MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number
Problem
In experiments that rely on echo timing, uncertainty in ambient temperature leads to an uncertainty in the calculated distance. Let the echo time be t for a reflector at fixed distance d.
(i) Starting from the temperature dependence of the speed of sound, obtain an expression for the fractional error dΔd in terms of the fractional error TΔT.
(ii) If the air temperature is 300K with an uncertainty of ±2K, estimate the maximum percentage uncertainty in the distance determined from the echo method.
(iii) Comment on how significant this source of error is in ordinary field measurements.