Can We Make a Cloud in the Laboratory?

Meteorology Beyond the Syllabus: Making a Cloud — Why Does Air Suddenly Become Visible?

Look up at almost any British sky and there is a good chance that you will see clouds.

We become so accustomed to them that it is easy to forget just how extraordinary they are.

A cloud can contain an enormous quantity of water, yet remain suspended in the atmosphere. It can appear seemingly from nowhere, grow rapidly, disappear again, or develop into something capable of producing torrential rain, hail or snow.

But perhaps the most interesting question is much simpler:

Why can we see a cloud at all?

There is water vapour in the atmosphere around us virtually all the time. If water vapour makes clouds, why isn't the air around us permanently white and misty?

The answer takes us into some fascinating meteorology involving temperature, pressure, humidity, condensation and the behaviour of rising air.

Better still, we can demonstrate much of it in the laboratory.

---

Water Vapour Is Invisible

The first misconception worth tackling is one that I regularly encounter when teaching science:

water vapour is not the white material that we see above a boiling kettle.

Water vapour is water in its gaseous state, and it is invisible.

The visible white mist above a kettle consists primarily of tiny liquid water droplets that have formed after the invisible water vapour has cooled and condensed.

That distinction is enormously important when we start thinking about clouds.

A cloud is not simply a mass of water vapour.

It consists of vast numbers of microscopic liquid water droplets, ice crystals, or a mixture of the two.

So our real question becomes:

What makes invisible water vapour suddenly condense into visible droplets?

---

Let's Make a Cloud

One of the things I particularly enjoy about teaching science in a laboratory is being able to turn an apparently enormous natural phenomenon into something that can be investigated on a bench.

We obviously cannot fit a thunderstorm into the laboratory.

But we can reproduce one of the fundamental physical processes responsible for cloud formation.

A classic demonstration uses a strong transparent container containing moist air. A small amount of water provides a source of water vapour. A suitable method is then used to increase and subsequently reduce the pressure.

There are several versions of the experiment, including commercially produced cloud chambers and demonstrations using robust pressure-rated transparent vessels.

Important safety point: pressure demonstrations should only be performed with apparatus designed to withstand the pressure differences involved. Ordinary glass jars or improvised containers should not be pressurised.

The dramatic moment occurs when the pressure is suddenly reduced.

A faint white cloud can appear inside the container.

Increase the pressure again and it may disappear.

Reduce it again and the cloud returns.

That immediately raises a much more interesting scientific question.

Why?

---

It Isn't Simply the Pressure

It is tempting to say:

"Reducing the pressure makes a cloud."

But that skips the most interesting physics.

When a parcel of air expands rapidly, it has to do work on its surroundings. If there is insufficient time for much heat to enter from outside, the expansion is approximately adiabatic.

As the air expands, its temperature falls.

This is called adiabatic cooling.

The chain of events is therefore approximately:

Pressure falls -> air expands -> air cools -> relative humidity rises -> saturation is reached -> condensation occurs -> cloud droplets form.

That sequence is one of the keys to understanding real weather.

---

Relative Humidity — What Does 70% Actually Mean?

Weather forecasts frequently give a figure for relative humidity.

Perhaps:

Relative humidity: 70%

It is easy to interpret that as meaning that 70% of the air consists of water.

It doesn't.

Relative humidity compares the amount of water vapour actually present with the amount required for saturation at that temperature.

In simplified form:

Relative humidity = (actual water vapour / water vapour required for saturation) x 100%

The crucial point is that the amount of water vapour needed for saturation depends strongly on temperature.

Warm air can reach equilibrium with a larger concentration of water vapour than cold air.

Consequently, we can take some moist air, leave the amount of water vapour in it almost unchanged, cool it down and cause its relative humidity to rise.

Eventually:

Relative humidity = 100%

The air has reached saturation.

Cool it further and some of the water vapour can condense.

That is the beginning of our cloud.

---

The Dew Point

This introduces another weather term that students may have encountered without fully appreciating its importance:

dew point.

The dew point is the temperature to which air must be cooled, at roughly constant pressure and water-vapour content, for it to become saturated.

Imagine that the air temperature is 18°C but the dew point is 12°C.

The air is not saturated.

If that air cools towards 12°C, its relative humidity increases.

At approximately 12°C it reaches saturation.

Further cooling can produce condensation.

This explains much more than clouds.

It helps explain:

• dew on grass;

• condensation on windows;

• mist above water;

• fog;

• water appearing on the outside of a cold drink;

• condensation on bathroom mirrors.

The water appearing on the outside of a cold glass did not leak through the glass.

Water vapour already present in the surrounding air was cooled below its dew point and condensed onto the cold surface.

---

But Water Needs Somewhere to Condense

There is another part of the story.

Cloud droplets generally do not form completely spontaneously in perfectly clean air.

The atmosphere contains enormous numbers of tiny particles.

These can include:

• dust;

• sea salt;

• smoke particles;

• pollen;

• biological particles;

• sulphates and other aerosols.

Some of these act as cloud condensation nuclei.

Water molecules can collect around these microscopic particles and eventually produce tiny droplets.

This gives us another variable to investigate in our laboratory cloud.

Depending on the apparatus and demonstration method, introducing a very small concentration of suitable aerosol particles can make cloud formation much easier to see.

It produces an excellent comparison.

Moist air + cooling

compared with:

Moist air + cooling + condensation nuclei

The difference can be striking.

It also demonstrates an important principle of experimental science: a phenomenon may depend upon several conditions being satisfied simultaneously.

---

From a Laboratory Container to a Real Cloud

Now we can scale the experiment up.

Imagine a parcel of warm, moist air near the Earth's surface.

Something causes it to rise.

Perhaps the Sun has warmed the ground.

Perhaps air is being forced over a hill.

Perhaps two air masses are meeting along a weather front.

As the parcel rises, atmospheric pressure decreases.

The rising air expands.

Expansion causes cooling.

Eventually the temperature reaches the dew point.

Water begins condensing onto suitable nuclei.

Millions upon millions of microscopic droplets form.

A cloud becomes visible.

The same fundamental physics that we produced inside a transparent container is occurring kilometres above our heads.

---

Why Clouds Often Have Flat Bottoms

Once students understand the dew point, another familiar observation becomes much easier to explain.

Look at a group of fair-weather cumulus clouds.

They often have surprisingly flat bases.

Why should clouds forming independently have bases at roughly the same height?

