| Date | May 2011 | Marks available | 7 | Reference code | 11M.2.HL.TZ2.13 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 2 |
| Command term | Explain, Describe, and Determine | Question number | 13 | Adapted from | N/A |
Question
This question is about simple harmonic motion (SHM), wave motion and polarization.
A liquid is contained in a U-tube.
The pressure on the liquid in one side of the tube is increased so that the liquid is displaced as shown in diagram 2. When the pressure is suddenly released the liquid oscillates. The damping of the oscillations is small.
(i) Describe what is meant by damping.
(ii) The displacement of the liquid surface from its equilibrium position is x. The acceleration a of the liquid in the tube is given by the expression
\(a = - \frac{{2g}}{l}x\)
where g is the acceleration of free fall and l is the total length of the liquid column. Explain, with reference to the motion of the liquid, the significance of the minus sign.
(iii) The total length of the liquid column in the tube is 0.32m. Determine the period of oscillation.
Markscheme
(i) the amplitude of the oscillations/(total) energy decreases (with time); because a force always opposes direction of motion/there is a resistive force/ there is a friction force;
Do not allow bald “friction”.
(ii) the displacement and acceleration/force acting on (the surface); are in opposite directions;
(iii) \(\omega = \sqrt {\frac{{2g}}{l}} \);
\(T = 2\pi \sqrt {\frac{{0.32}}{{2 \times 9.81}}} \);
=0.80s;
(i) wave reflects at ends (of string);
interference/superposition occurs (between waves);
regions of maximum displacement/zero displacement form (that do not move);
one region of max displacement/antinode forms at centre with zero displacement/node at each end; {(allow these marking points from clear diagram)
(ii) the waves (in a string) are transverse and vibrate only in one plane;
light waves are transverse electromagnetic waves;
(and) for polarized light the electric field vector vibrates only in one plane;
Examiners report
(i) Although there were many suggestions that the wave is reflected at one end of the string and that this interferes in some way with the incident wave to produce the standing wave these were generally weak and incomplete. Some candidates focussed entirely on the shape of the standing wave (not really the question). It was rare to see 3 marks awarded; 2 was more common.
(ii) Candidates were vague as to the nature of polarized light (a clear description in terms of the field vectors was required), as to the description of the travelling wave on the string, and as to the way in which it could be used. Many will have seen the demonstration in the laboratory but could not describe it with clarity.
