A-Level The superposition principle, standing waves, interference and single-slit diffraction: worked solution

Question

(ii) A microphone is moved steadily along the straight line joining P to Q, where PQ is perpendicular to, and crosses, the line halfway between loudspeakers A and B. The microphone records the sound intensity along the way. Describe how the recorded intensity changes as the microphone travels from P across to Q.

Loudspeakers A and B act as two coherent sources whose sound waves overlap and interfere along PQ. The point where PQ crosses the line halfway between A and B is equidistant from both (path difference = 0), giving constructive interference, i.e. a maximum (loud). As the microphone moves outward from this central point toward P (or Q), the path difference from the two speakers increases, so the intensity falls to a minimum (soft), then rises to another maximum, and so on. The recorded intensity therefore alternates between loud maxima and soft minima, symmetrically about the loud maximum at the centre.