20 of 20 ideas
C.4 Standing waves and resonance: 20 ideas
Resonance lengths in a closed tube and the end correction
Research question. How does the first resonant length of a closed tube depend on the frequency of a speaker between 400 Hz and 1200 Hz, and what end correction does the data give?
- C.4 Standing waves and resonance
- SL and HL
- Easy data
- Overdone: on 4 sites
My take. Widely done, so it only earns credit if you do something extra. Focus on the end correction with two tube radii, or use it to find the speed of sound in a different gas like carbon dioxide released above the water.
Method, physics and where marks are lost+
- Independent variable
- Speaker frequency from 400 Hz to 1200 Hz in 100 Hz steps, giving 9 values, each with three repeats of the resonant length.
- What you measure
- Resonant length found by sliding the water level in a tall measuring cylinder or pipe, with a metre rule. Calculate 1/f and compare with 4(L + e)/v.
- Controlled variables
- Same tube diameter. Same speaker at constant output level held at the tube mouth at a fixed distance. Room temperature recorded at the start and end of each session. Same person judging the loudest point, or a phone microphone showing amplitude on a trace.
- Physics and graph
- For a closed pipe the first resonance has L + e = λ/4 = v/4f, with e about 0.6 r. Plot L against 1/f. The gradient is v/4 and the negative intercept is the end correction e.
- SL and HL
- SL can find v and check it against v = 331 + 0.6θ. A higher band comes from using the intercept for e and testing e = 0.6 r with tubes of two diameters, and using higher harmonics. HL depth is possible through discussing boundary conditions and damping of the resonance.
- Where marks are lost
- Research design: overused topic so a trivial version reads as copied, and no plan for how the resonance peak is decided. Data analysis: plotting L against f and forcing the line through the origin, which throws away the end correction. Evaluation: not commenting on temperature change and the broad resonance peak.
- Data
- Needs a tone generator with a speaker, a tall cylinder with water and a rule; main uncertainty is locating the loudest position by ear, so use a microphone app.
Guitar string tension against fundamental frequency
Research question. How does the tension in a 0.65 m steel guitar string, varied from 20 N to 60 N in 5 values, affect its fundamental frequency measured with a microphone and spectrum software?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Common: on 3 sites
My take. Common (listed on 3 sites) but sound. The best personal twist is using an instrument you play and checking μ independently; a weak version just repeats f against T.
Method, physics and where marks are lost+
- Independent variable
- Tension in 8 to 10 values from 20 to 60 N, set by hanging masses over a pulley or by a spring balance, each measured 3 times.
- What you measure
- Fundamental frequency from a microphone and frequency analysis software such as Audacity, with a tuner app as a check. The measured mass per unit length is found from a mass and length measurement of a spare piece.
- Controlled variables
- Vibrating length fixed with bridges and measured with a ruler. Same string, so material and diameter are unchanged. Plucking position and strength kept alike. Room temperature stable, since the string changes length.
- Physics and graph
- f = (1/2L)√(T/μ). Plot f² against T; the gradient is 1/(4L²μ), so μ can be found and compared with the value from weighing the string. A plot of f against √T also works.
- SL and HL
- SL students get the f² against T line and a value of μ. To reach the top band, compare μ from the gradient with the direct measurement, check the harmonic content, and consider stiffness and end effects. HL adds nothing specific but fits the treatment of standing waves.
- Where marks are lost
- Research design: tension changing as the string stretches or a poorly known T. Data analysis: linearising without uncertainty bars. Conclusion: not comparing gradient with the measured μ. Evaluation: ignoring the damping and pluck effects on the frequency.
- Data
- Needs a string setup, masses, a pulley and a microphone with software; tension calibration and frequency resolution are the main uncertainty.
Damping and Q factor of a driven oscillator
Research question. How does the added damping (card vanes of 0, 25 and 50 cm²) change the resonant frequency and quality factor of a driven mass on a spring?
- C.4 Standing waves and resonance
- HL topic
- Hard data
- Rarely listed
My take. Ambitious and rewarding, but hard to get clean data. Choose it only if a stable driver is available, and take many points near resonance.
Method, physics and where marks are lost+
- Independent variable
- Driving frequency, 0.5 to 2.0 Hz in steps of about 0.1 Hz (15 values) around resonance, at three damping levels set by vane area of 0, 25 and 50 cm².
- What you measure
- Steady-state amplitude of the mass, from video with a ruler behind or a motion sensor. Q = f₀/Δf found from the full width of the curve at 1/√2 of the peak amplitude.