Near the surface, different parcels of rising air may have broadly similar temperature and humidity.

As those parcels rise, they cool.

At approximately the altitude where their temperature reaches the dew point, condensation begins.

That produces the visible cloud base.

The flat underside of a cumulus cloud is therefore not simply an interesting shape.

It is evidence of atmospheric physics that we can actually see.

---

An Experiment Within the Experiment

This demonstration becomes much more useful educationally if students do more than simply watch a cloud appear.

We can turn it into an investigation.

Ask:

What conditions make the best cloud?

We could compare different starting conditions.

For example:

Investigation 1 — Humidity

Compare relatively dry air with air that has been allowed to become more humid.

Does the cloud form equally easily?

Investigation 2 — Temperature

Does changing the starting temperature affect the result?

Investigation 3 — Condensation nuclei

Compare relatively clean moist air with air containing a controlled, safe source of microscopic condensation nuclei.

Which produces the most visible cloud?

Investigation 4 — Pressure change

Using suitable pressure-rated equipment, investigate whether the magnitude or rate of pressure reduction affects the visibility of the cloud.

Now we have moved from a demonstration to genuine scientific investigation.

---

Measure It Rather Than Simply Watch It

This is where modern sensors can make the experiment particularly interesting.

Rather than merely saying:

"The cloud appeared when we reduced the pressure,"

we can try to measure what happened.

With suitable sensors and data-logging equipment we could record:

• temperature;

• pressure;

• relative humidity;

• time.

Plotting these against time allows students to look for the point at which the visible cloud forms.

A particularly interesting graph would show pressure and temperature changing together.

We should observe that rapid expansion is accompanied by a temperature decrease.

That gives us direct experimental evidence for the physical process we are trying to explain.

For an A-level student, this is considerably more valuable than simply memorising the phrase "rising air cools."

We can actually make air expand, measure its temperature and watch the cloud appear.

---

Can We Measure the Dew Point?

There is another simple experiment that complements the cloud demonstration beautifully.

Take a shiny metal container containing water and gradually cool it by adding ice while monitoring the temperature.

Watch the outside carefully.

Eventually a faint film of condensation begins to appear.

Record the temperature.

That provides an experimental estimate of the dew point of the surrounding air.

Allow the container to warm again and note the temperature at which the condensation disappears.

Repeating the experiment and taking several measurements gives a better estimate.

We have now turned a term from a weather forecast into something measurable in the laboratory.

---

Why Fog Is Really a Cloud at Ground Level

Once we understand cloud formation, fog becomes much less mysterious.

Fog is essentially a cloud forming at or very close to the Earth's surface.

Instead of air necessarily rising thousands of metres before cooling sufficiently, the air near the ground reaches saturation.

One familiar mechanism occurs on clear nights.

The ground loses thermal radiation and cools.

Air close to the ground is then cooled.

If its temperature falls to the dew point, water can condense into tiny suspended droplets.

Visibility falls.

Fog forms.

This is why cool, clear and relatively calm nights can sometimes produce mist or fog the following morning.

---

Mountains Can Make Clouds

The same idea explains why clouds frequently form around hills and mountains.

Moist air moving towards high ground can be forced upwards.

As it rises:

pressure decreases -> air expands -> temperature falls.

If the air cools to its dew point, cloud forms.

Continue the process and precipitation may follow.

This is orographic uplift, and it helps explain why mountainous regions can have very different rainfall patterns on opposite sides of the same range.

Suddenly our small laboratory cloud is helping us understand entire landscapes.

---

Clouds Are Evidence of Moving Air

One of the most useful changes in thinking is to stop regarding clouds simply as objects.

A cloud is often better regarded as evidence of a process.

It can tell us something about:

• where air is rising;

• where air is cooling;

• where saturation has been reached;

• atmospheric stability;

• moisture distribution;

• fronts and convection.

This is why learning only a catalogue of cloud names misses much of the interesting science.

Yes, recognising cumulus, cumulonimbus, cirrus and stratus is useful.

But it is far more powerful to look at a cloud and ask:

What must the atmosphere be doing to produce that?

---

A Connection With Sailing

Meteorology becomes particularly interesting when it affects something you actually do.

As a sailor, I am constantly interested in what the sky is telling me about the atmosphere.

Clouds are not merely scenery above the boat.

Developing cumulus can indicate convection. A growing cloud can reveal active rising air. Changes in cloud structure may accompany changes in wind, approaching rain or the arrival of different air.

On inland water, where the wind can already be strongly influenced by trees, banks and surrounding terrain, watching the sky adds another source of information.

The laboratory demonstration therefore connects very naturally with a much larger skill:

learning to read the atmosphere rather than merely receiving a weather forecast.

---

A Connection With Flying

The same physics matters enormously in aviation.

A rising parcel of moist air can eventually reach its condensation level and form cloud.

Pilots and meteorologists therefore care about quantities such as:

• air temperature;

• dew point;

• cloud base;

• atmospheric stability;

• humidity;

• pressure.

The difference between air temperature and dew point can provide useful information about how close the atmosphere is to saturation.

A simple school laboratory experiment has therefore taken us into real operational meteorology.

---

Why Doesn't the Cloud Immediately Fall?

This raises another excellent student question.

If a cloud consists of liquid water droplets, why don't they immediately fall?

The answer is largely one of scale.

Cloud droplets are extremely small. Their terminal velocities can consequently be very low, while atmospheric turbulence and upward-moving air can help keep them suspended.

But droplets can collide and combine, and ice processes can also cause precipitation particles to grow.

Eventually some become sufficiently large that gravity wins.

Then we get rain.

So there is another fascinating progression:

water vapour -> condensation -> cloud droplets -> droplet/ice growth -> precipitation.

A visible cloud is only one stage in a much larger atmospheric process.

---

Why This Goes Beyond the Syllabus

Students studying GCSE and A-level science encounter many of the ingredients separately.

They learn about:

• changes of state;

• gas pressure;

• energy transfer;

• latent heat;

• particles;

• temperature;

• convection;

• specific heat capacity.

But meteorology provides an opportunity to combine those ideas into a real physical system.

That is one reason I enjoy taking science beyond the formal syllabus.

The objective isn't simply to give students more facts to remember.

It is to show them that the topics they study are connected.

Physics does not stop at the edge of the physics textbook.

Chemistry does not stop when the chemistry lesson ends.

Biology, physics, chemistry, geology, geography and mathematics all meet when we try to understand the real world.

