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A-level Physics required practicals

Stationary waves on a stretched string

AQA 3.3.1.3 · RP1

A-level Physics (7408) · Required practical 1 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.

Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works

Investigate how the resonant frequency of a stretched string depends on its vibrating length, tension and mass per unit length.

Apparatus

  • Vibration generator driven by a signal generator
  • String, pulley, mass hanger and slotted masses
  • Metre rule and balance
  • Frequency display or oscilloscope connected to the drive signal
  • Clamp stand, boss and clamp

Apparatus & techniques (AT)

AT a · analogue measurement

A metre rule provides the analogue length readings for the vibrating length L and the measured string sample.

AT b · digital instruments

A digital balance gives the string-sample mass for mu, and the signal generator frequency display or oscilloscope supplies the frequency at resonance.

AT c · accuracy methods

Long string samples, repeated node readings and a fixed mode reduce the percentage uncertainty in the derived quantities.

AT i · wave generation/measurement

The vibration generator produces stationary waves whose nodes, antinodes and resonant frequency are measured.

Safety

Hazard

A hanging mass can fall or pull the stand over.

Control

Secure the stands, keep feet clear, use a mass catcher and do not overload the string.

Hazard

A taut string may snap.

Control

Inspect the string, wear eye protection and keep faces away from the line of the string.

Method

  1. 1Measure the mass and total length of a sample of the string, then calculate its mass per unit length.
  2. 2Pass the string over the pulley, attach a known hanging mass and measure the vibrating length between the effective nodes.
  3. 3Start at low drive amplitude and adjust the signal frequency until a clear single-loop stationary pattern forms — the first harmonic — and record its resonant frequency.
  4. 4Change one quantity only: move the vibration generator to change length, change the hanging mass to change tension, or replace the string to change mass per unit length.
  5. 5Restore the first harmonic, repeat each resonance judgement and record the spread before changing the next setting.

CPAC focus (editorial)

This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.

  • CPAC 2: Editorial focus: choose useful ranges of L, T or mu while keeping the mode and remaining variables fixed.
  • CPAC 4: Editorial focus: record repeated resonance frequencies and measured node-to-node lengths with units and resolution.
  • CPAC 5: Editorial focus: linearise the predicted relationship and report a gradient with an uncertainty-based conclusion.

Variables

Independent

Vibrating length L, tension T or mass per unit length mu

Dependent

Resonant frequency f of the first harmonic

Control

  • The other two string quantities not being varied
  • The stationary-wave mode and effective node positions
  • Drive amplitude and the same vibration generator

Results & processing

  • For the first harmonic, use f = (1 / 2L) x sqrt(T / mu), with tension T found from the hanging weight; a higher mode n obeys f = (n / 2L) x sqrt(T / mu), so the linearisations below hold only with the mode fixed.
  • A graph of f against 1/L, f squared against T, or f against 1/sqrt(mu) should be linear when the other quantities and the mode are fixed.
  • Use the gradient and its uncertainty to test the predicted relationship rather than judging proportionality from two readings.

Analysis skills

  • Linearise f = (1 / 2L) x sqrt(T / mu) as f against 1/L, f squared against T, or f against 1/sqrt(mu).
  • Use a best-fit gradient and max/min acceptable gradients to compare the measured constant with the wave model.

Uncertainty

Sources

  • Uncertain effective node positions and vibrating length
  • Balance resolution in mass per unit length and uncertainty in the hanging mass
  • A finite frequency interval over which resonance appears strongest

Calculations

  • For f proportional to T1/2 mu−1/2 L−1, add percentage uncertainty in L to half the percentage uncertainties in T and mu.
  • Use half the range of repeated resonance frequencies as an estimate of random uncertainty where appropriate.

Interpretation

  • A non-zero graph intercept may indicate an effective-length offset or unaccounted string tension rather than disprove the model by itself.
  • Agreement should be judged against gradient uncertainty, not from whether plotted points look roughly straight.

Exam angles

  • Identify valid quantitative controls when one string property is varied.
  • Read a period or frequency correctly from an oscilloscope time-base and retain justified significant figures.
  • Explain what repeats can establish and what separate evidence is needed to claim the string is uniform.

Where students lose marks

Calling frequency a control variable even though frequency is adjusted to find each resonance.

Fix: Name the controlled string property or drive condition quantitatively; frequency is the measured resonant outcome.

  • Examiner report: P3-25 · PDF p. 4

Measuring to the clamp or pulley instead of between the effective nodes.

Fix: Measure the part of the string that actually vibrates and state how the node positions are identified.

Assuming repeat readings prove that the string is uniform.

Fix: Repeats estimate scatter in locating resonance; measure several string samples or positions to test uniformity.

Improve the method

  • Use a long measured sample when finding mass per unit length so balance and ruler resolution form smaller percentages.
  • Keep the drive amplitude low enough that the effective vibrating length and tension are not altered appreciably.
  • Approach resonance from above and below and use the midpoint of the frequency interval over which the pattern is judged strongest.

Source references

  • Specification: PSpec 3.3.1.3 · PDF p. 19

Try it — exam-style

Hard
ORIGINAL

For the first harmonic, L = (0.800 +/- 0.002) m, T = (28.8 +/- 0.3) N and mu = (5.00 +/- 0.10) x 10−3 kg m−1. Calculate f and its absolute uncertainty using percentage uncertainties added with the powers in f = (1 / 2L)sqrt(T / mu).

[5 marks]

Total for this question: 5

Medium
ORIGINAL

A student varies the hanging mass to test f squared proportional to T. State two quantities that must be controlled and explain why frequency is not one of them.

[3 marks]

Total for this question: 3

Questions are written in the style of past AQA papers — never copied from them.

Drill it properly

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