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)
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