- Controlled variables
- Driver amplitude (same throw of the vibration generator or motor crank); mass and spring (unchanged); time allowed at each frequency for transients to die (at least 20 s); vane shape and orientation.
- Physics and graph
- Resonance curve of amplitude against frequency; peak frequency drops slightly with damping, and Q = f₀/Δf. Plot amplitude against driving frequency for each damping level and compare widths and heights.
- SL and HL
- Resonance and damping curves at this depth suit HL. An SL student could plot the curves and describe them qualitatively. Top band: model the curves with a driven damped oscillator equation and fit b.
- Where marks are lost
- Research design: driver amplitude changing with frequency and steady state not reached. Data analysis: too few points near the peak to find the width. Evaluation: not commenting on how the peak shifts.
- Data
- Needs a variable-frequency driver (function generator with vibration generator) and an amplitude measurement; the main uncertainty is transients and non-constant drive.
End correction of open pipes of different radius
Research question. How does the internal radius of an open pipe (from 1.0 to 3.5 cm, six pipes) affect its end correction, found from the resonant frequencies of a 40 cm pipe?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A good choice for someone who likes wave work. The analysis is neat because two unknowns share one fit, so plan the fit before collecting.
Method, physics and where marks are lost+
- Independent variable
- Internal radius of six open tubes of equal length 40.0 cm: about 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 cm, measured with vernier callipers.
- What you measure
- First three resonant frequencies, found with a loudspeaker and function generator and a microphone (oscilloscope or app). End correction e found from the fit of f against n/(2(L+2e)).
- Controlled variables
- Physical length of tube (cut to the same length, measured with a ruler); air temperature (recorded, taken as constant); loudspeaker position and distance (fixed); sound level from the generator.
- Physics and graph
- For an open pipe, fn = nv/(2(L + 2e)). Plot f against n for each tube: gradient v/(2(L+2e)) gives e if v is known. Then plot e against r, expecting e ≈ 0.6r.
- SL and HL
- SL can find e from the harmonics and compare with 0.6r. For a top-band result, treat speed of sound as a fitted value with uncertainty and handle its correlation with e.
- Where marks are lost
- Research design: pipes of differing length or wall material. Data analysis: assuming v with no temperature check. Evaluation: not commenting on how loudspeaker placement shifts resonances.
- Data
- PVC or cardboard tubes, a loudspeaker and a microphone with frequency-analysis software; the main uncertainty is picking the resonant peak.
Fundamental frequency of a vibrating string against its length
Research question. How does the fundamental resonant frequency of a nylon string under a fixed 20 N tension vary with vibrating length from 0.30 m to 0.80 m in 0.10 m steps?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A good clean topic with a firm theory to test. Personalise it with a real instrument string such as a guitar or violin string and compare with its tuned note.
Method, physics and where marks are lost+
- Independent variable
- Vibrating length set by a movable bridge: 0.30, 0.40, 0.50, 0.60, 0.70, 0.80 m, each measured three times.
- What you measure
- Resonance frequency found by sweeping a signal generator connected to a vibrator (Hz) and judging maximum amplitude; wavelength taken as twice the length, and wave speed v = fλ calculated.
- Controlled variables
- Tension: fixed with a hanging mass over a pulley, checked each run. String: same piece, same linear density measured with a balance and metre rule. Vibrator amplitude: constant generator setting. Temperature: room conditions.
- Physics and graph
- f = (1/2L)√(T/μ). Plot f against 1/L: gradient is half the wave speed, and √(T/μ) predicts it. Wave speed calculated at each length should be constant.
- SL and HL
- SL: f against 1/L and comparison of the speed with the value from T and μ. Top band: repeat by changing tension too, examine higher harmonics, and discuss end effects and the finding resonance peak width as the main uncertainty.
- Where marks are lost
- Research design: measuring frequency and wavelength as two independent outcomes when one follows from the other. Data analysis: judging resonance by eye without a repeat spread. Conclusion: no comparison with predicted speed. Evaluation: ignoring the vibrator not being a true node.
- Data
- Needs a signal generator, mechanical vibrator, pulley and masses; the main uncertainty is locating the exact resonant peak.
Pitch drift of a wire as its temperature changes
Research question. How does the fundamental frequency of a steel wire held between fixed supports change as its temperature is raised from 20 °C to 70 °C in steps of 10 °C?
- C.4 Standing waves and resonance
- SL and HL
- Hard data
- Rarely listed
My take. Physically interesting but hard to get clean data. Take it only if you can control tension precisely, and use a metal wire rather than a nylon string.
Method, physics and where marks are lost+
- Independent variable
- Wire temperature, 20 to 70 °C in 6 values, set by passing a small controlled current or by a warm air stream, with each value repeated three times.
