State what is meant by the principle of superposition of waves.

The diagram shows two point sources of sound, X and Y. Each source emits waves of wavelength 1.1 m and amplitude A. Over the distances shown, any decrease in amplitude can be neglected. The two sources vibrate in phase.

Points O and P are on a line 4.0 m from the line connecting X and Y. O is opposite the midpoint of XY and P is 0.75 m from O.

(i) Explain why the intensity of the sound at O is 4A².

(ii) Deduce that no sound is detected at P.

(when two similar waves meet) the resultant displacement is the (vector) sum of the individual displacements; 

Allow [0] for description in terms of amplitude. 

(i) (constructive interference gives) amplitude 2A; intensity is proportional to square of total amplitude (=4A²);

(ii) attempted use of Pythagoras to measure path difference;

path difference =0.55 (m);    

path difference = \(\frac{\lambda }{2}\) (so out of phase / destructive interference);

Attempted use of Pythagoras may appear on diagram for (b)(i). 

Few candidates stated the principle of superposition clearly enough to gain a mark – most talked about the sum of the amplitudes rather than of the displacements. 

(i) With hindsight having a distance of 4.0m as well as the 4A² was unfortunate and weaker candidates felt obliged to include the distance in their explanation. Of course this did make it clear to examiners that such candidates had very insecure knowledge of this topic. Most answers were unconvincing and highlighted the lack of understanding of this principle.

(ii) A minority of candidates used Pythagoras’s theorem to show that the path difference was half a wavelength leading to destructive interference. Weaker candidates tried to argue the case without performing any calculation.