The ceiling of an auditorium is fitted with a flat reflecting panel so that sound from a performer on the stage reaches the audience sitting at the back rows by reflection.
(i) The performer’s mouth (point P) is 2.0m above the floor and the panel is fixed horizontally 8.0m above the floor. A listener’s ear (point L) is 1.5m above the floor and 20m horizontally away from P. Draw a side-view diagram marking P, L, the panel, the incident ray, the reflected ray and the normal at the point of incidence on the panel.
(ii) Treating the panel as an ideal plane reflector, determine the horizontal distance of the point of incidence from P so that the sound ray from P is reflected to L. Show all steps clearly.
(iii) Calculate the total path length of the sound from P to L via the panel and compare it with the straight-line distance between P and L.