^\circ$ ⁠.
The wave that gets farthest is the one that just grazes the core. If the waves travelled in straight lines, a line grazing a sphere of radius 3480 km would reach $2\arccos\dfrac{3480}{6371} \approx 114^\circ$ ⁠. The waves curve upward, because the rock is faster at depth, so the shadow begins earlier.
Step 4 of 5
Open this step
The P-wave shadow
Practice · Choose
Question
P waves travel through liquids, and still they have a shadow: between about $100^\circ$ ⁠ and about $140^\circ$ ⁠ from the quake no strong P waves arrive. Why?

Correct answer
- Correct In the liquid core they are slower, so they bend at its boundary and come out farther round
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
120 °
Time since the quake
Waves cross the Earth
Choices
Shown in a random order.
- Correct In the liquid core they are slower, so they bend at its boundary and come out farther round
- Wrong The liquid core stops them too, as it stops S waves
  Misconception: Thinks the P-wave shadow means P waves cannot cross the liquid core either.
  Feedback from the catalogue
  P waves travel through liquids: sound is a P wave in air and in water. The P shadow comes from refraction. In the liquid core P waves are much slower than in the mantle, so at the core’s boundary they bend sharply inward, like light entering water, and come out farther round. Between about $100^\circ$ ⁠ and about $140^\circ$ ⁠ no direct P waves arrive, and beyond that they arrive again.
- Wrong The inner core absorbs them
  Feedback
  The inner core actually reflects and bends some of them into the shadow: those are the faint waves that arrive there.
Feedback for a right answer
Refraction: the core acts like a diverging lens for P waves, and they skip the ring between $100^\circ$ ⁠ and $140^\circ$ ⁠.

Worked solution
1. In the lower mantle P waves travel at about 13 km/s, and in the liquid outer core at only about 8 km/s.
2. A wave passing into a slower material bends towards the normal, like light entering water (Snell’s law).
3. So P waves that hit the core bend inward, cross it, and come out on the far side, beyond $140^\circ$ ⁠. Between where the waves that miss the core end and where the waves that crossed it come out, a shadow is left.
The P shadow comes from refraction, and the S shadow from stopping. The two shadows together are what revealed the core.
Step 5 of 5
Open this step
The inner core
Practice · Choose
Question
In 1936 Inge Lehmann, a Danish seismologist, noticed that inside the P-wave shadow faint P waves arrive all the same. What did she conclude?

Correct answer
- Correct That inside the liquid core there is a solid inner core, which reflects and bends some of the waves into the shadow
Setup, choices and feedback
The Scene at this step
Wave type
P waves
Seismometer
120 °
Time since the quake
Waves cross the Earth
Choices
Shown in a random order.
- Correct That inside the liquid core there is a solid inner core, which reflects and bends some of the waves into the shadow
- Wrong That there is no core at all, and the shadow is a measuring error
  Feedback
  The S shadow and the broad P shadow have been measured again and again. The faint waves are an addition, not a contradiction.
- Wrong That the whole core is liquid right to the centre
  Feedback
  In an even liquid core there would be nothing to bend waves into the shadow. Another sharp boundary is needed inside.
Feedback for a right answer
A solid inner core. In the Scene you can see these faint waves reaching the seismometers inside the P shadow.

Worked solution
1. In an even liquid core, the waves that cross it come out only beyond about $140^\circ$ ⁠, and the shadow would be completely dark.
2. The faint waves in the shadow show there is another boundary inside the core, where the speed jumps again: an inner core, of radius about 1220 km.
3. P waves are faster in the inner core, and its boundary reflects and bends some of them into the shadow.
The inner core is solid, even though it is hotter than the outer core, because the pressure at the centre of the Earth, more than three million atmospheres, holds the iron solid.

Lesson 3 of 4 · About 30 minutes

Plate tectonics

The Earth's shell is broken into plates that move a few centimetres a year on a slowly flowing mantle. Distance is speed times time, and each kind of boundary builds something different: a ridge, a trench and volcanoes, mountains, or a fault.

