Musical instruments

• Stationary wave


  Energy is stored rather than transferred (unlike in a transverse or longitudinal wave – both are progressive)
• Stationary wave


  • Minimum amplitude/displacement = nodes
  • Maximum amplitude/displacement = antinodes
• Coherent waves


  Share the same frequency, wavelength and have a constant phase difference
• Harmonics


  Draw the first five harmonics on a stretched string
• Number of wavelengths


  • First harmonic
  • Third harmonic
  • Fourth harmonic
• Resonance


  Storing of energy in an oscillation or a stationary wave, the energy coming from an external source of appropriately matched frequency
• Resonance is what creates the collapse of many buildings and bridges
• Stringed Instruments


  v = wave speed, T = tension in the string, μ = mass per unit length of the string
• Wind Instruments


  • An open ended cylinder will naturally have maximum oscillations (antinodes) at both of its open ends, and one or more nodes in between
  • Closed end = node
  • Open end = antinode
• Harmonics available for open ended cylinders


  • Hint: With both ends open, an antinode would have to be at either end of the harmonic
• Practice Questions


  1. The free section of a stretched guitar string is 70 cm long and it produces a fundamental harmonic with a frequency of 450 Hz

  2. What is the wavelength of the fundamental vibration of this string?

  3. What is the speed of the waves travelling up and down the string?

  4. If the mass per unit length of this string is 0.001 kg/m, want must be the tension in the string?