ART. 213 - On the Amplitude of Aerial Waves which are but just Audible

Summary

The problem of determining the absolute value of the amplitude, or particle velocity, of a sound which is but just audible to the ear, is one of considerable difficulty. In a short paper published seventeen years ago I explained a method by which it was easy to demonstrate a superior limit. A whistle, blown under given conditions, consumes a known amount of energy per second. Upon the assumption that the whole of this energy is converted into sound, that the sound is conveyed without loss, and that it is uniformly distributed over the surface of a hemisphere, it is easy to calculate the amplitude at any distance; and the result is necessarily a superior limit to the actual amplitude. In the case of the whistle experimented on, of frequency 2730, the superior limit so arrived at for a sound just easily audible was 8·1 × 10⁻⁸ cm. The maximum particle velocity v and the maximum condensation s are the quantities more immediately determined by the observations, and they are related by the well-known equation v = as, in which a denotes the velocity of propagation. In the experiment above referred to the superior limit for v was ·0014 cm. per second, and that for s was 4·1 × 10⁻⁸. I estimated that on a still night an amplitude, or velocity, one-tenth of the above would probably be audible.