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The 7 steps and their answers

Step 1 of 7
Open this step
Moving plates
Practice · Choose
Question
The Earth’s outer shell is broken into plates, which move a few centimetres a year. What do they move on, and what moves them?

Correct answer
- Correct On a mantle of hot, solid rock that flows very slowly; they are pulled mainly by cold sinking plates and pushed from the ridges
Setup, choices and feedback
The Scene at this step
Boundary
Spreading ridge
Time
5 million years
Plate speed
5 cm per year
Cut away
Cut away
Choices
Shown in a random order.
- Correct On a mantle of hot, solid rock that flows very slowly; they are pulled mainly by cold sinking plates and pushed from the ridges
- Wrong They float on a sea of liquid magma, and its currents carry them
  Misconception: Thinks the plates float on a layer of liquid magma.
  Feedback from the catalogue
  The mantle is solid rock: S waves pass through it, and that is the proof. It is hot enough to flow like cold pitch, a few centimetres a year, over millions of years. Magma forms only in particular places, such as under ridges and above sinking plates, when hot rock loses pressure or takes in water.
- Wrong Earthquakes push them a little each time
  Feedback
  Earthquakes are the result of the motion, not its cause: the plates catch on each other, strain builds up, and in the end the rock breaks all at once.
- Wrong The Earth’s spin flings them sideways
  Feedback
  The spin is steady and even, and it cannot make plates move in different directions from one another.
Feedback for a right answer
Solid rock that flows slowly, and cold plates that sink and pull. There is no sea of magma down there.

Worked solution
1. S waves cross the mantle, so it is solid. But it is hot enough to flow like pitch, very slowly, in convection currents: hot material rises, cold material sinks.
2. An ocean plate moving away from a ridge cools and gets heavier. In the end it sinks into the mantle and drags the rest of the plate after it: slab pull is the main force.
3. At the ridges hot material rises, partly melts, and builds new sea floor that pushes sideways.
The plates move at about the rate fingernails grow.
Step 2 of 7
Open this step
How far they move
Practice · Calculate
Question
Plate speed is locked at 5 cm a year, and Time at $5$ ⁠ million years. How far apart have the plates moved?

Correct answer
250 km ± 2%
Setup, choices and feedback
The Scene at this step
Boundary
Spreading ridge
Time
5 million yearsfixed
Plate speed
5 cm per yearfixed
Cut away
Surface
Accepted within
± 2%
Computed from the Scene at this step’s setting
How far the plates have moved relative to each other: rate × time (1 cm a year for a million years is 10 km)/nodes/block/outputs/moved
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 25 km ± 3%
  Misconception: Is off by a power of ten converting centimetres a year over millions of years.
  Feedback from the catalogue
  One centimetre a year for a million years is a million centimetres: $10^6\ \mathrm{cm} = 10^4\ \mathrm{m} = 10\ \mathrm{km}$ ⁠. So a plate moving 5 cm a year covers 50 km in a million years, and 250 km in five million.
- 2500 km ± 3%
  Misconception: Is off by a power of ten converting centimetres a year over millions of years.
  Feedback from the catalogue
  One centimetre a year for a million years is a million centimetres: $10^6\ \mathrm{cm} = 10^4\ \mathrm{m} = 10\ \mathrm{km}$ ⁠. So a plate moving 5 cm a year covers 50 km in a million years, and 250 km in five million.
Feedback for a right answer
250 km: 50 km in every million years.

Hint
$d = v t$ ⁠. Convert first: one centimetre a year for a million years is $10$ ⁠ kilometres.