Meteorology is an excellent example.

---

Questions I Would Ask Students

After producing our laboratory cloud, I would resist the temptation simply to explain everything immediately.

Instead, I might ask:

Why did the cloud appear when the pressure fell?

Was it the pressure itself that caused the condensation?

What happened to the temperature?

Where did the water in the cloud come from?

Why was that water invisible before?

Why might condensation nuclei be necessary?

Would the experiment work as well with very dry air?

Why do clouds form when air rises over a mountain?

Why can a cold glass become wet on the outside?

Why does fog often form overnight?

These questions require students to connect observations with mechanisms.

That is a much deeper form of learning than memorising a definition.

---

A Cloud Is a Physics Experiment Happening Above Us

Perhaps the most impressive thing about this experiment is how ordinary the phenomenon initially seems.

We see clouds almost every day.

Yet explaining why one exists requires us to think about pressure, temperature, energy, phase changes, humidity, microscopic particles and atmospheric motion.

A cloud is therefore not simply something floating in the sky.

It is visible evidence that the atmosphere is changing.

Somewhere, air has cooled sufficiently for invisible water vapour to become microscopic droplets or ice crystals.

And once students have produced that process themselves in the laboratory, they may never look at a cloudy sky in quite the same way again.

Good science education should do more than teach us the names of things.

It should make us look at an everyday phenomenon and suddenly realise that there is an experiment taking place in front of us.

Sometimes that experiment is happening on the laboratory bench.

And sometimes it is several kilometres above our heads.

---

Try This Question

Next time you see a cloud forming, don't begin by asking:

"What type of cloud is that?"

Instead ask:

"What is the air doing that has caused that cloud to exist?"

That question takes us from learning meteorology to actually thinking like a meteorologist.

#Meteorology #Weather #Clouds #Physics #Science #ScienceEducation #STEM #BeyondTheSyllabus #GCSEScience #ALevelPhysics #PracticalScience #HomeLaboratory #WeatherScience #Atmosphere #LearningScience

 

Fourier's Extraordinary Idea — Making Complicated Waves From Simple Ones

What does a violin have in common with a mobile phone signal? Sines, cosines — and one extraordinary mathematical idea.

At A-level, students become very familiar with sine and cosine.

They sketch their graphs. They solve equations involving them. They differentiate and integrate them. In physics, they meet sinusoidal oscillations and alternating currents.

It is therefore quite easy to come away with the impression that sine and cosine are simply two particularly useful functions that happen to describe smooth, repetitive behaviour.

But there is a much bigger idea hiding behind them.

An idea so powerful that it appears in music, acoustics, electronics, radio, telecommunications, medical imaging, astronomy and digital image processing.

The idea is associated with the French mathematician and physicist Joseph Fourier:

A complicated repeating waveform can be constructed from a collection of much simpler sine and cosine waves.

That sounds remarkable.

Even better, we can actually see it happening.

Start With the Simplest Possible Wave

Consider:

sin(x)

There is nothing particularly surprising here. It is the familiar smooth oscillating curve.

Now add another sine wave:

sin(x) + (1/3)sin(3x)

The second wave has three times the frequency but only one-third of the amplitude.

The resulting graph starts looking slightly less like an ordinary sine wave.

Now add another:

sin(x) + (1/3)sin(3x) + (1/5)sin(5x)

Then another:

sin(x) + (1/3)sin(3x) + (1/5)sin(5x) + (1/7)sin(7x)

Something extraordinary begins to happen.

The smooth curves start producing something that increasingly resembles a square wave.

Keep adding the odd harmonics and the approximation becomes increasingly convincing.

In more general terms, an ideal square wave can be represented by an infinite Fourier series containing odd harmonics:

sin(x) + (1/3)sin(3x) + (1/5)sin(5x) + (1/7)sin(7x) + ...

There is a constant scaling factor if we want a particular amplitude, but that is not the important idea for our first investigation.

The important thing is what we have just done.

We have built something containing apparently sharp corners from functions that contain no corners at all.

Try It Yourself

This is an excellent investigation for an A-level Maths or Further Maths student because it needs surprisingly little equipment.

A graphical calculator, Desmos, GeoGebra or a spreadsheet is enough.

Plot:

y = sin(x)

Then:

y = sin(x) + sin(3x)/3

Then:

y = sin(x) + sin(3x)/3 + sin(5x)/5

Continue with:

• sin(7x)/7

• sin(9x)/9

• sin(11x)/11

and watch what happens.

Do not simply look at the final graph.

The interesting part is watching the square wave gradually emerge.

At first, there is no obvious reason why adding curved waves should produce anything remotely square.

Yet it does.

That is precisely the sort of mathematical experience I like students to encounter beyond the examination syllabus.

Rather than being told that mathematics is powerful, they actually see something happen that seems almost impossible.

But Look Carefully at the Corners

There is another interesting feature.

Zoom in near one of the sudden transitions in the square wave.

You may notice that the approximation overshoots and oscillates around the discontinuity.

Adding more terms does not simply make this little feature disappear.

This is connected with the Gibbs phenomenon, another fascinating piece of mathematics that students can investigate.

It is a useful reminder that saying an infinite series "becomes" a square wave needs some mathematical care.

That opens the door to deeper questions about:

• convergence;

• infinite series;

• approximation;

• discontinuities;

• limits.

Suddenly a visually simple experiment has taken us into some quite sophisticated mathematics.

So What Did Fourier Actually Realise?

Joseph Fourier was studying the flow of heat in the early nineteenth century.

In trying to solve problems involving heat conduction, he developed the idea that complicated functions could be represented using combinations of trigonometric functions.

At the time, this was mathematically controversial.

Today, Fourier analysis has become one of the fundamental tools of mathematical physics and engineering.

A general Fourier series can be written in the form:

f(x) = a0/2 + a1 cos(x) + b1 sin(x) + a2 cos(2x) + b2 sin(2x) + ...

The precise coefficients depend upon the function we are trying to reproduce.

Students do not need to calculate all those coefficients to appreciate the central idea.

Think of it this way:

Fourier analysis gives us a mathematical recipe for taking a complicated signal apart and discovering which simple frequencies are hiding inside it.

And that takes us from pure mathematics straight into music.

What Does a Musical Note Really Look Like?

Play a pure sine wave through a loudspeaker.

It sounds rather plain.

Now play middle C on a piano.

