Physics IA · C · Wave behaviour · topic 20 of 30
Vibrating string: is f really proportional to 1/L? · IB Physics IA idea: guide, sample graph and step-by-step plan
clean theory, clean graph. nice.Every guitarist shortens a string to raise the note. You're going to test the rule they follow without thinking, and find out how exact it is.
- ✓ you like music or guitars
- ✓ you can read a frequency from an app
- ✓ you want a clean straight-line test
The big idea
← the gradient is your second result!A string fixed at both ends vibrates in standing waves, and the fundamental frequency is f = (1/2L)√(T/μ). So f should be proportional to 1/L, with a gradient that depends on tension and mass per unit length. A graph of f against 1/L is a straight line through the origin. The tension must stay fixed, and so must the string. Then the gradient lets you work out the wave speed and μ and compare with a direct measurement.
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 →
Keep L fixed and hang different masses, measuring f each time.
→ A different graph (f² against T); the gradient gives μ; and friction at the pulley becomes your main systematic error.Repeat with a thick and a thin string, or two materials.
→ Two gradients and two values of μ, each checked with a ruler and a balance.Drive the string with a vibrator and find resonances by sweeping the frequency.
→ You find the harmonics too, so you can test the pattern as well as the fundamental.At one length, find the first four resonances and plot f against harmonic number.
→ A straight line through the origin if the string is ideal; any curvature is the stiffness of the string.Record each note and find the frequency by a spectrum analysis.
→ Smaller uncertainty than reading from a tuner; the evaluation compares two methods.Use a guitar, a ukulele or a monochord.
→ A purpose for your introduction; the tuning pegs make tension control harder, so say how you managed it.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 mode, which app or analysis, how repeated).
- Says what stays fixed: tension and how you check it, the string, how you pluck, the room.
- Says what you will compare your result with (the 1/L law, the value of μ you measure separately, or both).
- Is narrow enough to finish with at least 6 lengths and repeats, over a range of at least a factor of two.
The set-up
One way to set it up. Draw your own version, with your real string, tension and bridge positions, 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 string length sets pitch in a guitar, a piano or a harp; what you expect and why.
Standing waves on a string; the equation for the fundamental; why f depends on 1/L, T and μ; what your graph should look like if the theory holds.
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
How you set the length and tension; how you excite the string; how you read the frequency and which mode it is; how you measure μ; repeats.
Short and specific: a falling mass, a snapping string, loud notes in a shared room.
One table: length, each frequency reading, with the app resolution and the length uncertainty in the headers.
How you get 1/L and its uncertainty; how you take the mean frequency; how you get v and μ from the gradient; one worked example each.
f against 1/L with error bars and a best-fit line; what the gradient means physically; whether it goes through the origin.
Answer the question with numbers: how well f follows 1/L, and how the gradient-based μ compares with the direct measurement.
Strengths, weaknesses ranked by effect (tension drift, frequency reading, pulley friction, string stiffness), and improvements tied to each.
Every source you used for theory or method.
What your Physics IA graph could look like
does it go through the origin?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 reading.
- Error bars on every point. The length error becomes small in 1/L, so the vertical bars are the long ones.
- A second line shows what a hidden change of tension would do to the gradient.
- Start the axes at zero, because the line is predicted to pass through the origin and you can test that.
- Another graph to consider: f against 1/L for two tensions on one set of axes, to test the √T dependence in the gradients.
Which uncertainty matters most?
Rank by the effect on your result (here, μ found from the gradient), not on the raw readings. Because μ depends on the gradient squared, the fit uncertainty doubles.
Your game plan
measure μ separately, it's your checkTick steps off as you go. We'll remember on this device.
0 of 10 done
- Read and predictFind the wave-speed equation for a string and the standing-wave condition. Sketch the graph you expect and say what its gradient represents.
- Trial run (1 lesson)Pluck at a few lengths. Does the app lock on to one note? Is the reading a harmonic, not the fundamental? Does the mass swing, or the bridge slip? Fix these now.
- Fix the tensionChoose the hanging mass. How will you show that the tension does not change as you move the bridge? Think about the pulley, and the string slipping.
- Decide lengths and repeatsChoose at least 6 lengths across a factor of two or more. Decide how many times to pluck at each, and how you will judge the right mode.
- Measure μ directlyWeigh a known length of string with a good balance. This is your independent check on the gradient, so measure it carefully.
- Collect the dataRecord every reading with units and resolution, in a quiet room. Note anything odd, such as a buzz or a drifting note.
- ProcessConvert to 1/L, find mean frequencies with uncertainties, and decide how the length uncertainty carries over.
- Graph and comparePlot f against 1/L with error bars, fit a line, and check whether it passes through the origin. Compare the μ from the gradient with your direct value.
- EvaluateRank the weaknesses by effect on your result. Link each improvement to a specific problem you saw.
- 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
- Reading the wrong frequency: background noise or a harmonic, not the fundamental.
- Changing the tension by accident as you move the bridge, or letting the string slip over the pulley.
- Measuring L from the wrong points: from the clamp, rather than from bridge to bridge.
- A string that stretches or is not uniform, so μ is not the same along its length.
- Reading to the nearest hertz and calling that the uncertainty, without any repeats.
- Forcing the line through the origin without checking whether the data want to go there.
More Physics IA ideas like this
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- Mass on a spring: does the spring's own mass matter?●○○
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.