Worked solution
1. $d = v t = 5\ \mathrm{cm/yr} \cdot 5 \times 10^6\ \mathrm{yr} = 2.5 \times 10^7\ \mathrm{cm}$ ⁠.
2. $2.5 \times 10^7\ \mathrm{cm} = 2.5 \times 10^5\ \mathrm{m} = 250\ \mathrm{km}$ ⁠.
A pace you cannot feel adds up to a whole ocean: in a hundred million years, 5000 km.
Step 3 of 7
Open this step
Three hundred kilometres
Practice · Reach the target
Question
Plate speed is locked at 2.5 cm a year, as in the Atlantic Ocean. Change Time until the plates have moved 300 km apart, and press Check.

Goal
- 300 km ± 1%
  At the start of the step: 0 km
Setup, choices and feedback
The Scene at this step
Boundary
Spreading ridge
Time
0 million years
Plate speed
2.5 cm per yearfixed
Cut away
Surface
Read from the Scene at
How far the plates have moved relative to each other: rate × time (1 cm a year for a million years is 10 km)/nodes/block/outputs/moved
One setting that reaches it
Boundary
Spreading ridge
Time
11.9 million years
Feedback for a right answer
$12$ ⁠ million years: 25 km in every million.

Feedback for a wrong answer
Not yet. If the plates have not reached 300 km, add time; if they have gone past, take some away.

Hint
2.5 cm a year is 25 km in every million years.

Worked solution
1. $v = 2.5\ \mathrm{cm/yr} = 25\ \mathrm{km}$ ⁠ per million years.
2. $t = \dfrac{d}{v} = \dfrac{300}{25} = 12$ ⁠ million years.
$12$ ⁠ million years ago there were already apes on Earth, and the Atlantic Ocean was about 300 km narrower than today.
Step 4 of 7
Open this step
An ocean opens
Practice · Calculate
Question
The Atlantic Ocean is about 5000 km wide, and it is opening at the ridge in its middle at about 2.5 cm a year. Roughly how many million years ago were America and Africa joined?

Correct answer
200 ± 3%
Setup, choices and feedback
The Scene at this step
Boundary
Spreading ridge
Time
20 million years
Plate speed
2.5 cm per year
Cut away
Cut away
Accepted within
± 3%
A fixed value in the question
Wrong answers it recognises
- 2000 ± 3%
  Misconception: Is off by a power of ten converting centimetres a year over millions of years.
  Feedback from the catalogue
  One centimetre a year for a million years is a million centimetres: $10^6\ \mathrm{cm} = 10^4\ \mathrm{m} = 10\ \mathrm{km}$ ⁠. So a plate moving 5 cm a year covers 50 km in a million years, and 250 km in five million.
- 20 ± 3%
  Misconception: Is off by a power of ten converting centimetres a year over millions of years.
  Feedback from the catalogue
  One centimetre a year for a million years is a million centimetres: $10^6\ \mathrm{cm} = 10^4\ \mathrm{m} = 10\ \mathrm{km}$ ⁠. So a plate moving 5 cm a year covers 50 km in a million years, and 250 km in five million.
Feedback for a right answer
About $200$ ⁠ million years, in the days of the first dinosaurs, when Pangaea began to break up.

Hint
$t = \dfrac{d}{v}$ ⁠, with $v = 25\ \mathrm{km}$ ⁠ per million years.

Worked solution
1. $v = 2.5\ \mathrm{cm/yr} = 25\ \mathrm{km}$ ⁠ per million years.
2. $t = \dfrac{5000}{25} = 200$ ⁠ million years.
That is just what the rocks show: the oldest sea floor in the Atlantic, near the coasts, is about $180$ ⁠ million years old, and at that time the supercontinent Pangaea broke up. The coasts of Brazil and West Africa still fit each other like jigsaw pieces.
Step 5 of 7
Open this step
A trench and volcanoes
Practice · Choose
Question
The Boundary is an ocean plate going under a continent, and Cut away has cut the block open. Where do volcanoes form at a boundary like this?

