Two high cliffs stand facing each other on opposite sides of a narrow valley. A hiker standing midway between them shouts once and hears two successive echoes, the first after 0.40s and the second after 0.60s. The air temperature is 15∘C, at which the speed of sound is 340ms−1.
(a) Prove that the two echoes originate from the two different cliffs rather than from multiple reflections between the same cliff and the hiker.
(b) Determine the distance between the two cliffs.
(c) If the temperature falls to 5∘C overnight, calculate how the times of the first and second echoes will change, assuming the hiker and the cliffs remain in the same positions.