| Date | May 2014 | Marks available | 5 | Reference code | 14M.3.SL.TZ1.20 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate, Deduce, and Discuss | Question number | 20 | Adapted from | N/A |
Question
This question is about interference.
Two radio stations, A and B, broadcast two coherent signals. The separation d between A and B is much less than the distance D from the stations to the receiver R. Point P is at the same distance from A and B.
The graph shows how the intensity of the radio signal varies with position as the receiver is moved along line L. The position of the receiver is zero when the receiver is at P.
(i) Deduce that the two sources A and B are 180º out-of-phase.
(ii) The wavelength of the radio signal is 40m. Calculate the ratio \(\frac{D}{d}\).
The receiver R then moves along a different line M which is at 90º to line L.
Discuss the variation of the intensity of the radio signal with position as the receiver is moved along line M.
Markscheme
(i) intensity at P is zero hence complete destructive interference occurs;
point P is at the same distance from A and B / path difference is zero;
destructive interference comes from a 180º phase difference in the signals;
(ii) separation between minima s=3(km);
\(\frac{D}{d}\left( { = \frac{s}{\lambda } = \frac{{3000}}{{40}}} \right) = 75\);
R is always equidistant to stations A and B / signals from A and B are always out of phase;
intensity is always zero;
Examiners report
This question discriminated very well and a full range was seen in the quality of answers. Well prepared candidates showed a good understanding and ability to apply the concept of interference. Lesser prepared candidates were not able to analyse the intensity-position graph. In (a)(i), candidates repeated the question without additional information and did not gain marks in (a)(ii) because they did not have enough information.
(b) discriminated well between, as evidenced by candidates, those that analysed the situation and those that attempted to remember some information from problems with similar context. Well prepared HL candidates realized that point P has no special position on the line M. (b) was very poorly answered at SL. The explanation of why the intensity is always zero was generally unclear and did not signify thought.