Correct answer
- Correct On the continent, above the sinking plate, some way from the trench
Setup, choices and feedback
The Scene at this step
Boundary
Ocean under continent
Time
10 million years
Plate speed
5 cm per year
Cut away
Cut away
Choices
Shown in a random order.
- Correct On the continent, above the sinking plate, some way from the trench
- Wrong In the trench itself, where the plates meet
  Feedback
  At the trench the plate is still cold, and only beginning to sink. The magma forms deeper, about a hundred kilometres below the surface.
- Wrong In the middle of the ocean plate, far from the boundary
  Feedback
  In the middle of a plate there are volcanoes only over a hot spot, like Hawaii. Here they form because of the sinking.
Feedback for a right answer
On the continent, above the sinking plate: the water it releases melts the mantle.

Worked solution
1. The ocean plate sinks into the mantle and carries water with it, bound into the rock of the sea floor.
2. At a depth of about a hundred kilometres the heat and pressure release the water into the mantle above the plate.
3. The water lowers the melting point of the rock, and it partly melts. The magma, lighter than the rock round it, rises and builds a volcanic arc on the continent.
That is how the Andes and Japan were built, and how the “Ring of Fire” round the Pacific formed.
Step 6 of 7
Open this step
Continents collide
Practice · Predict, then look
Question
At the last boundary an ocean plate sank under a continent. The Boundary is changed so that two continents collide. What will happen to one of them?

Correct answer
- Correct Neither will sink: they will crumple and build high mountains
Setup, choices and feedback
The Scene at this step
Boundary
Ocean under continent
Time
10 million years
Plate speed
5 cm per year
Cut away
Cut away
Choices
- Correct Neither will sink: they will crumple and build high mountains
- Wrong One will sink into the mantle, like the ocean plate
  Misconception: Thinks a continental plate sinks into the mantle at a collision, as an ocean plate does.
  Feedback from the catalogue
  Continental crust is lighter than the mantle, like a plank in water, so it does not sink. Ocean crust, which is heavier, sinks once it has cooled and aged. When two continents meet, neither goes down: they crumple and pile up into high mountains, with a deep root beneath. That is how the Himalayas and the Alps were built.
- Wrong They will stop as soon as they touch, and nothing will happen
  Feedback
  The forces that drive the plates do not stop, and the continents go on pushing into each other for millions of years.
Once the prediction is locked in, the Scene changes
Boundary
Continents collide
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
They crumple into mountains, with a deep root beneath. The Himalayas have been built this way for fifty million years.

Worked solution
1. Continental crust is made of light rocks, like granite, and is lighter than the mantle beneath it: it floats on it, like a plank in water.
2. So it does not sink. When the ocean between two continents closes, the continents push into each other, crumple and pile up.
3. The mountains that form sit on a deep root of crust, like an iceberg: for every kilometre of height, about five kilometres of root.
That is how the collision of India and Asia built the Himalayas, and it goes on: Everest still rises by a few millimetres a year.
Step 7 of 7
Open this step
Sliding past
Practice · Choose
Question
The Dead Sea Transform, which runs along the Arava, the Dead Sea and the Sea of Galilee, is a boundary where the Arabian plate and the Sinai plate slide past each other. What would you expect along it?

Correct answer
- Correct Earthquakes, but no volcanoes
Setup, choices and feedback
The Scene at this step
Boundary
Sliding past
Time
5 million years
Plate speed
5 cm per year
Cut away
Surface
Choices
Shown in a random order.
- Correct Earthquakes, but no volcanoes
- Wrong Earthquakes and volcanoes, as at every plate boundary
  Misconception: Thinks every plate boundary has volcanoes.
  Feedback from the catalogue
  Volcanoes need magma, and it forms in only two places: at spreading ridges, where the mantle rises and loses pressure, and above sinking plates, which release water into the mantle. At a boundary where plates slide past each other, like the Dead Sea Transform or the San Andreas Fault, neither happens: there are earthquakes, but no volcanoes.
- Wrong Nothing: plates sliding past each other do not affect each other
  Feedback
  The plates catch on each other, strain builds up, and it is released in earthquakes. In 1927 a quake like that badly hit Jerusalem, Nablus and Jericho.
Feedback for a right answer
Earthquakes only. In the Scene, at the “Sliding past” boundary, you can see the fields, the river and the road torn and offset.

