IV. On the propagation of sound in the free atmosphere and the acoustic efficiency of fog-signal machinery: an account of experiments carried out at father point, quebec, September, 1913

Abstract

The theory of the propagation of sound-waves of small amplitude such as are produced by ordinary acoustic instruments has received repeated experimental verification on almost every point. Over such distances as are available for indoor experiments, the atmosphere may be regarded as a homogeneous medium of constant temperature, The variations of pressure in such sound-waves are so small medium may be considered as a perfectly elastic fluid for which the relation between pressure and volume (per unit mass) is expressed by the adiabatic law p v ^γ = const. or p/p ₀ = (ρ/ρ ₀ ) ^γ ............(1) where p ₀ and ρ ₀ refer to the pressure and density at standard temperature and pressure. It has long ago been verified by experiment that in the extremely rapid compressions and rarefactions which constitute sound-waves, equalization of the resulting inequalities of temperature by thermal conduction cannot take place with sufficient rapidity to bring about uniformity of temperature : the compressions and rarefactions may therefore be considered to take place under conditions of no heat-transfer, that is, under adiabatic conditions, γ is a constant which for air has the value γ = 1 ·414. It was first pointed out by Laplace that under these conditions the Newtonian formula for the velocity of sound, should be modified to √( p ₀ / ρ ₀ ), should be modified to a = √(γ p ₀ /ρ ₀ )......(2) Applying the above formula to the propagation of sound in air at standard pressure and temperature, and inserting p ₀ = 1·013 x 106 dynes/cm.2, ρ _o = 1·293 x 10-3gr./cm.3, we obtain for the calculated velocity of sound the value a = 332 metres/sec. = 1089 feet/sec., in good agreement with observation.