Compute the derivative of the speed of sound in air with respect to the absolute

Question

Compute the derivative of the speed of sound in air with respect to the absolute temperature, and show that the differentials dv and dT obey dv/v=1/2dT/T

(b) Use this result to estimate the percentage change in the speed of sound when the temperature changes from 0°C to 15.4°C.
1) %

(c) If the speed of sound is 340 m/s at 0°C, estimate its value at 15.4°C using the differential approximation.
2) m/s

(d) How does this approximation compare with the result of an exact calculation? (Enter the value from the exact calculation.)
3) m/s

Explanation / Answer

a) speed os sound in air is given by
   v= (3RT/m)0.5
taking the log and thereafter derivative of the expression with respespect to v, one can get
   dv/v= 0.5dT/T

b) 2.82%

c) 349.5897m/s

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