Worked solution
1. At a boundary like this no new sea floor forms, as at a ridge, and no plate sinks, as at a trench.
2. So there is no magma, and there are no volcanoes.
3. But the plates do not slide freely: they stick, strain builds up over years, and the rock breaks all at once in an earthquake.
The Arabian plate moves north about half a centimetre a year relative to the Sinai plate. Since the transform formed, its two sides have moved about 105 km past each other.

Lesson 4 of 4 · About 25 minutes

The Earth's magnetic field

Liquid iron flowing in the core makes the magnetic field like a dynamo, which is why the field can flip. The sea floor keeps the flips in stripes, and from their width the spreading rate is measured.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
A magnet that is not
Practice · Choose
Question
The Earth’s magnetic field looks like the field of a big bar magnet. Why can it not come from a permanent iron magnet in the core?

Correct answer
- Correct The core is far hotter than the temperature at which iron loses its permanent magnetism
Setup, choices and feedback
The Scene at this step
Time
0 million years ago
Spreading rate
5 cm per year
Show the magnetic record
Off
Choices
Shown in a random order.
- Correct The core is far hotter than the temperature at which iron loses its permanent magnetism
- Wrong It can, and that really is where it comes from
  Misconception: Thinks the Earth's field comes from a giant permanent magnet of iron in the core.
  Feedback from the catalogue
  Iron loses its permanent magnetism above its Curie temperature, about 770 °C, and the core is hotter than 4000 °C. The field is made another way: liquid iron, which conducts electricity, flows through a magnetic field, by the law of induction that drives currents in it, and the currents make the field again. That is a dynamo, which is why the field can also change and flip, something a permanent magnet does not do.
- Wrong The core is too far from the surface
  Feedback
  A magnet’s field does weaken with distance, but it does not vanish. The problem is that at such a temperature iron cannot be a permanent magnet at all.
Feedback for a right answer
Too hot for a permanent magnet. The field is made again all the time, by a dynamo of liquid iron.

Worked solution
1. In the Unit on magnetism we saw that in a permanent magnet the magnetic domains of the iron are lined up the same way.
2. Above the Curie temperature, about 770 °C for iron, thermal motion destroys that order, and the permanent magnetism disappears.
3. The core is hotter than 4000 °C, so the field has to be made again all the time, by electric currents in the liquid iron.
The fact that the field flips from time to time does not fit a permanent magnet either.
Step 2 of 6
Open this step
Which pole is which
Practice · Choose
Question
The north end of a compass needle points north. Which pole of the Earth’s “magnet” is near the geographic North Pole?

Correct answer
- Correct A magnetic south pole, because opposite poles attract
Setup, choices and feedback
The Scene at this step
Time
0 million years ago
Spreading rate
5 cm per year
Show the magnetic record
Off
Choices
Shown in a random order.
- Correct A magnetic south pole, because opposite poles attract
- Wrong A magnetic north pole, which is why it is called that
  Misconception: Thinks the magnetic pole near the geographic North Pole is a north pole, so a compass's north end points to a north pole.
  Feedback from the catalogue
  Opposite poles attract. The north end of a compass needle is a magnetic north pole, and it is pulled towards the geographic North Pole. So what is there is actually a south pole of the Earth’s magnet: the field lines leave the Earth near the South Pole and enter near the North.
- Wrong Neither: the magnetic poles are on the equator
  Feedback
  The magnetic axis is tilted only about ten degrees from the spin axis, so the magnetic poles are close to the geographic ones.
Feedback for a right answer
A magnetic south pole. The name is geographic; the physics is the other way round.

