An architect is designing a rectangular lecture hall that is 12m wide and 7m high. To prevent echoes that would interfere with speech, she wishes to limit the length of the hall so that any sound reflected from the rear wall does not return as a distinct echo to a speaker standing at the front.
(i) If the speed of sound inside the hall at 30∘C is 349ms−1, determine the greatest permissible length of the hall.
(ii) The architect later installs an air-conditioning system that lowers the hall temperature to 20∘C, reducing the speed of sound by 6ms−1. Find the new maximum length that still avoids echoes.
(iii) Comment briefly on how temperature control in large auditoriums can be used as an additional parameter to manage echo formation.