A factory whistle designed for a particular pitch requires that the speed of sound in the surrounding air increase by exactly 5% relative to its value at 20∘C. Assume air composition remains unchanged.
a. (i) Obtain a general relation between the fractional increase in the speed of sound and the corresponding rise in absolute temperature for a fixed gas.
b. (ii) Using this relation, calculate the temperature (in ∘C) at which the whistle will produce the desired pitch.