Please help I do not understand how to do this one. The speed of sound in air de
ID: 1742339 • Letter: P
Question
Please help I do not understand how to do this one. The speed of sound in air depends on die temperature of the air: v= 1.4KT/m where k is Boltzmann's constant, T is the air temperature in Kelvin, and m is the average mass of the molecules in the air. (The factor of 1.4 is because sound propagation is an adiabatic process, not an isothermal one.) Compute the speed of sound at 0 degree C. (Hint: The mass of an O2 molecule is 5.31 times 10 degree 6 kg and the mass of an N2 molecule is 4.65 times 10"26 kg. Earth's atmosphere is 22% oxygen and 78% nitrogen. Use a weighted average to determine the average mass of air molecules.) Compute the speed of sound at 1 degree C. How many meters per second does the speed of sound increase for every degree Celsius?Explanation / Answer
Hi, Mass of each air molecule will be m =[(5.31*10-26kg)(0.22) +(4.65*10-26)(0.78)]/[0.22+0.78] = 4.7952*10-26kg Then speed of sound at 0oC will be v =[(1.4)(1.38*10-23m2kgs-2K-1)(273K)/(4.7952*10-26kg)]1/2 = 331.65m/s Now at 1oC v =[(1.4)(1.38*10-23m2kgs-2K-1)(274K)/(4.7952*10-26kg)]1/2 = 332.26m/s Speed increases by 0.61m/s per every degree of rise intemperature.