Physics IA · C · Wave behaviour · topic 16 of 30

Ripple tank: how does depth change the wave speed? · IB Physics IA idea: guide, sample graph and step-by-step plan

a stretch, but a real physics story

Waves slow down over shallow water, which is why they bend towards a beach. You're going to measure how much, and test the maths.

Difficulty●●● Stretch
KitStandard: ripple tank, strobe or video, ruler
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like waves and refraction
  • ✓ you can film a screen and measure from video
  • ✓ you want a stretch with a real theory behind it

The big idea

← where does the simple rule fail?

In shallow water, wave speed is about √(gh), so it falls as the water gets shallower. That is the rule behind refraction at a sloping beach. But a ripple tank is not very shallow compared with its wavelengths, so the simple rule starts to fail as depth grows. Fix the frequency, change only the depth, and measure speed as frequency times wavelength. Then test where √(gh) works and where it does not. That is a good IA.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Use refraction, not speed

Make a shallow region with a submerged plate and measure the angle of refraction.

→ Your analysis uses Snell's law for waves; the ratio of sines gives the ratio of speeds, and you compare with √(h₁/h₂).
Change the frequency too

Repeat the depth series at two or three frequencies.

→ Tests the dispersion: the simple rule should work better at low frequency; a richer conclusion.
Plot v² against h

Use your data to test whether v² is proportional to depth.

→ A straight line through the origin if the theory holds; the gradient gives g, which you compare with 9.81.
Use video analysis

Film the waves from above with a ruler in view and measure wavelength frame by frame.

→ Smaller uncertainty in wavelength and no need for a strobe; the evaluation compares methods.
Look at the effect of the beach

Compare reflections with and without absorbers at one depth.

→ A different dependent variable; reflections become a systematic error you quantify.
Use a simulation too

Compare your data with a wave tank simulation or the full dispersion relation.

→ Adds a theory curve that does not rely on a shallow-water approximation.

Your Physics IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable and its range (which depths, in mm, and how many values).
  • Names one dependent variable and how you will find it (speed from frequency times wavelength, and how you read both).
  • Says what stays fixed: frequency (how you check it), tank level, temperature, the dipper.
  • Says what you will compare your result with (the shallow-water rule, a corrected form, or both).
  • Is narrow enough to finish with at least 6 depths, a repeat at each, and a check that the tank is level.

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The set-up

One way to set it up. Draw your own version, with your real tank, lamp and ruler, for the Method section.

h4λdipper: fixed frequency,check it with a strobelamp: shadows of thewave crests on the screensloping foam beach:cuts reflectionsdepth h: ruler, severalplaces, tank levelscreen with a ruler:measure over 4 stripes

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; why wave speed and depth matter for tsunamis, harbours and beaches; what you expect and why.
Background physics~450
The wave equation v = fλ; the shallow-water speed and the condition for it to hold; why a ripple tank may break that condition; your predicted graph.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
Method~400
How you set and measure depth; how you fix and check the frequency; how you measure wavelength from the screen; how you handle magnification and reflections.
Safety, ethics, environment~60
Short and specific: water near mains-powered lamps and motors.
Raw datatable
One table: depth, frequency, wavelength readings and the scale factor, with the uncertainty in each header.
Processing~250
How you find the wavelength and its uncertainty from several stripes; how you correct for magnification; how you find v and propagate the uncertainty.
Graphs and analysis~350
The graph you choose and why, error bars, and where the data leave the simple rule.
Conclusion~450
Answer the question with numbers: how speed changes with depth, and how far the simple rule works.
Evaluation~650, the biggest part!
Strengths, weaknesses ranked by effect (depth range, magnification, reflections, frequency drift), and improvements tied to each.
Referencesnot counted
Every source you used for the theory of water waves.

What your Physics IA graph could look like

draw both theories ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

02468101214160510152025303540Water depth h / mm (± 0.5 mm)Wave speed v / cm s⁻¹ (± 1.5)with a finite-depth correction (f = 4 Hz)shallow-water rule √(gh)your data, with error barsdata fall below √(gh) as thewater gets deeper: why?ILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity and its unit, with the uncertainty of the depth you set.
  • Error bars on every point. Depth is hard to measure to better than half a millimetre, so say how you did it.
  • Both the simple rule and a corrected form are drawn, so the reader can see where the simple one fails.
  • The scale starts at zero, so the square-root shape is clear.
  • Another graph to consider: v² against h. If √(gh) holds it is a straight line; curvature at large h shows where the rule stops working.

Which uncertainty matters most?

Rank by the effect on your comparison with theory (here, at h = 6 mm). Depth is measured so coarsely that it is often the weak link, not the wavelength.

Depth reading (± 0.5 mm at 6 mm)4.2%Strobe frequency (± 0.1 Hz of 4)2.5%Screen scale (± 2 mm of 100 mm)2%Wavelength over 4 stripes (± 2 mm)0.9%biggest effect: discuss this first!% uncertainty in v or in the √(gh) prediction at h = 6 mmILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

calibrate the screen BEFORE you start

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind the speed of water waves in terms of depth, and the condition that makes the shallow-water form valid. Decide which depths you expect to follow it and which not.
  2. Trial run (1 lesson)Set up the tank and see stripes on the screen. Is the tank level? Do reflections muddle the pattern? Can you measure over several wavelengths? Fix these before you plan the range.
  3. Fix the frequencyChoose a frequency, and decide how you will show it stays the same as the depth changes. A strobe or video frame count both work.
  4. Calibrate the screenPut a ruler in the beam so you know how much the shadow pattern is magnified. Measure the scale factor again if you move the lamp.
  5. Decide depths and repeatsChoose at least 6 depths across as large a range as the tank allows. Measure the depth in several places, and write down why.
  6. Collect the dataMeasure the wavelength across several stripes, at every depth, and repeat. Note reflections and anything that drifts.
  7. ProcessFind λ and its uncertainty, correct for magnification, and calculate v = fλ with an uncertainty.
  8. Graph and comparePlot v against h with error bars, add the shallow-water line, and decide whether v² against h tells you more.
  9. EvaluateWhere does the simple rule fail, and is it the physics or the method? Rank the weaknesses and link each improvement to one.
  10. Write, then checkWrite in the order of the layout above, then run the checklist below before your teacher's draft.

Physics you'll need

Traps to avoid in this Physics IA

  • A small depth range: change the depth by a few millimetres and your trend sits inside the error bars.
  • Stray reflections from the tank walls, which overlap the pattern and distort the wavelength.
  • Forgetting that the shadow on the screen is magnified, so every wavelength is too long.
  • A tank that is not level, so the depth is different at the dipper and at the far end.
  • Letting the frequency drift between depths and never checking it.
  • Using √(gh) at depths where it is not valid, then blaming the data for the mismatch.
  • Forgetting surface tension: for short ripples it speeds the waves up by a few per cent, which can hide or mimic the depth effect. Mention it, and use a low frequency.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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