12 Superposition

Question 1

Principle of Superposition

Answer 1

When two waves meet, the resultant displacement is the vector sum of the displacements due to each individual wave.

Question 2

What is meant by the term coherent?

Answer 2

Sources are said to be coherent if they have constant phase difference (i.e. the phase difference of the sources does not change with time).

Question 3

Characteristics of stationary waves: wave pattern

Answer 3

• The wave pattern does not appear to move in either direction along the wave and the positions of the crests and troughs of the wave are fixed with time.

Question 4

Characteristics of stationary waves: nodes and antinodes

Answer 4

• Particles at displacement nodes do not oscillate because the component waves travelling in opposite direction superpose destructively (destructive interference) at these points. The total phase difference is an odd integer multiple of pi radians. The positions of nodes do not change with time.
• Points at displacement antinodes oscillate with maximum amplitude because the component waves travelling in opposite direction superpose constructively (constructive interference) at these points. The total phase difference is zero or an even integer multiples of pi radians. The positions of antinodes do not change with time.

Question 5

Characteristics of stationary waves: loops

Answer 5

• The stationary wave is divided by nodes and antinodes into equal segments (or “loops”), and each segment is of the same length. The distance between 2 adjacent nodes, or 2 adjacent antinodes is half a wavelength.
• All particles (except nodes) in the stationary wave are oscillating with simple harmonic motion at the same frequency, but not at the same amplitude. Amplitude of vibration is zero at the nodes, maximum at the antinodes.

Question 6

Tube with two ends closed

Answer 6

Question 7

Tube with one end closed and one end open

Answer 7

Question 8

Tube with two ends open

Answer 8