| Date | November 2013 | Marks available | 2 | Reference code | 13N.3.SL.TZ0.16 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | State | Question number | 16 | Adapted from | N/A |
Question
This question is about waves.
State the principle of superposition.
The diagram shows a plan view of a harbour with a floating barrier that has two openings of equal width.
Plane water waves from the open sea are incident on the barrier and the openings act as point sources of waves. The distance from the openings to XOY is much greater than the wavelength of the wave. O is equidistant from the openings.
The graph shows the variation of the magnitude of the wave amplitude that is observed along the line XOY.
(i) State why the two sets of waves emerging from the openings are coherent.
(ii) Explain how the disturbance at point A arises. You may draw on the diagram of the harbour to illustrate your answer.
(iii) The wavelength of the waves is doubled. State and explain the effect that this change will have on the graph.
The harbour in (b) is modified to have many narrower openings. The total width of the openings remains the same. Outline two ways in which the variation of wave amplitude along XY changes from that shown on the graph in (b).
Markscheme
net displacement of the medium;
equals the resultant/sum of individual displacements;
Award [1 max] for reference to amplitude rather than displacement.
Award [0] for reference only to troughs and crests.
(i) division of wavefront so constant phase;
(ii) interference/superposition occurs at A;
between waves from each opening;
waves arrive in phase / path difference is one wavelength;
producing a (1st order) maximum;
Award [3 max] for clear points that appear on diagram.
(iii) maxima occur when the path difference is an integral number of wavelengths;
because wavelength doubles, larger distances/angles required to achieve same path difference;
successive maxima fringes are twice as far/further apart;
or
quotes double slit/grating formula;
substitute 2λ into equation and states all other terms stay constant;
successive maxima fringes are twice as far/further apart;
Assuming spacing of openings stays the same.
same separation of maxima;
maxima increase in amplitude/intensity;
maxima narrower/sharper;
formation of secondary maxima;
Award [2 max] for other reasonable responses if the response clearly states an assumption that the openings are closer or further apart than before.