Then play the same note on an organ.

Then a guitar.

Then a violin.

They are all playing approximately the same fundamental frequency, so why don't they sound identical?

Because a musical instrument generally does not produce just one frequency.

It produces a fundamental frequency together with additional harmonics and other spectral components.

The relative strengths and behaviour of these components contribute enormously to the characteristic sound of the instrument.

This means Fourier's mathematical idea gives us a way of looking inside a musical sound.

A Superb Practical Investigation

This is where I would take the mathematics off the page.

Record the same musical note played on several different instruments.

For example:

• piano;

• organ;

• guitar;

• violin;

• flute;

• electronically generated sine wave.

Try to keep the fundamental note the same.

Now examine each recording using audio software capable of displaying a frequency spectrum.

Instead of displaying amplitude against time, display amplitude against frequency.

Suddenly the differences become visible.

The pure sine wave should have a strongly concentrated fundamental frequency.

A real instrument may show the fundamental plus a whole collection of additional frequency components.

A student can now ask:

Which harmonics are strongest?

Are even and odd harmonics equally prominent?

How rapidly do the higher harmonics decrease?

Does the spectrum change as the note develops?

What happens during the attack of the note?

Why does a flute look different from a violin?

We have transformed listening to music into mathematical investigation.

My Organ Becomes a Mathematics Laboratory

This is one reason I particularly like Fourier analysis as a teaching topic.

An electronic organ or synthesiser provides an extraordinary experimental laboratory for investigating sound.

I can select one sound, record a note and examine its spectrum.

Then I can change the registration or instrument sound while keeping the actual musical note unchanged.

What changed?

Not primarily the note being played.

What changed was the mixture of frequencies producing it.

With suitable software, students can both hear and see the difference.

That is a much richer experience than simply being told that musical instruments contain harmonics.

And an organ provides an especially interesting connection because organ stops are explicitly associated with different pitches.

An 8-foot stop sounds at the written pitch.

A 4-foot stop sounds an octave above.

A 2-foot stop sounds another octave higher.

Other stops introduce different harmonic relationships.

We can therefore build complicated sounds by combining components — conceptually remarkably close to the mathematical idea we have just explored.

From Fourier to Synthesisers

Now reverse the problem.

Instead of analysing an existing sound, suppose we want to create one.

Start with a sine wave.

Add another sine wave at twice the frequency.

Perhaps add another at three times the frequency.

Change their amplitudes.

Listen again.

We are performing additive synthesis.

A synthesiser can construct a complicated sound from simpler components in much the same spirit as our mathematical Fourier construction.

This creates a wonderful Maths + Physics + Music crossover experiment:

1. Construct a square-wave approximation mathematically.

2. Generate the corresponding frequencies electronically.

3. Listen to the result.

4. Examine its spectrum.

5. Compare mathematical prediction with the actual sound.

A formula has become something we can hear.

Square Waves Are Not Just Mathematical Curiosities

Square waves are extremely important in electronics.

Digital systems often switch between two voltage levels.

An idealised digital signal therefore contains sudden transitions rather than smooth sinusoidal changes.

But Fourier analysis tells us something important.

Producing those sharp transitions requires high-frequency components.

Remove enough of the higher frequencies and the edges become rounded.

This matters when transmitting digital information.

A communications system with limited bandwidth cannot reproduce arbitrarily rapid changes perfectly.

Suddenly our little graph of:

sin(x) + sin(3x)/3 + sin(5x)/5 + ...

has led us towards real questions about data transmission and communications engineering.

Radio — Finding Signals Hidden Inside Signals

Radio gives us another application.

A radio receiver is surrounded by electromagnetic signals.

Different transmitters operate at different frequencies, and information is encoded onto signals in various ways.

Fourier methods allow engineers to examine signals in terms of their frequency components.

Rather than asking:

"What is the signal doing at this particular moment?"

we can ask:

"Which frequencies are present, and how strong are they?"

Those are two different ways of looking at the same information.

This distinction between the time domain and the frequency domain is one of the most important conceptual steps students can take.

Two Ways of Looking at the Same Thing

Imagine recording one second of music.

We could plot:

amplitude against time.

That shows us how the air pressure — or electrical signal from the microphone — changes during that second.

That is the time domain.

Alternatively, we could analyse the same recording and plot:

amplitude against frequency.

Now we can see which frequencies contribute to the sound.

That is the frequency domain.

Neither representation is inherently "the real signal".

They are two mathematical views of the same phenomenon.

That idea extends far beyond music.

Fourier Analysis and Images

An image may seem to have little to do with sound.

But mathematically there is a connection.

A digital photograph contains variations in brightness and colour across space.

Slow changes correspond to low spatial frequencies.

Fine details and sharp edges involve higher spatial frequencies.

Fourier techniques can therefore be applied to images.

They can help with:

• filtering;

• sharpening;

• noise reduction;

• compression;

• pattern analysis;

• astronomical imaging;

• medical imaging.

Once students understand the idea with a sound wave, it becomes much easier to appreciate how the same mathematics can be applied elsewhere.

Spectroscopy — A Particularly Interesting Connection

Fourier mathematics also appears in spectroscopy.

Some spectroscopic techniques record signals that are not initially in the form of the familiar spectrum we ultimately want.

A Fourier transform can convert measured information into a frequency spectrum.

Fourier transform infrared spectroscopy — FTIR — is an important example.

Once again, the basic philosophy is similar:

A complicated measured signal can reveal its hidden frequency components through mathematics.

For a student studying both Maths and Chemistry or Physics, this is a wonderful example of subjects meeting each other.

The Fast Fourier Transform

There is, however, a practical problem.

Real digital signals may contain thousands or millions of data points.

Calculating their frequency components directly can require enormous amounts of computation.

This is where the Fast Fourier Transform, usually abbreviated FFT, becomes important.

The FFT is an efficient family of algorithms for computing a discrete Fourier transform.

Its impact on computing, engineering and signal processing has been enormous.

When audio software instantly displays the frequency spectrum of a recording, mathematics and algorithms are working behind the scenes.

The student sees a graph appear almost immediately.

Hidden underneath it is some extraordinarily elegant mathematics.

A Challenge for an A-Level Student

Here is a good investigation.

Create a spreadsheet containing values of x.

Calculate:

y1 = sin(x)

Then:

y2 = sin(x) + sin(3x)/3

Then:

y3 = sin(x) + sin(3x)/3 + sin(5x)/5

Continue until perhaps the first ten odd harmonics have been included.

