RP01: Stationary Waves on a String

• Equipment:

  • Signal Generator
  • Vibration Generator
  • Stand
  • Pulley
  • Wooden Bridge
  • 100g masses with holder
  • Metre ruler
  • 1.5m long string
  • Balance
• Method:

  • Measure mass of string on a balance and record.
  • Set up as shown in diagram
  • Adjust the length l so that it is 1.000m, measured using the metre ruler.
  • Increase the frequency f until the string oscillates at the first harmonic.
  • Read and record f.
  • Reduce l by 0.100m and adjust f again until first harmonic is achieved.
  • Repeat until l is equal to 0.500m.
  • Repeat experiment twice.

  
• Graphs and Calculations:

  • Plot a graph of the mean value of f against 1/l and draw a line of best fit.
  • The wave speed will be two times the gradient.
  • $\lambda =$$2l \rightarrow v=$$2fl =$$\frac{2f}{l} =$$2G$ where G is gradient.
  • The tension of the string is equal to the weight of the hanging mass (if 100g, 0.981N) and its mass per unit length can be found by dividing the mass of the string by its length (1.5m).
  • The speed of the wave is also given by $v=$$\sqrt\frac{T}{\mu}$ which can be compared to the value obtained by the graph.
• Safety:

  • The stand couple topple over causing injury.
  • A counter weight or clamp can be used if stand is deemed unstable.
• Improvements:

  • The experiment can be repeated with different masses to change the tension.
  • Can also be repeated with different thicknesses of string to change the mass per unit length in order to investigate the effect of changing these parameters.
  • An oscilloscope can be used to verify the signal generator's readings.
  • The signal generator should be left for about 20 minutes to stabilise.