1. Topic 11 – Wave Phenomena

2. Standing/stationary waves

3. Interference of waves
Remember that when two waves of the same frequency interfere, we can get constructive interference or destructive interference. + = = +

4. Formation of a standing wave
Standing wave (explanation by superposition with the reflected wave)
wave-on-a-string_en

5. Formation of a standing (stationary wave)
Two waves of same speed and wavelength and equal or almost equal amplitudes travelling in opposite directions superimpose and interfere
A standing wave is produced with nodes at points of destructive interference and antinodes at points of constructive interference

6. Travelling waves and standing waves
Travelling waves transfer energy, standing waves do not.
All points on a travelling wave have the same amplitude, in a standing wave they do not.
On either side of a node the points on a standing wave are 180° out of phase.

7. Boundary conditions

8. Formation of a standing wave by reflection
A travelling wave is reflected
The reflected wave is 180° out of phase with the original wave
The two waves travelling in opposite directions superimpose and interfere
A standing wave is produced with nodes at points of destructive interference and antinodes at points of constructive interference

9. Boundary conditions
For a standing wave on a stretched string, there has to be a node at each end
1st harmonic or fundamental
2nd harmonic
nodes
3rd harmonic
4th harmonic
antinodes

10. Boundary conditions
For sound waves in a tube it depends on whether the tube is open or closed
Standing longitudinal waves

11. Boundary conditions
For an open tube, there has to be an antinode at each end

12. Boundary conditions
For a tube closed at one end, there is a node at the closed end and an antinode at the other

13. Some standing wave investigations
We are now going to do two investigations involving standing waves