Plot each approximation.

Then investigate:

How many terms are needed before the graph looks convincingly like a square wave?

But do not stop there.

Try changing the coefficients.

What happens if every component has the same amplitude?

What happens if the amplitudes decrease more quickly?

What happens if even harmonics are introduced?

Can you deliberately create a different waveform?

Now the student is no longer merely following instructions.

They are experimenting with mathematics.

Could We Hear the Mathematics?

This would be my next step.

Generate the individual sine-wave components as sounds.

Listen first to the fundamental.

Then add the third harmonic.

Then the fifth.

Then the seventh.

The graph is gradually becoming more square.

But the sound is changing as well.

That is an extraordinarily powerful teaching moment.

The equation:

sin(x) + sin(3x)/3 + sin(5x)/5 + ...

is no longer simply ink on paper.

It is a graph.

It is an electrical signal.

And it is something we can hear.

Why Go Beyond the A-Level Syllabus?

A student might reasonably ask:

"Will Fourier series be on my A-level Maths examination?"

For most students, no.

But I think that is precisely why topics like this deserve occasional exploration.

The examination syllabus is necessarily selective.

It cannot contain everything interesting about mathematics.

If students only ever encounter mathematics that is immediately required for the next examination, they can develop a rather distorted picture of the subject.

Sine and cosine can become:

"those functions I need for the trig question."

Fourier transforms reveal something much bigger.

The trigonometric functions they have been manipulating are part of a mathematical language capable of describing and analysing the physical world.

Mathematics Is About Connections

Some of the most memorable lessons are those in which the artificial boundaries between school subjects disappear.

Fourier's idea connects:

Mathematics — functions, trigonometry, series and approximation.

Physics — waves, oscillations and electromagnetic signals.

Music — harmonics, timbre and synthesis.

Computing — digital sampling, algorithms and signal processing.

Electronics — waveforms, bandwidth and communications.

Chemistry — spectroscopy and molecular analysis.

It is difficult to think of many mathematical ideas with such an extraordinary reach.

The Bigger Lesson

There is something else I would want a student to take away from this investigation.

Mathematics is not simply about obtaining exact answers.

It is also about finding useful ways of representing complicated things.

A violin note looks complicated.

A radio signal looks complicated.

A square wave looks simple until we ask what frequencies are required to construct it.

Fourier's extraordinary insight gives us another way of looking at all of them.

Break the complicated thing into simpler pieces.

Understand the pieces.

Then understand how the pieces fit together.

That principle extends far beyond Fourier analysis.

It is one of the great strategies of mathematics and science.

Conclusion — Hear a Sine Wave Differently

The next time an A-level student sees:

y = sin(x)

I would like them to see more than a trigonometric graph.

That simple curve can become one component of a violin note.

Add others and it can approximate a square wave.

Analyse a complicated sound and sine waves can help reveal what is hidden inside it.

Extend the idea and we arrive at radio communications, digital electronics, spectroscopy and image processing.

That is why exploring mathematics beyond the syllabus can be so valuable.

Sometimes one familiar equation opens a door into an unexpectedly large part of science and technology.

And Fourier's extraordinary idea is a magnificent example.

A complicated world can sometimes be understood by adding together very simple waves.

#Mathematics #ALevelMaths #FurtherMaths #Fourier #FourierSeries #STEM #Physics #Music #Sound #Acoustics #Electronics #SignalProcessing #Engineering #MathsEducation #BeyondTheSyllabus #PrivateTuition

 

Centripetal Force — Why Going Twice as Fast Changes Everything

A practical investigation into mass, radius and rotational speed

There are some equations in physics that students can learn perfectly well without really appreciating what they mean.

Centripetal force provides a particularly good example.

The familiar relationship is:

F = mv^2/r

where:

• F is the centripetal force,

• m is the mass of the moving object,

• v is its speed,

• r is the radius of its circular path.

It looks straightforward enough.

But hidden inside that equation is a result that is surprisingly unintuitive:

the force depends on the square of the speed.

That means going twice as fast does not require twice the centripetal force.

It requires four times as much.

Go three times as fast and the required force becomes nine times as large.

That is something students can calculate on paper.

It is much more memorable when they can actually investigate it.

Circular Motion Is Constant Acceleration

One of the first conceptual difficulties is the word acceleration.

Ask a student:

"Can an object travelling at a constant speed be accelerating?"

A common answer is no.

That seems perfectly reasonable if acceleration has become mentally associated with a car getting faster.

But acceleration means a change in velocity, and velocity includes direction as well as speed.

Imagine an object travelling around a circular path at a perfectly constant speed.

Its speed may not change at all.

Its direction is changing continuously.

Therefore its velocity is changing continuously.

Therefore it is accelerating.

That acceleration is directed towards the centre of the circle and is called centripetal acceleration.

The corresponding resultant force must also act towards the centre.

Hence the name:

centripetal = centre-seeking.

The Force Is Not Pulling the Object Around the Circle

There is another useful idea to establish before beginning the experiment.

The instantaneous velocity of the moving object is tangential to its circular path.

The centripetal force acts approximately at right angles to that velocity, towards the centre.

The force is therefore continually changing the object's direction.

Remove that inward force and the object does not continue travelling around the circle.

It travels away approximately along the tangent.

That is an excellent idea to demonstrate physically if the apparatus allows it.

It also helps address the persistent misconception that an outward force must be keeping the object in circular motion.

For the laboratory analysis, what we need is an inward resultant force.

Three Variables — Three Experiments

I particularly like this investigation because the same apparatus can reveal three different mathematical relationships.

Rather than changing everything at once, I would divide the work into three investigations:

1. change the mass while keeping speed and radius constant;

2. change the radius while keeping mass and speed constant;

3. change the speed while keeping mass and radius constant.

That last experiment is the most interesting.

But I would not start with it.

The first two establish the method and give students relatively intuitive relationships before we encounter the surprise.

Experiment 1 — What Happens If We Increase the Mass?

Keep the radius and rotational speed constant.

Then increase the rotating mass.

From:

F = mv^2/r

if v and r remain constant:

F proportional to m

Double the mass and the required centripetal force should double.

Triple the mass and it should triple.

This is a simple linear relationship.

Students can collect several values and plot:

centripetal force against mass

If the experiment behaves well, the graph should be approximately a straight line through the origin.

This is already more useful than simply checking one calculated answer.

