12.4 Stationary waves

Question 1

How is a stationary wave formed?

Answer 1

When two waves with the same frequency (and ideally same amplitude) travelling in opposite directions are superposed.

• As they have the same frequency, at certain points they are in anti-phase.

At these points their displacements cancel out - forming a node (a point where the displacement is always zero, thus amplitude and intensity are zero).

• At other points when the two waves are always in phase, an antinode is formed - point of greatest amplitude thus intensity.

Question 2

Properties of stationary waves:
- Energy transfer?
- Wavelength?
- Phase differences?
- Amplitude?

Answer 2

• Energy transfer: No net energy transfer, The two waves that form the stationary wave carry equal and opposite amounts of energy.
  Since they are traveling in opposite directions, their net energy transfer cancels out.
• Wavelength: Twice the distance between adjacent nodes or antinodes is equal to the wavelength of the progressive waves that created the stationary waves.
• Phase differences: Particles in the same segment (between two nodes) oscillate in phase (0° phase difference). Particles in between two adjacent nodes oscillate out of phase (180° phase difference). Nodes remain fixed, while antinodes oscillate with maximum amplitude.

Question 3

Describe two similarities between progressive and stationary waves.

Answer 3

• Both progressive and stationary waves share the same wavelength and frequency.
• Both comprised of oscillations