practical 1 - stationary waves on a string

• stationary waves

  • wave that stores energy but doesn't transfer it
  • two waves with same wavelength traveling in opposite directions interfere
  • undergo superposition
• nodes

  • point of zero displacement
  • occur where to waves are in antiphase destructively interfere
  • cancel each other out

  antinode

  • point of maximum displacement
  • where two waves in phase constructively interfere to form a maximum

  standing wave

  • at fundamental frequency
  • one central antinode
  • node at each end
• waves apparatus

  • vibration generator driven by signal generator generates wave in string
  • bridge - triangular prism
  • moved along string to alter length of oscillating region
  • signal generator operated for several minutes before use to stabilise frequency
  • counterweight / g-clamp used to counteract stand toppling over
• equipment

  • signal generator
  • vibration generator
  • stand
  • pulley
  • wooden bridge
  • 100g masses with holder
  • metre ruler
  • 1.5m long string
  • balance
• method

  • set up apparatus
  • adjust length to 1m measured using metre ruler
  • increase frequency until string oscillates at first harmonic
  • reduce length by 0.1m and adjust to first harmonic
  • measure and record frequency repeating until length 0.5m
  • repeat experiment twice more and record mean frequency for each length
  • measure mass of string on balance and record
• graphs and calculations

  • plot graph of mean value of frequency against 1/length
  • draw line of best fit
  • $\lambda=$$2l\ \rightarrow\ v=$$2fl\ =$$\ 2G$
  • G is gradient
  • tension of string equal to weight of hanging mass
  • mass per unit length found by dividing mass of string by its length
  • speed of wave $v=$$\sqrt{\frac{T}{\mu}}$
• safety

  • stand could topple over and cause injury

  precaution

  • counterweight used
• improvements

  • experiment can be repeated with different masses to change tension and thicknesses of string to change the mass per unit length
  • oscilloscope can be used to verify signal generator's readings
  • signal generator should be left for 20 minutes to stabilise