- What you measure
- Fundamental frequency from a phone spectrum analyser or a signal generator matched to resonance with a small driver coil, and wire temperature from a thermocouple taped to the wire.
- Controlled variables
- Wire length fixed by rigid clamps. Starting tension set with the same hanging mass. Same wire and same plucking or driving position. Ambient air movement kept low with a screen.
- Physics and graph
- f = (1/2L)√(T/μ). Heating changes tension because the wire expands against fixed ends or hangs under a load, so plot f² against temperature. For a rigid frame, tension drops as the wire lengthens, so the gradient relates to the thermal expansion coefficient and Young's modulus.
- SL and HL
- SL students describe the frequency shift and link it to tension change. Top band work predicts the gradient from the expansion coefficient and Young's modulus and compares it with the measured one. The frame's own expansion should be evaluated.
- Where marks are lost
- Research design: no way to measure wire temperature reliably. Data analysis: tiny frequency changes hidden by resolution. Conclusion: explaining the result without a quantitative model. Evaluation: not commenting on uneven heating or the frame expanding.
- Data
- Needs a thermocouple and a spectrum app with fine resolution; the main uncertainty is that the frequency shift is small, and heating must not damage the wire.
Resonance lengths of a closed air column and the end correction
Research question. How does the first resonant length L of an air column closed at one end, made with a tuning fork or a speaker tone, vary with driving frequency f from 256 Hz to 1024 Hz in 6 steps, and what end correction does this give for a tube of 30 mm internal diameter?
- C.4 Standing waves and resonance
- SL and HL
- Easy data
- Rarely listed
My take. A solid, cheap choice, but common in some form. Making the end correction the actual target, and testing it with two tube diameters, makes it yours.
Method, physics and where marks are lost+
- Independent variable
- Driving frequency from a signal generator and speaker: 256, 320, 384, 512, 768 and 1024 Hz (6 values). Each resonant length found 5 times by sliding the water level up and down.
- What you measure
- Resonant length L of the air column (tube in a tall measuring cylinder of water, metre rule, ±1 mm). Calculate 1/f and the speed of sound from the gradient.
- Controlled variables
- Tube diameter, kept by using one tube throughout. Air temperature, read on a thermometer at the start and end. Speaker amplitude, held at one generator setting and one distance from the tube mouth. Same listener or a phone decibel app to judge the loudest point.
- Physics and graph
- For a closed pipe, L + e = λ/4 = v/(4f), with e ≈ 0.6r. Plot L against 1/f. The gradient is v/4 and the intercept is minus e. Compare v with 331 + 0.6T.
- SL and HL
- SL students get v and e from the straight line and compare with the accepted value. Stronger work also finds the second resonance (3λ/4) to remove e without assuming it, tests e against tube radius using two tubes, and treats the fuzzy resonance peak as a proper uncertainty.
- Where marks are lost
- Research design: judging resonance by ear with no way of reducing bias. Data analysis: ignoring end correction, so the line does not pass through the origin. Evaluation: not explaining the effect of temperature drift or the broad resonance peak.
- Data
- Needs a signal generator, speaker, tall cylinder and tube; the main uncertainty is locating the loudest point, about ±5 mm.
Resonant frequency of a water-filled glass at different temperatures
Research question. How does the water temperature (10 to 80 degrees Celsius, 8 values) in a wine glass affect the fundamental frequency of the ring produced when it is tapped?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. Fun and cheap, but the effect may be almost nothing. Make it personal by using your own glass, and state in advance that a null result is acceptable if the resolution is good enough to show it.
Method, physics and where marks are lost+
- Independent variable
- Water temperature from 10 to 80 degrees Celsius, about 8 values, set with ice and a kettle and read with a digital thermometer. Three taps at each value.
- What you measure
- Frequency from a phone spectrum app or a microphone with Audacity, taken as the peak of the FFT. Also record the temperature right after the taps.
- Controlled variables
- Water volume fixed at a marked level with a measuring cylinder; same glass and same tapping point and tool; microphone distance kept at 10 cm; room noise kept low.
- Physics and graph
- Glass rim modes depend on the glass stiffness, mass and the liquid loading it. Water density changes very slightly with temperature. Plot f against temperature and check for a linear or null trend; discuss glass expansion and modulus.
- SL and HL
- SL students plot f against temperature and describe the trend with uncertainties. Top band work considers cooling during the run, the added mass of the liquid and whether the change is bigger than the frequency resolution.
