Physics IA · C · Wave behaviour · topic 15 of 30

Sound level and distance: does 1/r² hold? · IB Physics IA idea: guide, sample graph and step-by-step plan

simple kit, real physics. easy to start.

Walk away from a speaker and it gets quieter, but by how much? You're going to test a law with a phone and find out what the room does to it.

Difficulty●○○ Gentle
KitBasic: phone sound meter app, speaker, tape
TimeAbout 8 hours
FitsSL and HL
  • ✓ you like measuring everyday things
  • ✓ you have a phone and a speaker
  • ✓ you want to learn about decibels and logs

The big idea

← the room is your twist

A point source in free space spreads its power over a sphere, so intensity falls as 1/r². The sound level in decibels is a logarithm of intensity, so the level should fall by 20 dB for each factor of ten in distance, and a graph of level against lg r is a straight line of gradient −20. Rooms are not free space: echoes add sound that does not fall with distance. Test the law, then measure how far the room breaks it. That is the investigation.

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 →

Go outdoors

Repeat on a field or a quiet courtyard, away from walls.

→ Close to free-field conditions; compare with the indoor graph to measure the effect of the room.
Test a different source

Compare a speaker with a buzzer, a tuning fork or a handclap.

→ Tests whether the law depends on the source type; adds a comparison and a fair-test issue.
Calibrate the phone

Check the app against a calibrated meter, or test its response at several levels.

→ Turns the weakest part of the method into a result; the evaluation becomes more rigorous.
Use a pure tone

Play a single frequency, then compare two or three frequencies.

→ Tests whether the law depends on frequency, and shows how a tone creates standing-wave patterns in a room.
Test the effect of a barrier

Put a wall, a box or a layer of cloth between the source and the microphone.

→ A different independent variable; the graph becomes level against the barrier thickness or material.
Convert to intensity

Turn dB into relative intensity and test I against 1/r² directly.

→ A different graph and an easier test of the theory; the log conversion is a step in processing.

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 distances, in m, and how many values).
  • Names one dependent variable and how you will record it (the app, its averaging, how many readings).
  • Says what stays fixed: the source, its volume and frequency, the microphone height and direction, the room.
  • Says what you will compare your result with (the 1/r² law, a free-field prediction, or both).
  • Is narrow enough to finish with at least 6 distances over a decade, and repeats at each.

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The set-up

One way to set it up. Draw your own version, with your real room, distances and equipment, for the Method section.

rspeaker: fixed volume,same tone every runphone app: micfaces speaker,same heightecho off the wall: itadds to the direct soundtape measureon the floor

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 sound spreading matters for concerts, classrooms and noise on a building site; what you expect and why.
Background physics~450
Intensity and the inverse square law; the decibel scale and why it is logarithmic; the predicted graph in decibels against lg r.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
Method~400
How you place the source and microphone; how you set the volume and tone; how you read the app (averaging, how many seconds); background noise; repeats.
Safety, ethics, environment~60
Short and specific: hearing safety at high levels and consideration for people nearby.
Raw datatable
One table: distance and each level reading, with the app's resolution in the headers and the background level noted.
Processing~250
How you average readings and find the uncertainty; how you turn distance into lg r; one worked example for each.
Graphs and analysis~350
Level against lg r with error bars; a best-fit line; the gradient compared with −20 dB per decade.
Conclusion~450
Answer the question with numbers: the gradient you find, and where the data leave the straight line.
Evaluation~650, the biggest part!
Strengths, weaknesses ranked by effect (room echoes, the reading's flicker, microphone calibration, source directionality), and improvements tied to each.
Referencesnot counted
Every source you used for the theory and for the app.

What your Physics IA graph could look like

a log axis makes it a straight line!

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different, and a real room will bend it more. example only

-0.4-0.20.00.20.40.60.86065707580859095100lg(r / m) (r ± 0.02 m)Sound level / dB (± 1.5 dB)free field: 80 − 20 lg rsame source in a reverberant roomyour data, with error barsthe data flatten at large r:the room is adding soundILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity and its unit, with the uncertainty of the reading.
  • Error bars on every point. A phone app flickers by a decibel or two, so average over a fixed time.
  • A free-field line and a room line are both drawn. The gap between them is a measure of the room.
  • The scale does not start at zero because the decibel scale has no useful zero here. Say so.
  • Another graph to consider: relative intensity against 1/r², which should be a straight line through the origin in free field.

Which uncertainty matters most?

Rank by the effect on your gradient, not on the raw readings. Here, a systematic room effect is as big as the random flicker of the app.

App reading flicker (± 1.5 dB)11.8%Room echoes (systematic)9.7%Distance at 0.5 m (± 2 cm)1.9%Distance at 4 m (± 2 cm)0.1%biggest effect: discuss this first!% effect on the gradient (about −18 dB between 0.5 m and 4 m)ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

check the app BEFORE you trust it

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

0 of 10 done

  1. Read and predictFind the inverse square law and the definition of sound level in decibels. Work out what your graph should look like, and what the gradient should be.
  2. Trial run (1 lesson)Measure the background level, then a few distances. Does the reading wander? Does moving the phone change the level? Does a nearby wall matter? Fix these before you plan.
  3. Check the appTest the app's response over the range of levels you will use, ideally against another meter. Decide how much you can trust it, and write it down.
  4. Fix the sourceChoose the volume and tone, and decide how you will keep them the same. Switch off the phone's automatic gain if it has one.
  5. Decide distances and repeatsChoose at least 6 distances spread over a decade, for example 0.5 m to 5 m. Decide the averaging time and the number of readings at each.
  6. Collect the dataMeasure from the speaker centre to the microphone each time. Record the background level before and after. Note any outside noise.
  7. ProcessAverage the readings, find the uncertainty, and convert distance to lg r. Decide how to subtract background, if you do.
  8. Graph and comparePlot level against lg r with error bars. Find the gradient and compare it with the free-field prediction. Where do the data leave the line?
  9. EvaluateRank the weaknesses by effect on the gradient. Link each improvement to a specific problem.
  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

  • Echoes in the room: reflected sound adds to the direct sound and flattens the trend at large distance.
  • An uncalibrated phone microphone: the app may compress loud sounds or boost quiet ones.
  • Plotting level against distance and forcing a curve, instead of using lg r to get a straight line.
  • Forgetting the background level, which dominates when the source is far away.
  • Pointing the microphone in different directions, or holding the phone by hand.
  • Treating the speaker as a point when it is a large box close to the microphone.

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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