We are testing the form of a physical relationship.

A prediction worth making first

Before taking measurements, I would ask:

"If I double the rotating mass, what do you expect to happen to the force?"

Most students will probably predict that the force doubles.

Good.

Write that prediction down.

We will shortly encounter a variable for which intuition is much less reliable.

Experiment 2 — What Happens If We Increase the Radius?

Now keep mass and speed constant and change the radius.

The equation predicts:

F proportional to 1/r

Increasing the radius therefore reduces the required centripetal force, provided the linear speed really remains constant.

This needs careful thought because rotational experiments can introduce an important complication.

If we keep angular speed constant rather than linear speed, increasing the radius also increases the object's linear speed.

Since:

v = 2 pi r / T

or:

v = omega r

changing r while keeping the rotation rate constant does not keep v constant.

That can completely change what students observe.

This is an excellent experimental-design discussion.

It shows why physics is not merely about substituting numbers into equations.

We must understand what we are actually controlling.

Experiment 3 — Now Change the Speed

This is where the experiment becomes especially interesting.

Keep mass and radius constant.

Change only the linear speed.

Then:

F proportional to v^2

Before revealing that relationship, I would ask students for predictions.

Suppose our original speed is v and our original force is F.

What happens if we double the speed?

A very tempting prediction is:

2v gives 2F.

But that is not what the physics predicts.

Because speed is squared:

2v gives 4F.

Similarly:

3v gives 9F.

and:

4v gives 16F.

The required force rises extremely rapidly.

That is the result I want students to experience rather than merely memorise.

Make the Relationship Visible With Graphs

This experiment also provides an excellent opportunity to teach students something about graph transformations.

Plot:

F against v

and the result should be a curve.

That already tells us that force is not directly proportional to speed.

Now calculate v^2 for every measurement and plot:

F against v^2

The graph should become approximately linear.

That is powerful.

We have transformed experimental data to test a proposed mathematical model.

Instead of simply saying:

"The equation says F is proportional to v^2,"

we have asked the experiment whether that relationship appears to be true.

That is much closer to the way experimental physics actually works.

A Numerical Example

Suppose we have:

m = 0.50 kg

r = 1.0 m

v = 2.0 m/s

Then:

F = mv^2/r

F = 0.50 x 2.0^2 / 1.0

F = 2.0 N

Now double the speed:

v = 4.0 m/s

F = 0.50 x 4.0^2 / 1.0

F = 8.0 N

The speed has doubled.

The force has increased from 2 N to 8 N.

Now consider:

v = 6.0 m/s

F = 0.50 x 6.0^2 / 1.0

F = 18 N

That rapidly increasing force is why speed matters so enormously in circular motion.

Try It Interactively

A useful way of developing intuition is to change just one quantity at a time. Start with a mass of 2 kg, speed of 4 m/s and radius of 2 m, then double the speed while leaving everything else unchanged.

The important question is not simply "What is the new force?"

It is:

"Can you predict the new force before changing the control?"

That turns the equation into a physical model.

Why This Matters Outside the Laboratory

The squared speed relationship is not merely an examination curiosity.

It appears whenever objects move around curved paths.

Cars travelling around bends

A vehicle travelling around a bend requires an inward resultant force.

At modest speeds that force may be easily provided by the interaction between tyres and road.

Increase the speed and the required force rises as v^2.

This immediately explains why taking the same bend substantially faster is not merely slightly more demanding.

Roller coasters

Circular and curved sections of roller-coaster track can produce large accelerations because relatively high speeds combine with relatively small radii.

Satellites and planets

Orbital motion is another form of curved motion.

Gravity provides the inward force needed to continually change the direction of the velocity.

An orbiting spacecraft is not travelling because there is no gravity.

Quite the opposite.

Gravity is fundamental to maintaining the orbit.

Laboratory centrifuges

Centrifuges exploit rapid rotational motion to separate materials.

Increasing rotational speed can have a dramatic effect because of the squared relationship.

A Particularly Good Student Challenge

Once students have collected their measurements, I would give them an unknown data set.

Do not tell them which variable was changed.

Give them values of force and another quantity and ask:

"Does this look like F proportional to x, F proportional to x^2, or F proportional to 1/x?"

Now they must investigate.

They could:

• inspect ratios;

• calculate x^2;

• calculate 1/x;

• plot alternative graphs;

• decide which produces the best straight line.

That turns a centripetal-force practical into a much broader lesson about mathematical modelling and experimental evidence.

What Would I Measure With Modern Equipment?

This is one of those experiments where modern sensors can transform the lesson.

Instead of merely watching a rotating mass and measuring a hanging weight, we can potentially record force continuously while also determining rotational period or speed.

The interesting part is then the graph.

Students can see the force changing rather than simply receiving one number at the end of the experiment.

With suitable data-logging equipment, I would want to display the measurements live.

That gives us opportunities to stop the experiment and ask:

"Why has the force just increased?"

"What would happen if we increased the speed by another 20%?"

"What graph should we get?"

Students become participants in the investigation rather than spectators waiting for an answer.

Experimental Problems Are Part of the Science

Real experiments rarely produce perfect textbook graphs.

There may be:

• friction;

• uncertainty in radius;

• fluctuations in rotational speed;

• sensor calibration errors;

• vibration;

• difficulty measuring the exact centre of rotation;

• uncertainty in timing.

That is not a reason to avoid the experiment.

It is one of the reasons to do it.

Students can add error bars, repeat measurements and identify anomalous results.

They can also ask whether a discrepancy means the theory is wrong or simply that the experiment has limitations.

That distinction lies at the heart of good experimental science.

One Important Safety Point

Rotating apparatus deserves respect.

A small mass moving quickly possesses substantial kinetic energy, and the forces on attachments increase rapidly with speed.

The apparatus should therefore be properly secured, rotating components checked before use, speeds kept within the equipment manufacturer's limits, and observers kept clear of the plane of rotation.

Ironically, the very relationship we are investigating explains why this becomes increasingly important as the apparatus gets faster.

The Bigger Lesson — Equations Should Make Predictions

For me, this is the real value of an experiment like this.

Students sometimes encounter equations as instructions:

"Find the numbers, substitute them and calculate the answer."

But an equation is much more interesting than that.

It is a model of how nature behaves.

The equation:

F = mv^2/r

makes three distinct predictions.

Increase mass and force increases proportionally.