- Where marks are lost
- Research design: the water cools during measurement, so the true temperature is unknown. Data analysis: frequency resolution of the app is coarser than the change. Conclusion: a physical explanation is asserted without evidence.
- Data
- Needs a glass, thermometer and a spectrum app; the main uncertainty is FFT resolution, so use a long recording window.
Resonant frequency of an LC circuit as coil turns change
Research question. How does the number of turns N on an air cored solenoid, from 20 to 120 in steps of 20, affect the resonant frequency of a parallel LC circuit with a fixed 100 nF capacitor?
- C.4 Standing waves and resonance
- HL topic
- Needs care
- Rarely listed
My take. Good for HL students with an oscilloscope. It gives a clear prediction to test. Twist: insert an iron rod partly into the coil and find how f changes with insertion depth.
Method, physics and where marks are lost+
- Independent variable
- Number of turns on the coil, 6 values from 20 to 120, built on the same former and each tested 3 times.
- What you measure
- Resonant frequency found by sweeping a signal generator and locating the peak amplitude on an oscilloscope (frequency error about ±1% of reading). Inductance is then calculated from f.
- Controlled variables
- Capacitance, using one measured capacitor. Coil length and diameter, kept fixed by winding on one former (turns spaced evenly along the same length). Drive amplitude, held constant on the generator. Core material, air only.
- Physics and graph
- f = 1/(2π√(LC)) and for a long solenoid L ∝ N², so f ∝ 1/N. Plot 1/f against N, which should be a straight line through the origin. The gradient gives 2π√(C·μ₀A/l).
- SL and HL
- Because the LC oscillation and inductance sit in HL topics of induction, this fits HL best. An SL student could attempt it by treating it as a resonance study but would need to self teach inductance. Top band work checks the L ∝ N² prediction against a measured L from an LCR meter and considers coil resistance.
- Where marks are lost
- Research design: coil with too few turns gives frequencies too high to measure, and the stray capacitance is not considered. Data analysis: not linearising the relationship. Conclusion: overclaiming agreement with L ∝ N² for a short coil. Evaluation: leaving out the coil resistance and probe capacitance.
- Data
- Needs a signal generator, an oscilloscope, coil formers and enamelled wire. The main uncertainty is stray capacitance and finding the peak.
Ringing pitch of a stemmed glass versus liquid fill level
Research question. How does the depth of tap water, varied from 0 to 80 mm in steps of 10 mm, in a thin-walled stemmed glass change the frequency of its fundamental ringing tone, measured with a microphone and spectrum software?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A cheap, sound-based investigation that works well if you actually test a model rather than only describing the trend. Twist: repeat with two glass shapes or add a second mode so the conclusion is not just 'higher volume, lower pitch'. Because several sites list the basic version, use a modelling angle to stand out.
Method, physics and where marks are lost+
- Independent variable
- Height of water in one glass, 0, 10, 20, 30, 40, 50, 60, 70 and 80 mm (9 values), set with a syringe and checked against a ruler taped outside. Each level is struck 5 times.
- What you measure
- Fundamental frequency in Hz, taken from the strongest peak in a Fourier spectrum (Audacity or Phyphox) recorded by a phone or USB microphone. Mean and spread of the 5 strikes per level; percentage change from the empty glass is calculated.
- Controlled variables
- Same glass throughout, so wall thickness and shape do not vary. Same strike: a small rubber-tipped rod released from a fixed height, at the same spot on the rim. Water temperature kept at room value, checked with a thermometer. Microphone held at a fixed 10 cm distance, and the glass held on a foam pad to avoid damping differences.
- Physics and graph
- The rim vibrates in a standing-wave mode, and water adds mass that moves with the wall, lowering the frequency. Treat it as a mass-spring system, f = (1/2π)√(k/meff), where meff = mglass + a·mwater. Plot 1/f² against water mass (from volume and density): the line should be straight, with the gradient giving a/(4π²k)... in short, gradient = 4π²·a/k and the intercept relates to the empty glass. Note that the added water mass only approximately fits at low levels, so check where the straight line fails.
- SL and HL
- SL: collect the frequencies, plot f against depth, describe the fall and give a sensible uncertainty. Better SL work linearises 1/f² against water mass and comments on the fit. HL depth: build the effective mass model with a fitted coefficient a, test whether the intercept matches the mass of the glass part that vibrates, compare the fundamental with the second mode, or model how the added fluid loading changes with depth. Also justify why the residuals show a trend.
