a) Calculate the derivative of the speed of sound in air by respect to the absolute temperature, and show that the differentials dv and dT obey dv/v = 1/2 dT/T.
b) Use this result to estimate the percentage change in the speed of sound when the temperature changes from 0°C to 24.8°C.
c) If the speed of sound is 332 m/s at 0°C, estimate its value at 24.8°C using the differential approximation.
d) How does this approximation compare by the result of an exact calculation? (Enter the value from the exact calculation.)