4.8 Stationary Waves

Stationary Wave

A wave formed by superposition of waves with the same wavelength moving in opposite directions. They do not transfer energy

Their superposition creates constructive and destructive interference

Nodes

Points of destructive interference where the two waves cancel each other out resulting in zero amplitude

Antinode

Points of constructive interference creating points of maximum amplitude

Fundamental mode of vibration (1st harmonic)

The lowest frequency in a harmonic series where a stationary waves forms.

Stationary Wave in Strings

Length of a string on a stationary wave is 1/2λ.

Calculating Wave Speed

v = (T/u)^1/2 (u=mass T= tension)

For the fundamental mode of vibration, the length of the string is equal to 1/2λ

Stationary Waves At an Open Pipe

Antinodes occur at open ends

Lowest frequency is produced when length is 1/2 λ

Stationary Waves At an Closed Pipe

Nopdes occur at both ends

Lowest frequency is produced at 1/4 λ

Resonance

Occurs when the frequency of the wave is equal to the natural frequency of air column

Constructive interference produces stationary waves

Dictated by pipe length