Worked solution
1. Like poles repel, and opposite poles attract.
2. The north end of the needle is the north pole of a small magnet, and it is pulled northward.
3. So near the geographic North Pole there is a south pole of the Earth’s field. The field lines leave the Earth in the southern hemisphere, and enter in the northern.
The name “the north magnetic pole” describes the place, not the kind of pole.
Step 3 of 6
Open this step
Reversals
Practice · Predict, then look
Question
Today the compass over the ridge points north. Time is taken back to $1.4$ ⁠ million years ago. Which way will the compass point?

Correct answer
- Correct South: the field was reversed
Setup, choices and feedback
The Scene at this step
Time
0 million years ago
Spreading rate
5 cm per year
Show the magnetic record
Off
Choices
- Correct South: the field was reversed
- Wrong North, as today
  Misconception: Thinks the Earth's magnetic field has always pointed the way it does today.
  Feedback from the catalogue
  The field flips: over millions of years the magnetic north and south poles swap, on average a few times every million years, with no fixed pattern. The last flip was about $773{,}000$ ⁠ years ago. We know this from rocks, each of which “froze” the direction of the field at the moment it cooled.
- Wrong Nowhere, because there was no field
  Feedback
  The field gets very weak only for a few thousand years, during the flip itself. Between flips it is as strong as today.
Once the prediction is locked in, the Scene changes
Time
1.4 million years ago
The Scene then shows: -1 · The field at `time`: 1 normal, as today, −1 reversed/nodes/earth/outputs/polarity
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
South. The field has flipped dozens of times in the last ten million years.

Worked solution
1. $1.4$ ⁠ million years ago the Earth was in a period of reversed field, the Matuyama, which lasted from about $2.6$ ⁠ million years ago to about $773{,}000$ ⁠ years ago.
2. In a reversed field the magnetic poles swap places, and the north end of the needle points south.
The reading $-1$ ⁠ means a reversed field, and $1$ ⁠ a field like today’s. During a flip the dynamo weakens, the field tangles, and within a few thousand years it comes back the other way round.
Step 4 of 6
Open this step
Stripes on the sea floor
Practice · Calculate
Question
Spreading rate is locked at 5 cm a year, and Time on today. Show the magnetic record shows the magnetic stripes in the sea floor. The last flip was $773{,}000$ ⁠ years ago. How far from the ridge, on each side, does the central stripe reach?

Correct answer
19.33 km ± 3%
Setup, choices and feedback
The Scene at this step
Time
0 million years agofixed
Spreading rate
5 cm per yearfixed
Show the magnetic record
On
Accepted within
± 3%
Computed from the Scene at this step’s setting
Distance from the ridge to the edge of the stripe on it, each side, at half the spreading rate/nodes/earth/outputs/stripeHalfWidth
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 38.65 km ± 3%
  Misconception: Uses the full spreading rate for one side of a ridge, instead of half of it.
  Feedback from the catalogue
  The spreading rate is the rate at which both plates move apart from each other. Each plate moves only half of it, away from the ridge. So sea floor of age $t$ ⁠ is $\tfrac12 v t$ ⁠ from the ridge, on each side. At a ridge spreading at 5 cm a year, each side moves only 2.5 cm a year.
Feedback for a right answer
About 19.3 km on each side: half the rate, times the time since the flip.

Hint
Each side of the ridge moves at half the spreading rate.

Worked solution
1. Each plate moves away from the ridge at half the rate: 2.5 cm a year, that is 25 km in every million years.
2. The sea floor that has cooled since the last flip, $0.773$ ⁠ million years ago, has reached $0.773 \cdot 25 \approx 19.3\ \mathrm{km}$ ⁠ from the ridge.
3. So the central stripe, in today’s field, is about 39 km wide: about 19.3 km on each side.
Getting about 39 km for each side means using the full rate for one side.
Step 5 of 6
Open this step
A fast ridge
Practice · Reach the target
Question
At a fast ridge in the Pacific the central stripe reaches about 50 km from the ridge on each side. Change Spreading rate until the stripe in the Scene reaches 50 km on each side, and press Check.

