d) Stretched strings

a) stationary (standing) waves using microwaves, stretched strings and air columns

ei) stationary wave patterns for a stretched string and air columns in closed and open tubes

g) fundamental mode of vibration (1st harmonic); harmonics

fundamental mode of vibration (1st harmonic) = minimum frequency of stationary wave through a material

using a stretched string to produce a stationary wave

• string is stretched between two points

  • points act as nodes

• string is plucked

  • produces a progressive wave

    • travels along the string

    • reflects off the points

      • produces two progressive waves

      • superpose and produces a stationary wave

fundamental wavelength = ½λ → λ = 2 × length of the string

all harmonics → integer multiples of the fundamental frequency