- Where marks are lost
- Research design: choosing the water volume but not the glass geometry, so the relation is not comparable across glass shapes, or not explaining how the microphone position and the strike are held constant. Data analysis: reading the pitch by ear or a tuner app without uncertainty, and ignoring the FFT frequency resolution (set by the recording length). Conclusion: claiming a simple 'more water means lower frequency' without testing any model, or forcing a straight line through a curved trend. Evaluation: not spotting that water-glass coupling is not a simple added mass at low levels, that the glass may crack or the rim may not be the only vibrating part, and that strike-to-strike variation is not the only error.
- Data
- Needs a thin glass, a microphone or phone with a spectrum app and a syringe; the main uncertainty is the FFT resolution and the small change in pitch at low water levels.
Ringing time of a plucked string against vibrating length
Research question. How does the vibrating length of a guitar string, from 0.25 m to 0.65 m in steps of 0.05 m, affect the time taken for its sound level to fall to half its initial amplitude?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. Fun and personal if you play, but the frequency confound is serious. Use a monochord and analyse in cycles as well as seconds.
Method, physics and where marks are lost+
- Independent variable
- Vibrating length set by a movable bridge on a monochord or guitar, 0.25 to 0.65 m in 9 values, with 3 plucks each.
- What you measure
- Decay of sound amplitude recorded by a phone microphone at a fixed position using a free audio app; half-life of the envelope read off the waveform. Frequency also read from the spectrum.
- Controlled variables
- Tension fixed by tuning the open string to the same frequency check before each set, or by a hanging mass. Plucking displacement fixed with a jig. Microphone distance and room the same. Same string.
- Physics and graph
- Envelope A = A0 e-t/τ, so plot ln A against t and take the gradient for the damping constant. Then plot τ against length. Link to f = (1/2L)√(T/μ) to explain why frequency changes with L at fixed tension.
- SL and HL
- SL students extract a decay time for each length and describe the trend. Top band work separates the frequency effect from the length effect, for example by plotting the number of oscillations before decay. HL depth can add a damping model.
- Where marks are lost
- Research design: pluck force not truly constant, and frequency changing along with length. Data analysis: reading the decay by ear or by a stopwatch. Conclusion: overclaiming a cause when frequency and length change together. Evaluation: ignoring the sound produced by the body of the instrument.
- Data
- Needs a monochord and a phone or sound sensor; the main uncertainty is a repeatable pluck.
Second harmonic frequency of a stretched string against tension
Research question. How does the tension in a 0.80 m nylon or steel string (from 10 N to 60 N in 6 steps) affect the frequency of its second harmonic?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. Solid and reliable, but very commonly done in some form. Make it yours by using a real instrument string such as a guitar string and comparing with the tuning note.
Method, physics and where marks are lost+
- Independent variable
- Tension from hanging masses of 1.0 to 6.0 kg over a pulley (6 values). Five repeated frequency finds per tension.
- What you measure
- Frequency at which a vibration generator drives a clear two loop standing wave, read on the signal generator, or measured with a phone spectrum app from a plucked string. Best judged by maximum amplitude.
- Controlled variables
- Vibrating length: fixed between bridge and pulley, measured with a metre rule. String: same string throughout, with its linear mass density μ found by weighing a measured length. Drive amplitude: kept low and constant. Temperature: room conditions, no heating of the string.
- Physics and graph
- f = (n/2L)√(T/μ), so for n = 2, f = (1/L)√(T/μ). Plot f² against T; a straight line through the origin has gradient 1/(L²μ), which can be checked against the measured μ.
- SL and HL
- SL: get the straight line and compare the gradient with the calculated value. Top band: propagate uncertainty in μ and L, test other harmonics to confirm the n dependence, and discuss end effects and string stiffness.
- Where marks are lost
- Research design: masses not calibrated and the pulley friction ignored. Data analysis: plotting f against T and forcing a curve. Conclusion: no comparison of gradient with theory. Evaluation: finding resonance by ear with a wide uncertainty.
- Data
- Needs a vibration generator, signal generator, pulley and masses; the main uncertainty is picking the resonance peak and pulley friction.
Speed of sound in air, helium and carbon dioxide
Research question. How does the molar mass of a gas (air, helium, carbon dioxide, and mixtures of helium and air in 0 to 100% steps) affect the speed of sound found from resonance in a closed tube at 20 °C?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. Original and interesting because it links waves and gas theory. Use only safe gas quantities with the teacher's approval, and note that the gas cannot be pure.
Method, physics and where marks are lost+
- Independent variable
- Gas composition, five to six values: air, CO2, helium, and two or three helium and air mixtures, made in a balloon or bag and filled into the tube.
- What you measure
- Resonant frequency of a 0.50 m tube found with a tone generator and a phone microphone or oscilloscope, three repeats. Speed of sound calculated from v = 4Lf for the fundamental.
