e) Air columns

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

for stationary waves through a tube closed at one end

• at the closed end → a node

• at the open end → an antinode

fundamental wavelength = ¼λ → λ = 4 × length of the air column

all harmonics → odd multiple of the fundamental frequency

for stationary waves through a tube open at both ends

• at both open ends → an antinode

fundamental wavelength = ½λ → λ = 2 × length of the air column

all harmonics → integer multiples of the fundamental frequency