Increase radius, while maintaining the appropriate other conditions, and the relationship changes inversely.

Increase speed and force rises with the square of speed.

We can test those predictions.

That is what turns an equation into physics.

Conclusion — Twice as Fast Is Not Twice as Demanding

The most memorable moment in this experiment may come before any measurement is made.

Ask:

"If I make this object travel twice as fast around exactly the same circle, how much more force will I need?"

The intuitive answer is often:

"Twice as much."

Then perform the experiment.

The answer should be approximately:

four times as much.

That difference between intuition and evidence is precisely why practical physics is so valuable.

A student can memorise F = mv^2/r for an examination.

But watching the force rise dramatically as the apparatus speeds up gives that little superscript 2 a physical meaning.

And once you have actually seen what it does, it becomes considerably harder to forget.

 

Redi's Experiment — Do Maggots Really Appear From Nowhere?

Put a piece of meat outside for long enough and maggots may appear. But where did they come from?

Today, most school students would probably answer immediately: flies laid eggs on the meat.

But imagine living at a time when that explanation was far from obvious.

For centuries, people believed that living organisms could simply emerge from non-living or decaying material. Fleas might arise from dust. Mice were sometimes thought to originate from piles of grain and old cloth. Maggots seemed to emerge naturally from rotting meat.

It was an idea known as spontaneous generation.

Then, in the seventeenth century, Italian physician and naturalist Francesco Redi asked a wonderfully simple question:

What if the maggots are not coming from the meat at all?

And, crucially, he designed an experiment to test it.

---

Science Advances When We Test the Obvious

One of the things I particularly like about historical experiments is that they remind students that scientific knowledge did not arrive fully formed in a textbook.

Someone had to ask the question.

Someone had to devise a test.

Someone had to collect evidence.

And sometimes the experiment that changes our understanding of nature is surprisingly simple.

Redi's work is a wonderful example.

He did not need sophisticated electronics, DNA sequencing, microscopes connected to computers or expensive sensors.

He needed meat, containers, flies — and a clever experimental design.

The cleverness is the important part.

---

What Did People Believe Before Redi?

The idea of spontaneous generation had existed since antiquity.

At first sight, it is not difficult to understand why.

Leave fruit for a while and tiny flies appear.

Leave food uncovered and mould grows.

Leave meat to decay and maggots appear.

Without knowledge of microorganisms, eggs, spores and life cycles, the most obvious conclusion could be:

The living things came from the decaying material.

Observation alone appeared to support the idea.

But there was a problem.

Nobody had properly separated two possible explanations:

Hypothesis 1: Maggots are produced by the meat itself.

Hypothesis 2: Maggots develop from eggs deposited by flies.

That distinction transforms an observation into an experiment.

---

Francesco Redi's Clever Test

In 1668, Redi described experiments involving meat placed into different containers.

The basic principle can be simplified into three conditions.

Container 1 — Open

Meat was exposed to the surrounding environment.

Air could enter.

Flies could land on the meat.

Container 2 — Sealed

Meat was enclosed.

Flies could not reach it.

Container 3 — Covered with gauze

This was the particularly clever condition.

Air could still circulate around the meat, but flies could not physically reach it.

That third container was extremely important because it dealt with a possible objection.

Someone supporting spontaneous generation might have argued:

"Perhaps the sealed meat did not produce maggots because it had been deprived of air."

The gauze treatment helped test that alternative explanation.

Air could enter.

Flies could not.

That is excellent experimental design.

---

What Happened?

The results were striking.

In the open containers, flies could reach the meat and maggots subsequently developed.

In the sealed containers, flies could not reach the meat and maggots did not develop on it.

With gauze-covered containers, flies were attracted to the smell but could not reach the meat itself. Eggs and larvae could instead be associated with the gauze where the flies had access.

The evidence pointed towards a very different explanation from spontaneous generation:

The maggots were part of the fly's life cycle.

They were not being created by the meat.

---

A Brilliant Experiment Because It Controls One Critical Variable

This is where Redi's experiment becomes especially useful for teaching biology.

Students can easily concentrate on the slightly gruesome subject of maggots and miss the much more important scientific lesson.

Ask:

What was Redi actually changing?

Essentially, he was manipulating access by flies.

That gives us the beginnings of modern experimental terminology.

Independent variable

Whether flies can reach the meat.

Dependent variable

The appearance of fly eggs or larvae.

Important control variables

Ideally we would keep as many other factors as possible similar:

• type of meat;

• mass of meat;

• container size;

• temperature;

• location;

• light conditions;

• duration of exposure.

Suddenly an experiment from the 1600s becomes directly relevant to the way GCSE and A-level students are expected to think about practical investigations today.

---

Could We Recreate Redi's Experiment?

Yes, although I would modify the historical experiment considerably.

There is no educational reason to have large quantities of rotting meat sitting around.

A modern teaching demonstration could use very small samples in secure transparent containers, preferably kept outside in a controlled location and away from food-preparation or living areas.

Three identical transparent containers could be prepared.

A — Open to insects

A small sample is accessible to flies while the overall arrangement prevents interference by larger animals.

B — Physically sealed

The sample is enclosed so insects cannot reach it.

C — Fine gauze covering

Air and odours can pass through the covering, but flies cannot contact the sample.

The containers could then be observed over several days without students handling the contents.

The objective is not to produce the greatest number of maggots possible.

It is to observe where insects can and cannot gain access.

Any practical version should be securely contained, supervised and disposed of without reopening decomposing material unnecessarily.

---

Turn It Into a Proper Investigation

Rather than simply saying, "Look, maggots appeared," I would encourage students to collect evidence systematically.

A simple observation table might contain:

Day	Open sample	Gauze-covered sample	Sealed sample
0	No visible change	No visible change	No visible change
1	Record observations	Record observations	Record observations
2	Record observations	Record observations	Record observations
3	Record observations	Record observations	Record observations
4	Record observations	Record observations	Record observations

Students could record:

• number of fly visits observed;

• presence of eggs;

• presence of larvae;

• approximate number of larvae;

• visible decomposition;

• changes in colour;

• location of any eggs or larvae.

Photography would be particularly useful.

A photograph taken at the same time each day creates a visual record of change without repeatedly disturbing the experiment.

A macro camera or digital microscope could make the investigation even more interesting by allowing eggs and larvae to be examined without students having to handle them.

---

The Gauze Is the Most Interesting Part

If I were teaching this experiment, I would spend considerable time discussing the gauze.

