Physics IA · C · Wave behaviour · topic 21 of 30
Resonance tube: how long is the air column really? · IB Physics IA idea: guide, sample graph and step-by-step plan
a classic that needs a good graphEveryone says a closed tube resonates at a quarter wavelength. You're going to find out the air column is longer than the tube you can see.
- ✓ you like sound and music
- ✓ you can listen carefully for a peak
- ✓ you want to find the speed of sound and an end correction
The big idea
← the intercept is the clever bitIn a tube closed at one end, the fundamental resonance has a quarter of a wavelength in the tube: f = v/4(L + e), where e is the end correction, about 0.6 times the tube's radius. A graph of 1/f against L is a straight line, and its intercept shows the end correction, while its gradient gives the speed of sound. The experiment tests whether a simple formula needs a fudge factor, and why the air bulges out past the open end.
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 →
Repeat with two or three tubes of different radius.
→ Tests whether e is proportional to r; your analysis compares the intercepts.At one length, find the first three resonances (odd multiples only).
→ Tests the pattern of odd harmonics; a different graph of f against harmonic number.Warm the air in the tube a few degrees, or compare a cold and warm day.
→ Brings in v = 331 + 0.6T style variation; a systematic factor you quantify.Use a tuning fork and move the water level to find resonance lengths.
→ A different method: the difference between two resonance lengths gives half a wavelength, and cancels the end correction.Record the sound and find the peak with a spectrum analyser.
→ Smaller uncertainty for f than listening; the evaluation compares methods.Compare with an open tube, which has two end corrections.
→ A related test of the idea of end correction; more comparison to discuss.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 lengths, in cm, and how many values).
- Names one dependent variable and how you will find it (which resonance, how the peak is judged).
- Says what stays fixed: tube radius, air temperature, the speaker's position and level.
- Says what you will compare your result with (the quarter-wavelength rule, a corrected rule with e, or both).
- Is narrow enough to finish with at least 6 lengths and repeats, and says how you will deal with the end correction.
The set-up
One way to set it up. Draw your own version, with your real tube, speaker and ruler, for the Method section.
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.
Your question; why closed tubes matter for organ pipes, bottles and exhaust systems; what you expect and why.
Standing waves in a closed tube; node at the closed end and antinode near the open end; the equation with end correction; the predicted graph.
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
How you set L; how you find the resonance and judge the peak; how you measure the radius; temperature; repeats.
Short and specific: loud tones in a shared room, a tall tube, water on the floor.
One table: length and each resonant frequency, with the resolution of the ruler and of the generator in the headers.
How you find 1/f and its uncertainty; how you get v and e from the gradient and intercept; one worked example each.
1/f against L with error bars; best-fit and worst-fit lines; what the gradient and the intercept mean physically.
Answer the question with numbers: the speed of sound you find, the end correction, and how they compare with accepted values.
Strengths, weaknesses ranked by effect (peak judgement, temperature, end correction, background noise), and improvements tied to each.
Every source you used, including the speed of sound at your temperature.
What your Physics IA graph could look like
what does the intercept mean?Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only
- Axis labels name the quantity and its unit, with the uncertainty of the value you read.
- Error bars on every point. The width of the resonance peak usually decides the vertical bar.
- Two lines drawn, so the reader can see what the end correction does.
- The axes start at zero because the intercept is part of the answer.
- Another graph to consider: f against 1/(L + e) for a few trial values of e, to see which e makes the line straightest.
Which uncertainty matters most?
Rank by the effect on your result (here, speed of sound from one reading at L = 30 cm). Ignoring the end correction is a systematic error, and it still counts.
Your game plan
decide how you judge the peak, then stick to itTick steps off as you go. We'll remember on this device.
0 of 10 done
- Read and predictFind the standing-wave condition for a closed tube and the idea of end correction. Sketch the graph you expect and say what the intercept means.
- Trial run (1 lesson)Sweep the frequency at one length. Can you hear or see a clear peak? Is the loudest point the fundamental? Does the speaker's position change it? Fix these now.
- Decide how to judge the peakPick a rule for finding the resonance: loudest by ear, a microphone level, a screen reading. Apply it identically for every length.
- Measure the tubeMeasure the inside diameter in more than one place. You will need r, even if you only use it to compare e with 0.6r.
- Decide lengths and repeatsChoose at least 6 lengths across a wide range and repeat each. Decide how you will set L without moving the speaker.
- Collect the dataRecord each resonance with resolution and units. Note the room temperature at the start and the end.
- ProcessConvert to 1/f with uncertainties. Decide how the uncertainty of the peak enters the error bars.
- Graph and comparePlot 1/f against L, fit a line, and find the speed of sound and the end correction from the gradient and the intercept. Compare with accepted values.
- EvaluateRank the weaknesses by effect on the speed of sound. Link each improvement to a specific problem.
- 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
- Ignoring the end correction: the speed of sound comes out wrong by a few per cent and you do not know why.
- Choosing the resonance by ear and calling it exact: the peak is broad, so say how wide.
- Background noise or a nearby wall that shifts the apparent peak.
- Measuring L from the rim of the tube holder rather than to the water surface.
- Letting the air warm as the experiment runs without recording the temperature.
- Mixing up harmonics: a resonance at three times the frequency is not a new length.
More Physics IA ideas like this
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- Mass on a spring: does the spring's own mass matter?●○○
- Sound level and distance: does 1/r² hold?●○○
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.