Question

10. The speed of sound S (in m/s) is related to temperature by the formula S(T) 331.3 V1 +0.00366T where T is the temperature (in °C). (a) Find the rate of change of the speed of sound with respect to tem- perature, at a temperature of T = 21°C. Show the steps for obtaining your value, and give your value accurate to 4 decimal places (b) For temperatures near T 21 °C, does the speed of sound increase or decrease as temperature increases? Say which one, and give a brief reason based on your answer in part (a) above. (c) Use the linear approximation to estimate the increment in the speed of Sound AS, that results from an increase in temperature of 2.5 C from T- 21 °C. Show the steps for obtaining your estimate, and give your estimate accurate to 4 decimal places

Answer 1

ve ave guen the esuation (a) We need to find the ata chavgt y with respeet to T ds dT both sidee.dm m.x given esnahm dT dT o 003 o oo366 乙 ds dT 331. 2. 0:003 66 x2) ノー·-(0:0 o 366 dT

b)Leta plot thaph ao -273 c

ich mea ns n hear using Linea App inthion USmg l(x) = S(21). t s'(2-1 )-(OT) L 343 161 S842 x 2 S L () 34S.2 S66