Why not simply compare an open container with a sealed container?

Because that leaves another explanation available.

Perhaps something in the air is necessary for spontaneous generation.

Perhaps sealing the container prevents the supposed process from occurring.

The gauze condition separates two factors that would otherwise be mixed together:

access to air

and

access to flies.

That is the real brilliance of the experiment.

Students sometimes think experimental science is mainly about obtaining accurate measurements.

It isn't.

Before we can measure anything accurately, we need to ask whether the experiment actually distinguishes between competing explanations.

---

Correlation Is Not Enough

There is another important lesson here.

People had observed the relationship between rotting meat and maggots for generations.

Rotting meat appeared.

Maggots appeared.

Therefore, it seemed reasonable to conclude:

rotting meat produces maggots.

But two events occurring together does not prove that one directly causes the other.

There was another variable hiding in the background:

flies.

That idea extends far beyond Redi.

It is one of the most important principles students can learn from science.

Whenever two things appear to be connected, ask:

Could something else explain both observations?

That question matters in biology, medicine, psychology, economics, sociology and almost every other evidence-based subject.

---

From Maggot to Fly

The experiment also provides an excellent opportunity to investigate life cycles.

A fly does not suddenly appear as an adult.

The simplified sequence is:

egg -> larva -> pupa -> adult fly

The maggot is the larval stage.

Once students understand this, Redi's observations become much easier to interpret.

A fly lands on a suitable food source.

It lays eggs.

The eggs hatch.

Larvae feed and grow.

Eventually they pupate.

Adult flies emerge.

What once appeared to be spontaneous generation becomes an understandable biological process.

---

But Redi Did Not Finish the Story

This is another reason I like historical experiments.

Science rarely consists of one heroic experiment that answers everything forever.

Redi provided strong evidence against spontaneous generation in larger organisms such as flies.

But later, the discovery of microorganisms created a new problem.

Microscopic organisms seemed to appear in nutrient-rich liquids even when no obvious parent organisms were present.

Had spontaneous generation survived at the microscopic level?

The debate continued.

This eventually leads students towards another wonderful experiment.

Louis Pasteur and the swan-neck flask.

Pasteur showed that sterilised nutrient broth could remain uncontaminated when airborne microorganisms and particles were prevented from reaching it, even though air itself could still enter.

There is a beautiful progression here:

Redi -> flies and maggots -> microorganisms -> Pasteur -> germ theory -> modern microbiology.

A simple piece of meat therefore opens the door to a huge part of biological history.

---

Ask Students to Predict Before Showing Them the Result

I would not begin a lesson by explaining what Redi discovered.

I would show students the experimental arrangement first.

Three containers.

One open.

One sealed.

One covered with gauze.

Then ask:

What do you predict will happen?

More importantly:

Why?

Students could write their predictions before seeing the historical results.

Then ask another question:

What result would support spontaneous generation?

If maggots genuinely arose directly from the meat, preventing flies from reaching it should not necessarily prevent their appearance.

Then:

What result would support Redi's alternative explanation?

Maggots should occur only where flies have been able to deposit eggs.

Now students are doing something far more valuable than memorising the conclusion.

They are using hypotheses to generate predictions.

---

Can You Design a Better Experiment Than Redi?

This makes an excellent extension exercise.

Give students the original problem and ask them to redesign the investigation using modern knowledge.

They might suggest:

• identical containers;

• equal masses of meat;

• several replicates of each condition;

• controlled temperatures;

• photographic records;

• regular observation intervals;

• different mesh sizes;

• monitoring insect visits;

• recording temperature;

• blind analysis of photographs;

• repeating the investigation.

This introduces reliability, validity, replication and control variables without having to start with abstract definitions.

Students discover why those ideas matter because they are trying to improve a real experiment.

---

One Experiment, Several Levels of Teaching

Another strength of Redi's experiment is that it can be approached at very different levels.

Younger students

Where do maggots come from?

Explore the fly life cycle and make predictions.

GCSE Biology

Identify variables, controls, hypotheses and conclusions.

Discuss reproduction and life cycles.

A-level Biology

Consider experimental validity, replication, alternative hypotheses and the historical development of biological knowledge.

Beyond the syllabus

Discuss the philosophy of science.

What counts as evidence?

Can an experiment prove a theory, or does it merely provide evidence against competing explanations?

How should scientists respond when new observations challenge established beliefs?

Suddenly a jar containing a tiny piece of meat has become a lesson in scientific reasoning.

---

Why I Like Experiments Like This in Private Tuition

One advantage of individual or very small-group tuition is that there is time to follow the interesting question.

A syllabus might require a student to understand variables and experimental controls.

We could simply define them:

Independent variable — the factor deliberately changed.

Dependent variable — the factor measured or observed.

Control variables — factors kept as constant as reasonably possible.

Those definitions matter.

But I would much rather put an experiment in front of a student and ask:

"How could we find out whether the meat is actually producing the maggots?"

Now the terminology has a purpose.

The student needs a control because without one we cannot distinguish between explanations.

That is the difference between remembering scientific vocabulary and thinking scientifically.

---

The Bigger Lesson: Don't Just Accept the Explanation

Perhaps the greatest value of Redi's experiment is not really about flies.

It is about questioning explanations that everyone assumes must be true.

For generations, people had seen maggots appear on meat.

The observation was genuine.

The interpretation was wrong.

Redi did not solve the problem by arguing more forcefully.

He changed the conditions and looked at what happened.

That principle sits at the heart of experimental science:

If two explanations compete, design an observation that allows nature to distinguish between them.

---

From a Piece of Meat to Modern Biology

It is remarkable how much science can emerge from such a simple investigation.

A few containers.

Some gauze.

A little meat.

And one carefully framed question.

From it we can explore:

• reproduction;

• insect life cycles;

• experimental controls;

• independent and dependent variables;

• correlation and causation;

• hypotheses and predictions;

• reliability;

• experimental design;

• the history of biology;

• spontaneous generation;

• Pasteur;

• microbiology;

• germ theory;

• and the nature of scientific evidence itself.

That is why I enjoy taking students beyond simply learning the syllabus.

The best experiments do not merely demonstrate something we already know.

They make us ask:

How do we know it?

Redi's experiment is more than 350 years old, yet the question behind it remains completely modern.

When something appears to be obvious, what experiment could we devise to check that it really is true?

That is not merely learning biology.

That is learning how to be a scientist.