Required Practicals / AQA / Practical 1
1 AS 3.4.1.3

Stationary waves on a string

Investigate how the resonant frequency of stationary waves on a string depends on length, tension and mass per unit length.

Apparatus

  • Signal generator and mechanical vibration transducer
  • String or nylon thread of known mass per unit length
  • Pulley, slotted masses and hanger
  • Metre rule
  • Stands and clamps

Safety

  • Secure the pulley and stand so hanging masses cannot fall onto anyone below.
  • Use a low signal generator amplitude to prevent the string breaking under excessive vibration.

Method

  1. Thread the string from the vibration transducer, over a pulley and attach slotted masses to provide tension T = mg.
  2. Switch on the signal generator and slowly increase the frequency until a stable fundamental (first harmonic) standing wave forms with one loop.
  3. Record the resonant frequency f and measure the vibrating length L between the transducer and pulley.
  4. Repeat at different lengths (move the pulley) to investigate f vs L at constant T and mass per unit length.
  5. Repeat with different hanging masses (to vary T) at constant L; repeat with strings of different linear density.

Key Variables

Independent String length L (or tension T, or mass per unit length mu)
Dependent Resonant frequency f
Controlled Tension (when varying L or mu); Length (when varying T or mu); Mass per unit length (when varying L or T)

Analysis and Results

  • The fundamental frequency is given by $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$.
  • Plot f against 1/L at constant T and mu: expect a straight line through the origin with gradient $\frac{1}{2}\sqrt{\frac{T}{\mu}}$.
  • Plot f squared against T at constant L and mu: straight line through origin, gradient $= \frac{1}{4L^2\mu}$.
  • Wave speed on the string: $v = \sqrt{T/\mu}$. Check consistency using v = f multiplied by 2L.

Common Errors

  • Measuring L beyond the pulley rather than between the vibrator and pulley.
  • Not waiting for the wave to stabilise before recording frequency.
  • Plotting f against L (a curve) instead of f against 1/L (a straight line).
  • Ignoring the mass of the string when calculating tension from hanging masses.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 3 marks

A string of length 0.60 m and mass per unit length $4.0 \times 10^{-3}$ kg/m is held under a tension of 16 N. Calculate the fundamental frequency of vibration.

Q2 4 marks

Describe an experiment to investigate how the resonant frequency of a stretched string varies with tension. Include how you would display and interpret your results.

Q3 2 marks

State two differences between a stationary wave and a progressive wave.