A progressive wave transfers energy. A stationary wave does not transfer energy. State two other differences between progressive waves and stationary waves.

Question 6

(a) A progressive wave transfers energy. A stationary wave does not transfer energy. State two other differences between progressive waves and stationary waves. [2]

(b) A stationary wave is formed on a stretched string between two fixed points A and B.

The variation of the displacement y of particles of the string with distance x along the string for the wave at time t = 0 is shown on Fig. 5.1.

Fig. 5.1

The wave has a period of 20 ms and a wavelength of 1.2 m. The maximum amplitude of the particles of the string is 5.0 mm.

(i) On Fig. 5.1, draw a line to represent the position of the string at t = 5.0 ms. [2]

(ii) State the phase difference between the particles of the string at x = 0.40 m and

at x = 0.80 m. [1]

(iii) State and explain the change in the kinetic energy of a particle at an antinode between t = 0 and t = 5.0 ms. A numerical value is not required. [2]

Reference: Past Exam Paper – November 2015 Paper 21 Q5

Solution:

(a)

progressive: all particles have same amplitude

stationary: the particles do not have the same amplitude. There are nodes and antinodes

progressive: adjacent particles are not in phase

stationary: waves particles are in phase (between adjacent nodes)  [within a loop]             

(b)

(i)

{Period = 20 ms. This means that after 20 ms, the wave regains its original position.

After 5 ms, the wave has made a quarter of its period.}

{Wavelength = 1.2 m.

A stationary wave contains nodes (zero amplitude). This would be located at x = 0 m, x = 0.6 m (half the wave), 1.2 m (one wavelength), 1.8 m, 2.4 m, 3.0 …}

{Midway between 2 nodes, we have antinodes (maximum amplitude). So, antinodes are located at x- 0.30 m (crest), 0.9 m (trough), 1.5 m (crest), 2.1 m (trough) …}

wavelength 1.2 m (zero displacement at 0.0, 0.60 m, 1.2 m, 1.8 m, 2.4 m)

EITHER peaks at 0.30 m and 1.5 m and troughs at 0.90 m and 2.1 m

OR vice versa (but not both)

maximum amplitude 5.0 mm

(ii)

{They are in adjacent loops, so they have a phase difference of 180°}

180° or π rad

(iii)

{A particle at an antinode is moving with time.

At t = 0, the particle may be at equilibrium and it is moving.}

At t = 0, the particle has kinetic energy as the particle is moving.

{At t = 5.0 ms, the particle is at its maximum displacement and it is momentarily at rest. So, it would have no kinetic energy.}

At t = 5.0 ms, it has no kinetic energy as the particle is stationary

So, there is a decrease in kinetic energy (between t = 0 and t = 5.0 ms)