THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

248 11. Acoustics of Enclosed Spaces: Architectural AcousticsFigure 11.5. Geometric configuration for setting up the relationship between energydensity and intensity of sound.experimental measurements. The process of absorption in the medium or the enclosingsurfaces prevents the intensity from becoming infinitely large. Absorptionin the medium is fairly negligible in medium- and small-sized enclosures, so theultimate intensity depends upon the absorption power of the boundary surfaces. Ifthe enclosure’s boundary surfaces have high absorption the intensity will quicklyachieve the maximum which exceeds only slightly the intensity of the direct ray.If the enclosure has highly reflective surfaces, i.e., low absorption, a “live” roomensues; the growth of the intensity will be slow and appreciable time will haveelapsed for the intensity to reach its maximum.After a sound source is started in a live room, reflections from the wall becomemore uniform in time as the sound intensity increases. With the exception of closeproximity to the source, the energy distribution can be considered uniform andrandom in direction. In reality a signal source having a single frequency will resultin standing-wave patterns, with resultant large fluctuations from point to point inthe room. But if the sound consists of a uniform band of frequencies or a pure tonewarbling over at least a half octave, the interference effects of standing waves areobliterated.Referring to Figure 11.5, we establish the relationship between intensity (whichrepresents the energy flow) and energy density of randomly distributed acousticenergy. In the figure dS represents an element of the wall surface and dV the volumeelement in the medium at a distance r from dS. The distance r makes an angle θwith the normal NN ′ to dS. Let the average acoustic energy density E (in W/m 3 )beassumed uniform throughout the region under consideration. The acoustic energy