•• (a) 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 = ½ dT/T. (b) Use this result to estimate the percentage change in the speed of sound when the temperature changes from 0°C to 27°C. (c) If the speed of sound is 331 m/s at 0°C, estimate its value at 27°C using the differential approximation. (d) How does this approximation compare with the result of an exact calculation? 34
•• (a) 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 = ½ dT/T. (b) Use this result to estimate the percentage change in the speed of sound when the temperature changes from 0°C to 27°C. (c) If the speed of sound is 331 m/s at 0°C, estimate its value at 27°C using the differential approximation. (d) How does this approximation compare with the result of an exact calculation? 34
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Transcribed Image Text:34
(a) 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 = ½ dT/T. (b) Use this result to
estimate the percentage change in the speed of sound when the
temperature changes from 0°C to 27°C. (c) If the speed of sound
is 331 m/s at 0°C, estimate its value at 27°C using the differential
approximation. (d) How does this approximation compare with
the result of an exact calculation?
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