ANSWERS: 2
  • Does this help? http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/souspe3.html
  • "into 10 ki power minus 3 kg" doesn't make ant sense to me. But there are a number of ways to approach this problem. You probably have a formula that you teacher wanted you to use, but since you didn't supply that information... So, sound in a fluid is an adiabatic process. Temperature certainly changes as the molecules are pushed together and pulled apart by the vibration, but heat is conserved, so let's assume that the front of a pressure pulse moving through the air will have a constant velocity "w," depending on the properties of air. The uncompressed length of a section of the gas is w times t (speed times time gives distance), and the volume of that piece with cross sectional area A is A w t. If the density of the air is rho, then the mass is rho A w t. Now, you compress the section with a pressure differential dP, so the compression propagates due to the unbalanced force on the section dP times A. Newton's Laws of Motion state that an unbalanced force will create motion obeying the equation F = dp/dt, where p is momentum and F is force. So the force dP A is equal to the change in momentum is d( rho A w w t ) / dt. Since A and w are constant, this reduces to A w w d(rho). Cancel the A's and the equation you get is that w squared is dP/d(rho) at constant entropy. This can be rewritten as w square equals 1 / (rho kappa-S), where "kappa-S" is the adiabatic compressibility, which is given by the equation kappa-S = 1 / ( gamma P), where gamma is the ratio between thermodynamic heat capacities. Since rho is the mass of a mole (M) divided by the volume of a mole (v), and Pv = RT for an ideal gas, w squared is gamma R T / M. Gamma is given also by the degrees of freedom of the molecules as 1 + 2/f, and air is diatomic, having 5 degrees of freedom, gamma is approximately 1.4 for air. R is 8.31 J/mol K, at "STP," T= 273.15K, P=101.3 kPa, so the speed of sound squared is 1.4 * 8.31 J/mol K * 273.15 K / 0.029 kg/mol = 109580 m2/s2. Take the square root and you get 331.029 m/s

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