Goal
- 50 km ± 2%
  At the start of the step: 19.33 km
Setup, choices and feedback
The Scene at this step
Time
0 million years agofixed
Spreading rate
5 cm per year
Show the magnetic record
On
Read from the Scene at
Distance from the ridge to the edge of the stripe on it, each side, at half the spreading rate/nodes/earth/outputs/stripeHalfWidth
One setting that reaches it
Spreading rate
13 cm per year
Feedback for a right answer
About 13 cm a year, five times the Atlantic’s, so the stripes there are five times as wide.

Feedback for a wrong answer
Not yet. If the stripe is too narrow, raise the rate; if too wide, lower it.

Hint
Each side moves at half the rate: $50\ \mathrm{km} = \tfrac12 v \cdot 0.773$ ⁠ million years.

Worked solution
1. $\tfrac12 v \cdot 0.773\ \mathrm{Myr} = 50\ \mathrm{km}$ ⁠, so $\tfrac12 v \approx 64.7\ \mathrm{km}$ ⁠ per million years, that is about 6.5 cm a year for each side.
2. The full rate: $v \approx 13\ \mathrm{cm}$ ⁠ a year.
That is close to the rate of the East Pacific Rise, the fastest ridge on Earth. The faster the ridge, the wider the stripes: from their width, and the known ages of the flips, the rate is measured.
Step 6 of 6
Open this step
Measuring the spreading
Practice · Calculate
Question
A ship towing a magnetometer over the Mid-Atlantic Ridge finds that the central stripe reaches 9.7 km from the ridge on each side. The last flip was $773{,}000$ ⁠ years ago. What is the ridge’s spreading rate, in centimetres a year?

Correct answer
2.51 ± 3%
Setup, choices and feedback
The Scene at this step
Time
0 million years ago
Spreading rate
5 cm per year
Show the magnetic record
On
Accepted within
± 3%
A fixed value in the question
Wrong answers it recognises
- 1.255 ± 3%
  Misconception: Uses the full spreading rate for one side of a ridge, instead of half of it.
  Feedback from the catalogue
  The spreading rate is the rate at which both plates move apart from each other. Each plate moves only half of it, away from the ridge. So sea floor of age $t$ ⁠ is $\tfrac12 v t$ ⁠ from the ridge, on each side. At a ridge spreading at 5 cm a year, each side moves only 2.5 cm a year.
Feedback for a right answer
About 2.5 cm a year, the rate of the Mid-Atlantic Ridge, just like the Mid-Atlantic preset in the Scene.

Hint
First find how far one side moves each year, then remember that the ridge opens on both sides.

Worked solution
1. One side: $\dfrac{9.7\ \mathrm{km}}{773{,}000\ \mathrm{yr}} = \dfrac{9.7 \times 10^5\ \mathrm{cm}}{7.73 \times 10^5\ \mathrm{yr}} \approx 1.25\ \mathrm{cm/yr}$ ⁠.
2. Both sides move apart, so the spreading rate is twice that: $v \approx 2.5\ \mathrm{cm/yr}$ ⁠.
This is how, in 1963, Fred Vine and Drummond Matthews explained the stripes: sea floor that forms at the ridge, cools and carries the direction of the field away with it. It was one of the strongest proofs of plate tectonics. Answering $1.25$ ⁠ means finding the rate of one side only.

Across the unit · 17 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

Index

Seismic waves

Two kinds of wave

Question

Correct answer

The Scene at this step

Choices

Worked solution

Arrival times

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

The gap grows

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

How far

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Reading distance from the gap

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

Three stations

Question

Correct answer

The Scene at this step

Choices

Worked solution

What is inside the Earth

The S-wave shadow

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

A liquid core

Question

Correct answer

The Scene at this step

Choices

Worked solution

The edge of the shadow

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

The P-wave shadow

Question

Correct answer

The Scene at this step

Choices

Worked solution

The inner core

Question

Correct answer

The Scene at this step

Choices

Worked solution

Plate tectonics

Moving plates

Question

Correct answer

The Scene at this step

Choices