- Controlled variables
- Tube length, measured with a rule and end correction included. Temperature, monitored with a thermometer at each run. Tube flushed with at least three volumes of gas. Same volume amplitude from the speaker.
- Physics and graph
- v = fλ and, for a closed tube, λ = 4(L + 0.6r). Kinetic theory gives v = √(γRT/M), so plot v² against 1/M, where the gradient is about γRT.
- SL and HL
- SL students compare measured speeds with the values expected from the equation. Top work considers how γ differs between monatomic and diatomic gases and the mixing fraction to get M.
- Where marks are lost
- Research design: 'acoustic properties' is too vague, so focus on speed only. Data analysis: gas contamination changes M. Evaluation: not correcting for temperature or the end effect.
- Data
- Helium and CO2 need to be available safely from a school supplier; leakage and air mixing at the open end are the main uncertainty.
Speed of sound in gases from resonance in a tube
Research question. How does the speed of sound in a closed tube filled with air, carbon dioxide and helium mixtures compare when found from resonance frequencies between 200 and 1500 Hz?
- C.4 Standing waves and resonance
- SL and HL
- Hard data
- Rarely listed
My take. Good but hard to keep clean. A safer version is to vary the tube length with air only, or to use small helium balloons under supervision, and to check the temperature dependence instead.
Method, physics and where marks are lost+
- Independent variable
- Gas composition, such as air, air with 25%, 50% helium, and carbon dioxide; at least 4 gases or mixtures. Sweep the frequency in 10 Hz steps and repeat 3 times.
- What you measure
- Resonant frequencies found with a signal generator, speaker and microphone on an oscilloscope, or a phone app for the amplitude; speed calculated from the tube length and the harmonics.
- Controlled variables
- Same tube length, checked with a metre rule; temperature measured with a thermometer for each gas; speaker and microphone at fixed positions; the tube sealed at one end with a stopper or a foil sheet.
- Physics and graph
- For a tube closed at one end, fn = n v/(4L) with odd n, and v = √(γRT/M). Plot resonant frequency against harmonic number; the gradient gives v/(2L). Compare v with the predicted value from the molar mass.
- SL and HL
- SL: the speed from the gradient for each gas and comparing with the accepted values. Top band or HL: derive v from γ and M, apply an end correction of 0.6r, and determine γ for the mixture.
- Where marks are lost
- Research design: changing gas without safety planning or a way to fill the tube and keep the concentration. Data analysis: ignoring the end correction. Evaluation: gas leaking or mixing with air, which changes the composition.
- Data
- Needs a signal generator, a tube, a microphone and safely handled gases; the main uncertainty is gas purity and leaks.
Speed of sound in humid air using a resonance tube
Research question. How does the relative humidity of air, from about 40% to 95%, affect the speed of sound in a resonance tube, at a fixed temperature near 25 °C?
- C.4 Standing waves and resonance
- SL and HL
- Hard data
- Rarely listed
My take. Risky because the expected change is smaller than most school setups can resolve. Only choose it if you plan the precision first, and correct for temperature using v = 331 + 0.6T. A careful null result is still acceptable.
Method, physics and where marks are lost+
- Independent variable
- Relative humidity of air in the tube: five to six values between roughly 40% and 95%, set by allowing damp air to enter, or using a humidifier, and read with a hygrometer, with 3 repeats each.
- What you measure
- Resonant lengths found for a tuning fork of fixed frequency using a tube with a moving water level or plunger. Speed v = 4f(L + 0.3d) for a closed tube, or from the gradient of successive resonance lengths. Humidity and temperature are logged at each run.
- Controlled variables
- Temperature, held within 0.5 °C using a thermometer inside the tube. Same tuning fork frequency, checked against a phone app. Same tube diameter and length. Same method of finding the resonance point, using the loudest sound.
- Physics and graph
- Humid air is less dense than dry air, so the speed of sound increases slightly with water vapour content. The full change from 40% to 95% is only about 0.3 to 0.5%, so v against humidity is very nearly flat and the uncertainty matters more than the trend. Plot v against humidity or against the vapour fraction.
- SL and HL
- SL: measure v for the humidities and state whether a change is seen within the uncertainty. Top band: predict the size of the effect from the molar mass of moist air and compare it with the resolution of the method. HL depth: use the ideal gas relation for speed in a mixture.
- Where marks are lost
- Research design: the effect is smaller than the uncertainty of the method and temperature changes swamp it. Data analysis: no uncertainty propagation. Conclusion: claiming a trend that lies within the error. Evaluation: not recognising that the design could not detect the expected effect.
