A physics club conducts an echo-ranging activity beside a vertical rock face. The same observer stands at a fixed position and claps once, measuring the round-trip times of the echo on two different days.
(i) If the echo times are t1 at temperature T1 and t2 at temperature T2, derive an expression for the ratio t1t2 in terms of T1 and T2.
(ii) On Day 1 the air temperature is 300K and the echo time is 0.80s. On Day 2 the temperature rises to 360K. Calculate the new echo time expected on Day 2.
(iii) Suppose a participant mistakenly uses the Day 1 value of the speed of sound to compute the cliff distance from the Day 2 echo time. Determine the percentage error introduced in the calculated distance.