- Data
- Needs a resonance tube, tuning forks, a hygrometer and a thermometer; the effect is under 0.5%, so precision and temperature control are hard.
Speed of sound through rods of different materials by resonance
Research question. How does the speed of longitudinal waves in solid rods of about 1 m length differ between aluminium, copper, steel, brass and glass, and does it agree with v = √(E/ρ) using data-book values?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. I changed the original to be feasible, since timing sound over short paths in liquids does not work at school. This gives clear numbers and good comparison with theory.
Method, physics and where marks are lost+
- Independent variable
- Rod material: 5 rods of similar length, with a repeat of the lengths for one material at 3 different lengths (0.5, 0.75, 1.0 m).
- What you measure
- Fundamental frequency of the rod held at its centre and tapped at one end, recorded with a phone spectrum app or microphone, 5 taps each. Calculate v = 2Lf and compare with √(E/ρ).
- Controlled variables
- Support position, at the exact midpoint by a foam clamp. Rod length, measured with a metre rule to ±1 mm. Tap strength and position. Temperature of the room.
- Physics and graph
- A rod free at both ends has f = v/(2L) and v = √(E/ρ). Plot f against 1/L for one material to check the gradient equals v/2, then plot v measured against v predicted for all materials.
- SL and HL
- SL students compare measured v with the predicted one for each material. HL depth: link the Young modulus to the atomic bonding picture, and analyse the frequency spectrum overtones as odd and even harmonics.
- Where marks are lost
- Research design: the input idea of timing a delay over a short path is far too crude, so use resonance. Data analysis: not propagating the density and modulus uncertainty. Evaluation: ignoring rod alloy differences from book values.
- Data
- Needs rods, a foam clamp and a phone spectrum app; frequency resolution of the app sets uncertainty, about ±1 Hz.
Tension and wave speed on a stretched string
Research question. How does the tension in a nylon string (2 to 20 N, six values) affect the speed of transverse waves found from standing-wave resonances at a fixed string length of 1.00 m?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A classic, so it needs a twist such as comparing strings of different μ or testing harmonics. Well within reach and gives a clean linear graph.
Method, physics and where marks are lost+
- Independent variable
- Tension from hanging masses of 0.2, 0.5, 1.0, 1.5, 2.0, 2.5 kg over a pulley (about 2 to 25 N), six values.
- What you measure
- Resonant frequency of the fundamental found by scanning a function generator connected to a vibration generator, with node positions checked. Wave speed v = 2Lf₁ (calculated).
- Controlled variables
- Vibrating length (fixed by two marked bridges at 1.00 m); string (same string, mass per unit length measured by weighing 2 m); driver amplitude (kept just large enough to see the loops); string temperature and stretch.
- Physics and graph
- v = √(T/μ) and v = fλ. Plot v² against T: the gradient is 1/μ, which can be checked against the measured μ. Alternatively plot f against √T.
- SL and HL
- SL can do the full analysis using v² against T and compare μ. To reach top band, discuss the resonance width, stretching of the string with tension and compare higher harmonics.
- Where marks are lost
- Research design: string length not held constant when the string stretches. Data analysis: judging resonance by eye with no estimate of frequency uncertainty. Evaluation: ignoring pulley friction and the end effect at the vibrator.
- Data
- Vibration generator, signal generator, pulley and masses; the main uncertainty is finding the exact peak of resonance.
Wave speed on wires of different materials
Research question. How does the fundamental frequency of wires of equal diameter, 0.40 mm, and equal length, 0.60 m, depend on their density for five metals at a tension of 40 N?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. Works but has fewer independent values than most IAs need, so measure each density yourself. A better twist is to vary diameter instead.
Method, physics and where marks are lost+
- Independent variable
- Density of wire material, five metals such as steel, copper, brass, aluminium and nichrome, using tabulated densities and checked by weighing a measured length of each.
- What you measure
- Fundamental frequency from resonance driven by a signal generator and coil, or a microphone spectrum; density also checked by mass on a balance divided by volume.
- Controlled variables
- Length fixed on a sonometer. Tension set with hanging masses. Diameter checked with a micrometer for every wire. Room temperature noted.
- Physics and graph
- f = (1/2L)√(T/μ), μ = ρA. Plot f² against 1/ρ, expecting a straight line with gradient T/(4L²A). Note magnetic wires respond differently to the driver coil, so a microphone or a mechanical driver is better.
- SL and HL
- SL students plot f² against 1/ρ and check the linear trend. Top band work uses measured densities, addresses the fact that only five values with limited spread are available, and quantifies the gradient uncertainty. Materials also differ in stiffness, which is a good evaluation point.
- Where marks are lost
- Research design: uncontrolled diameter between wires. Data analysis: using textbook densities without checking the wire's actual composition. Conclusion: ignoring that few materials limit the fit. Evaluation: not discussing that the wire is not perfectly flexible.
- Data
- Needs a sonometer and several wires of one gauge; the main uncertainty is the small number of materials and mismatched diameters.
Wire material and the fundamental frequency of a string
Research question. How does the linear mass density of strings of different materials (nylon, steel, cotton, copper, fishing line) affect the fundamental resonance frequency at 0.60 m length and 20 N tension?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A good choice once you replace 'material' with linear density, because then the graph is clean and the physics is testable. Twist: use strings from your own guitar or cello.
Method, physics and where marks are lost+
- Independent variable
- Linear mass density μ of five to seven strings, found by weighing 1 m lengths, covering about 0.1 to 5 g/m.
- What you measure
- Fundamental frequency found by tuning a signal generator and vibration driver until the amplitude of the standing wave peaks, with the frequency read from the generator to 0.1 Hz, or from a phone spectrum app.
- Controlled variables
- Vibrating length fixed between two bridges, measured with a metre rule. Tension set by hanging a fixed mass over a pulley and checking it does not change. Same drive amplitude. Same temperature and same clamps.
- Physics and graph
- f = (1/2L)√(T/μ). Plot f² against 1/μ or f against μ−1/2, gradient = √T/(2L). Material only enters through μ, which is the key conclusion.
- SL and HL
- SL students can show f ∝ μ−1/2 across the materials. Stronger work checks whether material affects f beyond μ, for example stiffness in steel. HL depth is not required, but higher harmonics add analysis.
- Where marks are lost
- Research design: 'material' cannot be controlled with a fixed diameter, since density and diameter both change μ. Data analysis: reading a broad resonance peak by ear. Evaluation: stretch of nylon changing tension.
- Data
- Needs a signal generator, vibration driver and a set of strings; the peak amplitude is broad, which limits frequency precision.
Wire thickness and pitch on a sonometer
Research question. How does the diameter of a steel wire, from 0.20 mm to 0.60 mm, affect its fundamental frequency at a fixed length of 0.60 m and tension of 50 N?
- C.4 Standing waves and resonance
- SL and HL
- Needs care
- Rarely listed
My take. A clean, well controlled investigation with a strong theoretical link. It is popular in some form, so use the gradient to extract a material property.
Method, physics and where marks are lost+
- Independent variable
- Wire diameter, 6 wires from 0.20 to 0.60 mm, each measured with a micrometer at 5 places along the wire.
- What you measure
- Fundamental frequency found by driving with a signal generator and a small coil until the wire resonates with maximum amplitude, or read from a microphone spectrum. Mass per unit length calculated from the diameter and density.
- Controlled variables
- Length fixed by the bridges on a sonometer. Tension set by the same hanging masses, checked on a newton meter. Same steel material, checked from the supplier. Same drive coil position.
- Physics and graph
- f = (1/2L)√(T/μ) with μ = ρπd²/4, so f ∝ 1/d. Plot f against 1/d, expecting a straight line through the origin with gradient (1/2L)√(4T/(ρπ)).
- SL and HL
- SL students plot f against 1/d and compare with the predicted gradient. Top band work uses the gradient to extract the wire density or tension and compares it against a known value. HL students can extend to comparing transverse and longitudinal waves.
- Where marks are lost
- Research design: wires of different materials mixed in. Data analysis: micrometer variation along the wire ignored. Conclusion: no comparison of gradient to theory. Evaluation: not commenting on the wire stiffness and end effects at thick diameters.
- Data
- Needs a sonometer, a micrometer and a signal generator; the main uncertainty is the resonance width and the tension reading.
Ideas were collected from public lists and published IA titles, merged when they are the same investigation, and rewritten from scratch. “On N sites” counts how many public lists carry the same investigation. How this list was made.
Frequently asked questions
What are good IB Physics IA ideas on standing waves and resonance?
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Good starting points with easy data that few sites list are resonance lengths of a closed air column and the end correction. Each one gives a straight-line graph from school equipment, which is what the Data analysis and Conclusion criteria need.
Which standing waves and resonance IA ideas are overdone?
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resonance lengths in a closed tube and the end correction and guitar string tension against fundamental frequency appear on three or more public lists. They still work, but they need a twist that shows your own thinking.
Can I do a standing waves and resonance IA at SL?
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18 of the 20 ideas use SL physics. The others rely on HL-only content and are marked as HL topics.